Research about coherent ultra-violet light sources based on nonlinear conversion with borate crystal

Transcription

1 Title Author(s) Research about coherent ultra-violet light sources based on nonlinear conversion with borate crystal 曲, 晨 Citation Issue Date Text Version ETD URL DOI /67066 rights

2 Doctoral Dissertation Research about coherent ultra-violet light sources based on nonlinear conversion with borate crystal QU chen March 2017 Graduate School of Engineering, Osaka University

3 Contents: Preface 1 Chapter 1. Introduction Background Inspection application for all-solid-state UV laser Introduction for UV laser processing Purpose of dissertation Structure of dissertation 6 References in Chapter 1 8 Chapter 2. Nonlinear optics theory and nonlinear optical crystals for UV light generation Introduction for optical nonlinear frequency conversion Introduction for nonlinear optics Analysis of SHG with Maxwell s theory Phase-matching condition Optics of uniaxial crystals Optics of biaxial crystals Phase-matching in uniaxial crystals Quasi phase-matching Optical parametric oscillator Nonlinear optical crystals for UV light generation Properties required for nonlinear crystals in UV light generation Commonly used borate crystals Summary 41 References in Chapter 2 42 Chapter nm VUV light generation with borate crystals Introduction for VUV light generation at 189 nm Experiment for 189 nm light generation 44 i

4 3-2-1 Scheme for 189 nm light generation SHG with LBO IR light generation with OPO Fourth harmonic and fifth harmonic generation with CLBO Summary for 189 nm light generation preparation nm light generation with borate crystals nm light generation results and discussions Phase-matching angles for LBO and CLBO Phase-matching angles for CBO nm light generation with CLBO and LBO Perspective Summary 66 References in Chapter 3 67 Chapter nm VUV light generation with borate crystals Introduction Introduction for VUV light generation in 170 nm-180 nm range Scheme for 179 nm light generation Experimental setup for 179 nm light generation Setup for DUV and IR light generation SHG with improved conversion efficiency KTP OPO and intra-cavity SHG PPLN OPO for IR light generation nm DUV light generation Summary for 179 nm VUV light generation system SFG for 179 nm VUV light generation nm light generation result Summary 83 References in Chapter 4 84 Chapter 5. Research about 355 nm UV light generation with CLBO All-solid-state 355 nm laser nm UV light generation with borate crystals 85 ii

5 5-1-2 CLBO s outlook for 355 nm UV light generation Method for walk-off compensation Principle for non-collinear phase-matching Method for achieving non-collinear phase-matching Prism-coupled device structure for non-collinear phase-matching Experiments for 355 nm light generation Setup preparation for 355 nm light generation nm light generation results of conventional CLBO nm light generation results of LBO nm light generation results of walk-off compensation device Summary 102 References in Chapter Chapter 6. Conclusions 105 List of abbreviations in the dissertation 107 Acknowledgement 109 Achievements 113 iii

6 Preface: Ultraviolet (UV) laser source used in industry, medical and research have drawn great attentions in recent years. Especially, nonlinear frequency conversion which considered as a good method for providing high power pulsed UV laser source, has become a hotspot in the fields of laser, photonics and crystal growth. In this dissertation, there are detailed introduction about the principal for nonlinear frequency conversion, 189 nm and 179 nm UV light generation systems with borate crystals, and the 355 nm light generation (third-harmonic generation of 1064 nm) demonstrated with CLBO. The structure of the dissertation In Chapter 1, there is an introduction about the background of needs for inspection laser source in semiconductor manufacture and processing laser source for industry use. Then, the research purpose of this dissertation and the ideas for the development of all-solid-state UV laser source at 189 nm, 179 nm and 355 nm are shown. In Chapter 2, the basic principle involves in the UV light generation of by means of nonlinear optical effect is discussed. Firstly, the basic theory for nonlinear optics and fundamental expression for nonlinear (NLO) generation were given. Then, the optical properties for NLO crystals and the condition for achieving the phase-matching were introduced. At the second part of the chapter, NLO crystals used in UV light generation research and their properties are shown. In Chapter 3, current progress of the sub-200 nm deep-uv light generation by borate crystal and the background of the 189 nm system are introduced. After that, the all-solid-state 189 nm light generation system is presented. The phase-matching property for LBO, CBO and CLBO are investigated with the

7 system and the generation results are shown. A new Sellmeier formula for CBO found by our laboratory, which can make a better prediction to our experimental results than the former formula, was presented. In Chapter 4, the progress for deep-uv light generation till 170 nm is introduced. After that, the all-solid-state 179 nm light generation system is presented. Among it, the core part of an optical parametric oscillation based on KTP is introduced. The phase-matching property for LBO is investigated with the system, and the generated power is verified with fluorescence as it is too weak to be detected. In Chapter 5, I demonstrate the 355 nm (third-harmonic generation of 1064 nm) generated with CLBO crystal for the first time. In order to compensate the walk-off involved in the generation by Type II (eoe) CLBO to promote the conversion efficiency, I design a new prism-coupled device which takes the advantage of non-collinear phase-matching. A sample is made and the generation result is compared with conventional CLBO and LBO crystal in the 355 nm light generation. In Chapter 6, all results established in this work are summarized and concluded together.

8 Chapter 1. Introduction 1-1 Background LASER stands for Light Amplification by Stimulated Emission of Radiation. It is one kind of light with strong spatial coherence, narrow spectrum and high intensity. The original concept of laser derives from Quantum theory. The first functional laser was operated by Theodore Maiman in 1960 with ruby crystal as the gain medium [1]. Since the discovery, it has found applications in versatile areas such as science, medical, industry and military. Because of the high light intensity, nonlinear optical (NLO) effect resulted from the dielectric polarization responds nonlinearly to the electric field, could be realized by laser. As a typical second order nonlinear effect, second harmonic generation of ruby laser was observed with quartz crystal in 1961, which is the first NLO phenomenon discovered [2]. The experiment marked the beginning of an intense investigation into the realm of the nonlinear optical properties of matter. After that, nonlinear frequency conversion such as second harmonic generation (SHG), sum-frequency generation (SFG), and difference-frequency generation (DFG) began to play a big part in laser technology particularly for broadening the spectrum of the laser from infrared (IR) to ultraviolet (UV) range and extending its application field. Nowadays, UV laser has become useful tool in material processing and imaging, for it provides high photon energy and high resolution with short wavelength. Particularly, UV laser source realized by wavelength conversion based on diode-pumped solid-state laser and fiber laser draw the attention of researchers [3]. This kind of lasers has many merits expected in industry such as high beam quality, high running stability, and low maintenance cost. For the UV light generated with nonlinear optics theory based on solid laser system, NLO medium is of great importance. Borate crystals with high nonlinear effect, short absorption edge and high damage threshold, have become the best 1

9 Chapter 1. Introduction choice for this application [4]. Famous members in this big family include but not limited to: β-bab 2 O 4 (BBO), LiB 3 O 5 (LBO), CsLiB 6 O 10 (CLBO), CsB 3 O 5 (CBO) and KBe 2 BO 3 F 2 (KBBF). Among them, BBO, LBO, and CLBO are now in mass production and have become the powerful tool in the field. In this dissertation, I make the UV light generation with borate crystals aiming at two kinds of application Inspection application for all-solid-state DUV laser As semiconductor technology progressed, high performance optical metrology tool is wanted in advanced photomask manufacture. Direct approach is to use the lithography laser source, which is now equipped with 193 nm ArF excimer laser, for achieving enough resolution [5]. Although modern excimer technology can support kilohertz oscillation that is able to satisfy the demands for application of mask metrology and review, excimer laser itself is an improper choice for the application. The most important point is that excimer laser mode quality, which involves the spatial homogeneity and divergence properties of the laser beam, is too poor for such high precision application. As an alternative, sub-200 nm all-solid-state laser source can provide extreme narrow band bandwidth that fits for jobs like calibration and interferometric applications. What is more, it can deliver high equality coherent beam with high standard operation stability and need little maintenance that makes it attractive in mass production. To realize deep-ultraviolet (DUV) laser under 200 nm, many researchers gave their solutions. Some of the systems have become current service equipment in recent years. For example, Ohtsuki et al. reported a 193 nm all-solid-state laser system now installed in inspection system for Nikon Corp. [6]. The generation is realized by the eighth harmonic generation from the output of an Er-doped fiber amplifier operating at a wavelength of 1547 nm. The fiber amplifier system provides output pulses of a single frequency with a line-width less than 0.1 nm, an average power of 40 mw and 1.7 ns pulse width at a 1 khz repetition rate. Imai et al. reported their development for a highly reliable 198 nm light source 2

10 for semiconductor inspection based on dual fiber lasers [7]. As shown in Fig.1.1, to obtain the robustness and to simplify the configuration, the fundamental lights are run in the pulsed operation and all wavelength conversions are made in single-pass scheme. The khz level pulse repetition frequency (PRF) makes it equivalent to continuous wave (CW) light for inspection. The laser source is now equipped in the leading edge photo-mask inspection machines. Fig System for 198 nm light generation Introduction for UV laser processing High-average power UV laser have been in great demand for processing applications in industry [8, 9]. Particularly, UV light is superior to longer wavelengths in two ways for material processing. First, the short wavelength allows the production of smaller feature sizes than what is achieved with visible and IR light. It is explained as minimum focused spot diameter d, which is a function of the beam quality factor M 2, the wavelength λ, and the numerical aperture (NA) of the focusing lens: d M 2 / NA. (1.1) Second, the high energy photons delivered with UV light can directly atomize material in a process called photo-ablation. Since the surrounding material in the process is not thermally transformed or damaged, the ability of UV laser light in 3

11 Chapter 1. Introduction the producing has a nice evaluation. In recent years, a big progress for UV laser is in the area of diode-pumped solid-state (DPSS) lasers, where Nd-doped crystal (such as yttrium aluminum garnet: YAG) lasers utilize nonlinear crystals to transform the 1064 nm output to its third-(355 nm), fourth-(266 nm), or fifth-(213 nm) harmonic that has drawn more and more attention. This kind of UV laser has merits of high power and high pulse repetition rates that are critical to achieving a high system throughput and productivity. Coupled with physically compact, high beam quality, mechanically rugged and recent improvements in laser reliability, it is to be employed in an expanding range of applications and give greatly impact the industrial processing market. Especially, multi-watt, diode-pumped Q-switched 355 nm lasers are the ideal tools for high-precision micromachining applications in the microelectronics industry. To my knowledge, commercial 355 nm laser source has been employed in works including, without limitation, as UV Micro Via Drilling, Sapphire Scribing, Low-k Grooving, and Thin-Wafer Full-Cut Dicing [10, 11], that makes magnificent contribution to integrated circuit chip and LED production. 1-2 Purpose of dissertation As the next generation lithography laser source which utilized extreme ultraviolet (EUV) of 13.5 nm is ready for the mass market, upgrading for semiconductor industry comes to be urgent in the future. And there is no doubt that the market is still to be troubled by the suspicion about the Moore s law effectiveness. With half-pitch size getting close to the physics limit of silicon, to develop the UV laser source that is able to meet the future demands has become our important subject. First, to develop next generation inspection laser source used in photomask manufacture, shorter wavelength vacuum UV (VUV) laser source based on solid-state laser could be a reliable solution in my opinion. In this dissertation, I make VUV light generation with wavelength in the range of nm. Moving the VUV light generation range below 190 nm seems a big challenge. 4

12 The most commonly used medium in this range is KBBF that provides sufficient birefringence to directly generate 177 nm light [12], which equals to the sixth harmonic generation (6HG) of 1064 nm laser source, with SHG process from 355 nm light. In order to make the generation with commercial crystals, SFG method with DUV and IR is preferred. Borate crystal LBO, CBO, and CLBO are verified with phase-matching until 185 nm with a generation scheme that based on Nd:YAG laser. It makes SHG, 4HG (266 nm), and 5HG (213 nm) of the 1064 nm, use an optical parametric oscillator (OPO) to generate IR (about 1400 nm), and at last make the SFG. In this dissertation, I am going to build the system with a high-repetition rate 1064 nm laser to generate VUV light at 189 nm with high efficiency. For further VUV light generation in 170 nm-180 nm range, a scheme of SFG to 179 nm was found phase-matched with LBO and CBO. It is realized with DUV at 198 nm which was used as an application wavelength and is thought to be potential in future use. In this dissertation, a 179 nm VUV light generation system is to be built based on 1064 nm laser. LBO and CBO will be tested in the generation. Now, commercial all-solid-state 355 nm lasers are conventionally realized by LBO [13]. As the third harmonic generation (THG) of 1064 nm laser, they have a simple structure for the generation as shown in Fig.1.2. Based on 1064 nm laser source, after SHG LBO, 532 nm and residual 1064 nm light with orthogonal polarization direction interact in the second LBO to have the Type II SFG to generate 355 nm light. Fig.1.2. Scheme for THG generation based on all-solid-state laser system. With higher effective nonlinear coefficient, CLBO has been considered as a useful tool in the UV light generation. What is more, CLBO grown by self-flux 5

13 Chapter 1. Introduction method is thought to have better quality than LBO. Especially it has superiority in large size crystal used for nonlinear frequency conversion with large diameter beam. In this dissertation, 355 nm light generation by CLBO is to be researched. As walk-off effect is found a limitation in nonlinear frequency conversion, to compensate the large walk-off in THG by CLBO, a new method is to be discussed to improve the conversion efficiency. At last, as shown in Fig.1.3, it is known CLBO has been broadly used in UV light generation mainly at 4HG (4ω) and 5HG (5ω), and showed potential in 190 nm DUV light generations [14, 15]. With the researches carried out in this dissertation, the application range for CLBO in UV light generation is to be further extended. As an important part in UV light generation, CLBO is going to show us a brighter future. Fig.1.3. UV light generation range by CLBO. Blue lines stand for harmonic generations; purple lines stand for DUV generated with SFG; dashed line stand for wavelength to be discussed in this dissertation. 1-3 Structure of dissertation This dissertation mainly includes the principle introduction and 3 parts of research for UV light generation with borate crystals. In the principle introduction, I introduce the principle of nonlinear optics. Nonlinear frequency conversion process is to be described with Maxwell s equations, while the condition for achieving phase-matching with NLO crystal is to be discussed in detail. At last, commonly used borate crystals will be introduced. 6

14 In the introduction for the researches, first, a 189 nm light generation system is built. I test the phase-matching properties for the LBO, CBO and CLBO crystals in UV light generation around 190 nm. The three crystals also will be challenged with high efficiency UV light generation. Second, a 179 nm light generation system is built. It derives from a 198 nm light generation system based on 1064 nm laser system. I challenge the generation with LBO and CBO in air ambient with the system. Third, 355 nm light generation is realized with CLBO. The generation with CLBO has a problem of large walk-off in the SFG with Type II phase-matching. I employ non-collinear phase-matching realized by wedged cut structure, and make a prism-coupled CLBO device used in the generation for compensation. 7

15 Chapter 1. Introduction References in Chapter 1: [1] T. H. Maiman, Nature 187, 493 (1960). [2] P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961). [3] J. M. Bovatsek and R. S. Patel, Proc. SPIE 7585, 75850K (2010). [4] C. Chen, T. Sasaki, R. Li, Y. Wu, Z. Lin, Y. Mori, Z. Hu, J. Wang, S. Uda, M. Yoshimura, and Y. Kaneda, Nonlinear Optical Borate Crystals: Principals and Applications (Wiley, Germany, 2012) 1st ed., Chap. 3. [5] M. Rothschild, A. R. Forte, R. R. Kunz, S. C. Palmateer, and J. H. C. Sedlacek, IBM Journal of Research and Development 41, 49 (1997). [6] T. Ohtsuki, H. Kitano, H. Kawai, and S. Owa, Proc. Conference on Lasers and Electro-Optics, CPD9-1 (2000). [7] S. Imai, K. Matsuki, N. Kikuiri, K. Takayama, O. Iwase, Y. Urata, T. Shinozaki, Y. Wada, and S. Wada, Proc. SPIE H (2010). [8] N. Hodgson, M. W. Li, A. Held, and A. Krueger, Proc. SPIE 4977, 281 (2003). [9] H. Endert, M. Scaggs, D. Basting, and U. Stamm, J. Laser Appl. 11, 1 (1999). [10] C. Dunsky, Proc. IEEE 90, 1670 (2002). [11] W. Wiechmann, L. Eyres, J. Morehead, J. Gregg, D. Richard, and W. Grossman, JLMN-Journal of Laser Micro/Nanoengineering 2, 64 (2007). [12] C. T. Chen, J. H. Lu, G. L. Wang, Z. Y. Xu, J. Y. Wang, C. Q. Zhang, and Y. G. Liu, Chin. Phys. Lett. 18, 1081 (2001). [13] D. T. Thomas, M. S. Keirstead, and N. Hodgson, Proc. SPIE 4426, 493 (2002). [14] H. Kawai, A. Tokuhisa, M. Doi, S. Miwa, H. Matsuura, H. Kitano, and S. Owa, Proc. Conference on Lasers and Electro-Optics, CTuT4 (2003). [15] Y. Asakawa, J. Sakuma, H. Sekita, and M. Obara, Advanced Solid-State Photonics, OSA TOPS , (2004). 8

16 Chapter.2 Nonlinear optics theory and nonlinear optical crystals for UV light generation 2-1 Introduction for optical nonlinear frequency conversion In this section, the principle for nonlinear optics will be introduced. As a kind of second order nonlinear optical effect, nonlinear frequency conversion will be described from the fundamental to numerical analysis with Maxwell s equations. In order to generate sufficient output with the nonlinear process, the condition of phase-matching should be fulfilled. Nonlinear optical crystal with birefringence property is fit for the generation with the ability of achieving phase-matching. The phase-matching properties of the crystals will be discussed in detail. Most of theories introduced in this section are based on the reference from Nonlinear Optics (R. W. Boyd, Academic Press, 3rd edition, 2010) [1], Handbook of Nonlinear Optical Crystals (V. G. Dmitriev et al., Springer, 3rd revised edition, 1999) [2] Introduction for nonlinear optics Nonlinear optics is the research about the phenomenon raised as a consequence of the modification of the material s properties by presence of light, such as laser which provides sufficient electrical field strength. The word nonlinear means such phenomenon will occur when the response of a material system to an applied electrical field depends in a nonlinear manner on the optical field strength. In a general sense, it presents in terms of extending the frequency range of laser sources by means of harmonic generations and parametric oscillations etc. Nonlinear optical effects are analyzed by considering the response of the dielectric material at the atomic level to the optical field of an intense light wave E(t). The light travels through a material produces change in the spatial and 9

17 Chapter.2 Nonlinear optics theory and nonlinear optical crystals temporal distribution of electrical charges as the electrons and atoms react to the electromagnetic fields of the wave. The main effect of the forces exerted by the fields on the charged particles is a displacement of the valence electrons from their normal orbits. Such perturbation creates electric dipoles whose macroscopic manifestation is polarization P(t). The phenomenon described above can be written as the power series of electrical field strength: P t E t E t E t, (2.1) (1) (2) 2 (3) 3 ( ) 0[ ( ) ( ) ( )...] where ε 0 is the permittivity in vacuum, χ (i) is electric susceptibility. The equation is also based on the assumption that media is lossless and dispersionless that the polarization can responds instantaneously to the field. For small field strength this polarization is proportional to the optical field by the linear susceptibility χ (1). It is related to medium s refractive index corresponding to the linear optical properties like reflection and refraction. χ (1) is a tensor which has a quantity larger than other high order nonlinear optical susceptibilities by several orders. That can explain why reflection and refraction is usually meet while other nonlinear optical effect is hardly achieved without laser. For example, the second order nonlinear susceptibility χ (2) is of the order of about m/v. It will be effective only if the incident light wave has so strong electrical field strength that make χ (2) E 2 ~ χ (1) E. Nevertheless, in such cases, the reradiation comes from dipoles whose amplitudes do not faithfully reproduce the sinusoidal electric field that generates them. As a result, the distorted reradiated wave contains frequencies which are different from that of the original light. Consider an optical field which consists of two distinct angular frequency components (ω 1, ω 2 ) incident upon a second-order nonlinear optical medium, the nonlinear polarization has the form of: E() t E e E e i 1t i 2t, (2.2) 1 2 2i 1 t 2 i 2t i( 1 2 ) t i( 1 2 ) t P ( t) [ E e E e 2E E e 2 E E e ], (2.3) (2) (2) 2 2 *

18 χ (2) gives rise to nonlinear phenomenon expressed by the first and second term in the bracket of (2.3) stand for SHG, the third term stands for SFG, and the fourth term stands for DFG. On a higher order, χ (3) gives rise to nonlinear phenomenon like third harmonic generation, stimulated Raman, Rayleigh Scattering etc. that will be not discussed in detail. Phenomenon such as SHG, SFG and DFG resulted from χ (2) can be visualized by the consideration in terms of energy level transition for photons between the various frequency components of the field as shown in Fig.2.1. For example, in SHG, energy from two photons with angular frequency of ω combined, and a photon of 2ω is simultaneously created in single quantum-mechanical process. (a) (b) (c) Fig.2.1. Second order nonlinear effect: (a) SHG, (b) SFG, and (c) DFG (ω 3 >ω 2, ω 1 ). The solid line in the picture represents the atomic ground state; and the dashed lines represent what are known as virtual levels which are not energy eigenlevels of the free atom but rather represent the combined energy of one of the energy eigenstates of the atom and other photons of the radiation field. χ (2) comes to be effective in only non-centrosymmetric crystal that do not display inversion symmetry. Since liquids, gases, amorphous solids, and even many crystals display inversion symmetry, χ (2) vanishes identically for such media that not second-order nonlinear optical interaction produced consequently. The quantity of χ (2), which affect the strength of stimulated nonlinear effect, is determined by the anisotropicity of the molecule, crystal lattice in the material, and direction of the electrical field of input light. 11

19 Chapter.2 Nonlinear optics theory and nonlinear optical crystals In general case, the vector for spatially slowly varying field of the optical wave can be represented as the discrete sum of a number of angular frequency components as: i nt E( t) E( ) e, (2.4) n n where k stand for wavevector for each element wave. Similarly, nonlinear polarization can be expressed as: i nt P( t) P( ) e. (2.5) n n As P(t) and E(t) are vectors, χ (2) is a tensor of third rank which formed with 27 elements that acts as the constants of proportionality relating the amplitude of the nonlinear polarization to the product of field amplitudes. It could be written as (2) ijk, where the indices ijk refer to the Cartesian components according to dielectric axes xyz in the field. In this manner, for the example of SHG, the second order nonlinear polarization can also be expressed with the style of: P E E. (2.6) (2) i(2 ) 0 ijk j ( ) k ( ) jk, Here introduced a tensor called contracted susceptibility within a new notational device that is often used in engineering. It has quantity as: d ijk 1 (2) ijk. (2.7) 2 d ijk is symmetric in its last two indices for the two input waves are exchangable, so it becomes d il that can be generally represented with 3 6 matrix as: d d d d d d dil d d d d d d d d d d d d (2.8) So the second order nonlinear polarization can be written as: 12

20 P 2 i(2 ) 2 0dilEl ( ). (2.9) The nonlinear polarization leading to second-harmonic generation can be generally described in terms of d il by the matrix equation: 2 Ex ( ) 2 Ey ( ) Px (2 ) d11 d12 d13 d14 d15 d16 2 Ez ( ) Py (2 ) 2 0 d21 d22 d23 d24 d25 d 26. (2.10) 2 Ey( ) Ez( ) Pz (2 ) d31 d32 d33 d34 d35 d 36 2 Ez( ) Ex( ) 2 Ex( ) Ey( ) For a particular crystal, one way to determine the form of nonlinear optical susceptibility is to consider about the consequences of all the symmetry properties. By means of mathematical method known as group theory, it is found all crystals can be classified as belonging to one of 32 possible classes depending on what is called the point group symmetry of the crystal. Furthermore, as 21 out of 32 usually have one or more symmetry elements (axes or planes of different orders), which considerably decrease the number of independent components of the tensor d il, the general prescription for each of the crystal classes has been presented so far. Therefore, for describing the nonlinear effect of a certain kind of crystal in practical questions, it is convenient to use a scalar d eff which usually contains a few of elements from the tensor d il. The form of d eff mainly depends on the spatial relation between E and P that is commonly used in depicting refraction properties of crystals. Consequently, the SHG equation (2.9) could be simplified to such relationship where P and E stand for scalars in a certain direction: d E P. (2.11) 0 eff 13

21 Chapter.2 Nonlinear optics theory and nonlinear optical crystals Analysis of SHG with Maxwell s theory To consider SHG in a lossless nonlinear optical medium involving collimated, monochromatic, continuous wave input beam, analysis should be made with Maxwell s equations numerically. In order to save the space, the original four equations written with SI units are not shown. Solution of these equations in regions of space that contain no free charges ( 0, where ρ represents charge density), no free currents ( J 0, where J represents current density) and the material is nonmagnetic ( B 0H, where B represents magnetic flux density, μ 0 represents magnetic permeability in vacuum, H represents magnetic field strength) is interested in. Also, the material is considered to be nonlinear in the sense that the electric displacement field D and electric field E are related by D E P. (2.12) 0 where in general the polarization vector P depends nonlinearly upon the local value of the electric field strength E. To take the curl of curl-e Maxwell equation: B E, (2.13) t interchange the order of space and time derivatives on the right-hand side of the resulting equation, and replace B by ( D ) 0 to obtain the equation: t 2 0 D 0 2 E t. (2.14) This is the most general form of the wave equation in nonlinear optics. It could be simplified by using an identity from vector calculus to change the left term and isotropic source-free condition E D 2 2 0c t 0. (2.15) 14

22 For the P has linear part and nonlinear parts in this equation, to deal with the latter one, the P spilt and the nonlinear part is gotten: (1) NL P P P. (2.16) Similarly decompose displacement field D as: (1) NL D D P, (2.17) where the linear part is given as: D E P E. (2.18) (1) (1) (1) 0 0 As ε (1) is the dimensionless, relative permittivity which depends on the material. So (2.15) will become: E (1) 2 2 NL 2 E c 2 t 2 c 2 t P. (2.19) The equation has the form of a driven wave equation; the nonlinear response of the medium acts as a source term which appears on the right-hand side of this equation. Let s assume the configuration shown in Fig.2.2, where the applied waves fall onto the nonlinear medium at normal incidence. Fig.2.2. Process for SHG by a NLO crystal with a length of L. The solution to this equation for a plane wave at frequency 2ω propagating in the +z direction is: E( z, t) ( 2 ) i( k z 2 t) A2 e, (2.20) 15

23 Chapter.2 Nonlinear optics theory and nonlinear optical crystals (2 ) (2 where k n ) 2 / c stands for wavevector and the amplitude (A) of the wave is a constant. The amplitude of the nonlinear polarization can then be written according to (2.11) as: 2 0 eff ( ) P 2 d A e. (2.21) 2 i2( k z t ) As the elementary field can be written as: ( ) E( ) A e, (2.22) i( k z t ) substitute (2.20), (2.21), and (2.22) into the wave equation (2.19), calculate the second order differential of time t, simplify the equation on two sides to eliminate e iωt, and get: 2 2 d A ( ) (2 ) 2 (2 ) da2 4 deff (2 ) 2 i(2 k k ) z 2ik A e 2 2, (2.23) dz dz c The first term on the left-hand side of this equation is much smaller than the second term so that it can be neglected. This approximation is known as the slowly varying amplitude approximation: 2 da2 2 ideff (2 ) 2 i kz Ae (2 ) 2. (2.24) dz k c where the quantity: ( ) (2 ) k 2k k, (2.25) is called wavevector phase-mismatch. Equation (2.24) is known as a coupled-amplitude equation, because it shows how the amplitude of the 2ω varies as a consequence of its coupling to the ω. Note that for the special case where Δk=0, the amplitude A of the SHG wave increases linearly with z, and consequently that its intensity increases quadratically with z. It is known as the condition of phase matching. When this 16

24 condition is fulfilled, the generated wave maintains a fixed phase relation with respect to the nonlinear polarization and is able to extract energy most efficiently from the incident wave. When such perfect condition is not fulfilled, the intensity of the emitted radiation becomes smaller. The amplitude of SHG field at the exit plane of the nonlinear medium is given in the case by integrating equation (2.24) from z=0 to z=l, yielding: i kl 2 ideff (2 ) A L 2 eff (2 ) 1 2 ( ) i kz id A e A L e dz ( ) (2 ) 2 0 (2 ) 2 k c. (2.26) k c k As the field amplitude is defined by: I 0 2 2n c A, (2.27) the equation (2.26) can be transformed to: I 8 n d (2 ) A e i kl 1 ( k ) c k (2 ) eff 2 (2 ) (2.28) At last, the expression of SHG intensity can be written as the relation with incident intensity: 8 d (2 ) I sinc ( / 2), (2.29) eff 2 2 I2 L kl ( ) 3 2 ( n ) 0c where sinc(δkl/2)=sin(δkl/2)/(δkl/2). It should be noted that the efficiency of the SHG decreased as L increased for some oscillations occurred in such process. The reason for the behavior is that if L is greater than 1/Δk, the output wave can get out of phase with its driving polarization, and power can flow from the 2ω back into the ω. Therefore, it defines: L k; (2.30) coh 2/ as the coherent buildup length of the interaction. 17

25 Chapter.2 Nonlinear optics theory and nonlinear optical crystals With the phase-matched condition, in a certain generation, it is found crystal length L, input power intensity I, and effective nonlinear coefficient d eff determine the generated output with equation (2.29). There will also be discussions about such factors in the following experiments of generation Phase-matching condition It is required the phase-matching condition Δk=0 to get sufficient SHG output as described in (2.29). Also, the phase-matching condition can be understood as momentum reservation in the process that two photons interact and form the third photon as shown in Fig.2.1: ( ) ( ) (2 ) k k k, (2.31) 2k k, (2.32) ( ) (2 ) where k stands for wave vector which has k 2 n/. The phase-matching condition which indicates the relation of three waves with wavelengths and refractive indices is known as: n n. (2.33) (2 ) ( ) Note that in the optical transparency region in isotropic crystals (and also in anisotropic crystals for identically polarized waves), the equality for SHG will never be fulfilled because of normal dispersion (usually n (2ω) >n (ω) ), and the phase-matching condition will never be satisfied. Therefore, it is only possible to achieve phase-matching condition by making use of anomalous dispersion: to use anisotropic medium, for example NLO crystals, under the interaction of differently polarized waves. Consequently, it can be simply concluded that the combination of nonzero square nonlinearity of an optically transparent anisotropic medium with phase 18

26 matching is the necessary and sufficient condition for an effective two (for SHG) or three (for SFG) wave interaction. For the general case in SFG, the relation of the interacting three waves and their refractive indices can be written as: k k k, (2.34) ( ) ( ) ( ) and where λ 3 <λ 1, λ 2. ( ) ( ) n n n 1 2 ( 3 ). (2.35) On the other hand, from energy conservation for the photons interaction in SFG as shown in Fig.2.1(b), the relation for wavelength of the interacting three waves can also be express as: and consequently, 1 2 3, (2.36) (2.37) which is the commonly used instruction for calculation wavelength in SFG Optics of uniaxial crystals To discuss the phase-matching property, crystal birefringence is always discussed in polar coordinate system as shown in Fig.2.3. In uniaxial crystals there is one special direction exists called the optic axis. Usually, as the optic axis is defined parallel to z axis, the phase-matching property of the crystal mainly depends on polar angle θ and have little connection with azimuth angle φ. 19

27 Chapter.2 Nonlinear optics theory and nonlinear optical crystals Fig.2.3. Polar coordinate system for description of refraction properties of uniaxial crystal (k is the light propagation direction). As light wave propagates through the crystal, the plane containing the z axis and the wave vector k of the light wave is termed the principal plane. For linear polarized light, it is known as an ordinary beam or o beam (Fig.2.4a) if the light s polarization direction is normal to the principal plane. The beam polarized in the principal plane is known as an extraordinary beam or e beam (Fig.2.4b). (a) (b) Fig.2.4. Principal plane inside the uniaxial crystal with (a) ordinary beam and (b) extraordinary beam. The refractive index of the o beam is a constant for the frequency in the crystal, and does not depend on the propagation direction, whereas for the e beam it does. Thus, the refractive index in anisotropic crystals generally depends both on light polarization and propagating direction. The refractive indices of the ordinary and extraordinary beams in the direction normal to the z axis are termed the principal values of the refractive index and are 20

28 denoted by n o and n e, respectively as shown in Fig.2.5. The different between them is defined as birefringence Δn. The refractive index of the extraordinary wave on arbitrary direction is, in general, a function of the polar angle θ that determined by the equation: n e n o 2 1 tan o e n / n tan (2.38) If n o > n e the crystal is called negative, unless it is called positive. The dependence of the refractive index on light propagation direction inside the uniaxial crystal (index surface) is a combination of a sphere with radius n o (for an ordinary beam) and an ellipsoid of rotation with semi-axes n o and n e (for an extraordinary beam, the axis of the ellipsoid of rotation is the z axis). In the z axis direction the sphere and ellipsoid are in contact with each other. In a negative crystal the ellipsoid is inscribed in the sphere (Fig.2.5a), whereas in a positive crystal the sphere is inscribed in the ellipsoid (Fig.2.5b). (a) (b) Fig.2.5. Dependence of refractive index on light propagation direction and polarization in (a) negative and (b) positive uniaxial crystal and walk-off angle ρ. When a plane light wave propagated in a uniaxial crystal, the direction of propagation of the wave vector (vector k) generally does not coincide with that of the wave energy (vector S) which is also called Poynting vector. The direction of 21

29 Chapter.2 Nonlinear optics theory and nonlinear optical crystals S can be defined as normal to the tangent drawn at the point of intersection of vector k with the refractive index curve. For an ordinary wave the refractive index dependence is a sphere with radius n o. Therefore, the normal to the tangent coincides with the wave vector k. For an extraordinary wave the normal to the tangent (with the exception of the cases θ=0, θ=90 ) does not coincide with the wave vector k but is rotated from it by angle called walk-off angle: n n 2 arctan o / e tan, (2.39) where the upper signs refer to a negative crystal and the lower signs to a positive one. The walk-off angle also can be seen in Fig.2.5. From this structure, it is found the birefringence and walk off angle are intrinsic co-existence relation. The NLO crystal which has refractive ellipse with a large eccentricity that means large birefringence will also obtain a large walk-off angle. That is the reason NLO with outstanding phase-matching power also suffers from large walk-off effect Optics of biaxial crystals For biaxial crystals, the dependence of the refractive index on light propagation direction and its polarization (index surface) corresponds to a much more complex function than for uniaxial crystals. Similar to the case of a uniaxial crystal, the propagation direction of plane light wave is defined by two angles: polar θ and azimuthal φ except the optical axis is no longer parallel to z axis. Note that the use of terms ordinary (o) and extraordinary (e) waves for the general case of light propagation inside a biaxial crystal is senseless except in the principal planes of a biaxial crystal. In the plane xy the refractive index of the wave polarized normally to this plane is constant and equals n z, and that of the wave polarized in this plane changes from n y to n x with varying from 0 to 90. Hence, a biaxial crystal with n x <n y <n z in the plane x-y is similar to a positive uniaxial crystal with n o =n z and: 22

30 n e n y 2 1 tan 1/ ny / nx tan 1/2. (2.40) In the plane y-z the refractive index of the wave polarized normally to this plane is constant and equals n x, whereas for the wave polarizaed in this plane the refractive index changes from n y to n z with θ varying from 0 to 90. Hence, a biaxial crystal with n x <n y <n z in the plane y-z is similar to a negative uniaxial crystal with n o =n x and: n e n y 2 1 tan 1/ ny / nz tan 1/2. (2.41) It is easy to deal with practical question with the expression for birefringence in biaxial crystals,, for example, to make sure the phase-matching angle or walk-off angle in principle plane with the similar method as in uniaxial crystals. V z is an angle formed by one of the optic axes with the axis z which has different form in the two cases. It can help to estimate the spatial relation of the two optical axes. Vz Fig.2.6. Dependence of refractive index on light propagation direction in biaxial crystals under n x <n y <n z condition 23

31 Chapter.2 Nonlinear optics theory and nonlinear optical crystals Phase-matching in uniaxial crystals Generally, in order to achieve phase-matching through the use of birefringence crystal, the waves involve the interaction should have orthogonal polarization directions that they can be termed o beam and e beam as described in Fig.2.7 shows the dispersion of refractive indices in a negative crystal to illustrate the SHG (from λ ω to λ 2ω ). Since the difference between n o and n e gives the maximum value of the birefringence of the crystal, when the birefringence of λ ω and λ 2ω light have a part coincided, the phase-matching for SHG is possible. (a) (b) Fig.2.7. Dispersion of the refractive indices in a negative crystal. The phase-matching depends on the birefringence property: (a) phase-matching possible, (b) phase-matching impossible. If the input waves with frequency ω have the same polarization direction, while the radiation at 2ω has polarization in the perpendicular direction, Type I phase matching is realized, which has: ( ) (2 ) 2 o k e k. (2.42) This is called ooe interaction of phase-matching of Type I. Similarly, in positive crystals, there is also: (2 ) k ( ) 2k e o, (2.43) which is called eeo interaction of Type I phase-matching. 24

32 Typically, phase-matching is accomplished by tuning the direction of wavevector with respect to optical axis. Fig.2.8 illustrates how to find the direction of collinear (scalar) phase matching. For the ooe interaction, it has: ( ) (2 ) 2 ko k e ( PM), (2.44) or corresponding refractive indices relation as: n ( ) (2 ) o n e PM ( ). (2.45) Therefore, the phase-matching direction k for this case is formed when the circle (ω) 2k o intersects the ellipse k (2ω) e (θ) or when the circle of the ordinary refractive index at frequency ω crosses the ellipse of the extraordinary refractive index at frequency 2ω. (a) (b) Fig.2.8. Collinear (scalar) type I phase matching for SHG in uniaxial negative crystal in coordinates described by (a) refractive index function for o beam shown with dash and dot line curve, for e beam shown with dashed curve and (b) wave vector shown with different line for o beam and e beam. Also there is phase-matching occurred with input lights of different frequency. In the equation of SFG, the first symbol in the expressions refers to the wave with the lowest frequency, the third symbol to the wave with the highest 25

33 Chapter.2 Nonlinear optics theory and nonlinear optical crystals frequency (λ 3 >λ 2 >λ 1 or ω 3 >ω 2 >ω 1 ). For example, in negative crystal, it has ooe interaction like: ( ) ( ) o o e 1 2 ( 3 ) k k k. (2.46) While in positive crystal, there is eeo interaction like: k 3 k ( 1) ( 2 ) ( ) e k e o. (2.47) Fig.2.9. Collinear (scalar) type II phase-matching for SHG in uniaxial negative crystal in coordinates described by wavevector. Dash and dot line stands for o beam, while dash line stands for e beam. If the inputted ω waves have orthogonal polarizations, Type II phase matching takes place and the 2ω wave corresponds to an extraordinary wave in negative crystals: k k k ( ). (2.48) ( ) ( ) (2 ) o e e There is also Type II phase-matching in positive crystal shown as: k k k. (2.49) ( ) ( ) ( 2 ) o e o Accordingly, such phase-matching can be also written with refractive index relation as: 26

34 n n n ( ), (2.50) ( ) ( ) (2 ) o e e and: n n n. (2.51) ( ) ( ) ( 2 ) o e o For the case of SFG, it has interactions for Type II phase-matching like (oee): and (eoe) k k 1 2 ( 3 ) ( ) ( ) o e e k k, (2.52) ( ) ( ) e o k e 1 2 ( 3 ) k, (2.53) in negative crystals. While, there are oeo interaction: and eoo interaction: 3 k k k, (2.54) k ( 1) ( 2 ) ( ) o e o 3 k k, (2.55) ( 1) ( 2 ) ( ) e o o for SFG in positive crystals. Collinear phase-matching described above is usually used in SHG or SFG because of its simplicity in realization. However, it also has a limitation of walk-off effect occurred in the generation with phase-matching angle θ PM other than 0 or 90. For example, in a Type II (eoe) SHG realized with a negative uniaxial crystal (such as CLBO) as shown in Fig.2.10, there are walk-off angles (ρ (ω), ρ (2ω) ) between the Poynting vectors (S (ω) e, S (2ω) e ) and wavevectors (k (ω) e, k (2ω) e ) of the e beams. These walk-off angles will consequently exist between the Poynting vectors of the three interacting waves and cause the overlap reduction between the waves. As the result, the generated field intensity will get decreased and not fully comply with equation (2.29). 27

35 Chapter.2 Nonlinear optics theory and nonlinear optical crystals Fig Scheme for Type II phase-matching of SHG. Orange line and dashed line stand for wavevector and Poynting vector for the ω (o beam); while red and green lines stand for the ω and 2ω waves. Walk-off angle in the generation is given as the separation between the wave vector and Poynting vector. There is a factor called aperture length (l a ) that describes the impact of the walk-off effect. The conversion to the 2ω wave will cease to grow proportionally to the square of the crystal length beyond the aperture length. In Type I phase-matching, it is defined as: l (I) a w ; (2.56) 0 / while in Type II phase-matching, it has a form as: l 1.16 w /. (2.57) (II) a 0 where w 0 stands for radius of the beam. From the equations it is found that the walk-off effect should be evaluated with beam s aperture involved in the interaction. On the other hand, the walk-off effect will disappear when phase-matching angle becomes θ PM =90 that Poynting vector collimates with wave vector. This condition is often called non-critical phase-matching that is used to increase in the conversion efficiency. 28

36 Fig Configuration of twin-crystal mothed for walk-off compensation in a Type II second-harmonic generation. The figure is devoted to show the direction of each vector, so the length of line does not represent the real quantity of the vector. Since there is no way to eliminate the walk-off effect; several methods have been proposed to reduce the impact. One of most utilized method is to use a twin-crystal configuration [3], where two identically cut crystals are mounted with their optical axes symmetrically crossed. An example based on Type II SHG is shown in Fig.2.11, Poynying vector of e beams separate from their wavevector in opposite direction in the two cascaded crystals. Such configuration will improve the coverage area between the two ω waves and lift the conversion efficiency. It is also can be considered as an improvement in the aperture length of the generation. The method is effective for either Type I or Type II phase-matching and generations either the walk-off angle is occurred in input wave or generated wave. Another effort aimed at compensating the walk-off angle only within Type II phase-matching, involves the use of non-collinear phase-matching [4]. As the phase-matching conditions means the space resonance of the propagating waves physically, there is also one kind of non-collinear (vector) phase-matching that the interacting waves are not on the same direction. Fig.2.12 demonstrates the positions of scalar (angle θ PM ) and vector phase-matching of Type II for SHG in a negative uniaxial crystal. The phase-matching direction in the non-collinear case is determined by intersection of the ellipse k (2ω) e (θ) with the quasi-ellipse k (ω) o +k (ω) e (θ). Type II vector phase-matching is possible in the region θ PM θ PM π-θ PM. 29

37 Chapter.2 Nonlinear optics theory and nonlinear optical crystals As a Type II phase-matching SHG shown in Fig.2.13, the method for walk-off compensation takes the advantage of the separated angle between the wavevectors of the two input waves to compensate the deviation between the Poynting vectors of the waves. The practical application of the method in Type 355 nm light generation with CLBO will be one of the themes of the dissertation introduced in Chapter 5. Fig Scheme for collinear and non-collinear phase-matching for Type II SHG in a negative uniaxial crystal. k and θ PM stand for collinear phase-matching, while k' and θ PM stand for non-collinear phase-matching. Phase-matching angles calculation for Type II SHG given above is: n ( )sin( ) n ( )sin( ) 2 n ( )sin( ), (2.58) ( ) ( ) ( ) ( ) ( ) ( ) (2 ) (2 ) (2 ) e e e o o o e n ( )cos( ) n ( )cos( ) 2 n ( )cos( ), (2.59) ( ) ( ) ( ) ( ) ( ) ( ) (2 ) (2 ) (2 ) e e e o o o e n ( ) Tan( ) Tan( )[ ]. (2.60) ( ) ( ) ( ) ( ) e e 2 e o ( ) no Equations (2.58) and (2.59) are for the non-collinear phase-matching condition in Type II SHG, while (2.60) is for the collinear energy flow of o beam and e beam of ω. 30

38 Fig2.13. Walk-off compensation for Type II SHG with non-collinear phase-matching configuration Quasi phase-matching The efforts to meet phase-matching condition also face difficulty when NLO material posses insufficient birefringence to compensate for the dispersion of the linear refractive indices over the wavelength range of interest. Particularly, in generation in UV range, the problem of insufficient birefringence becomes increasingly acute. Fig Comparsion of the field strength variation of the generated wave along the nonlinear medium in nonlinear optical interaction. Red curve stands for the phase-matching condition. Green curve stands for the condition that wavevector mismatch is nonzero. Blue curve stands for quasi phase-matching condition. There is a method known as quasi phase-matching that can be used when normal phase-matching cannot be implemented [5]. It is realized with a structure 31

39 Chapter.2 Nonlinear optics theory and nonlinear optical crystals called periodically poled material which has been fabricated in such a manner that the orientation of one of the crystalline axis is inverted periodically as a function of position within the material. That means a periodic alternation of the sign of d eff, which can compensate for nonzero wavevector mismatch Δk, is realized. As shown in Fig.2.14, if the mismatch of interaction is nonzero, the consequent field strength of the generated wave will oscillate periodically with propagation distance. After the compensation for the influence of wavevector mismatching with quasi phase-matching, the generated field strength grows with propagation distance and approaches phase-matched condition. The period ( ) of the alternation of the crystalline axis has been set equal to twice the coherent length (L coh ) as defined in equation (2.30), of the nonlinear interaction as shown in equation (2.61) and Fig Each time the field strength of the generated wave grew to the maximum, it should have begun to decrease as a consequence of the wavevector mismatch. Thanks to a reversal of the sign of d eff, the field amplitude is able to continue to grow monotonically. 2L 2 / k. (2.61) coh Fig A periodically poled material used to realize a SHG from ω to 2ω. Arrows stand for crystalline axis which alternates in orientation with period Λ Optical parametric oscillator Optical parametric oscillation (OPO) is a useful configuration for nonlinear frequency conversion to generate wavelength that cannot be achieved with other methods. OPO requires phase matching condition to be achieved and is also considered as the opposite process of SFG. Similar as the wavelength relation given as (2.37), for OPO it has (λ 3 <λ 2 <λ 1 ): 32

40 (2.62) The shortest wavelength λ 3 act as pump light, while in generated waves, shorter wavelength λ 2 is called signal; longer wavelength λ 1 is called idler. So the relation turns to be: (2.63) pump signal idler OPO is practically based on NLO crystal that provides gain at both signal and idler when get pumped, and is schematically represented by an optical cavity which is built with dichroic mirrors. In this research, two singly resonant oscillators will be employed. The usage of OPO has a merit of a wide potential wavelength tuning range. The tuning is in most cases achieved by influencing the phase-matching conditions, e.g. by changing the crystal temperature, or the angular orientation of the crystal. Since high spatial coherence and high power intensity pump is preferred in OPO, diode laser cannot be directly used as the pump, which means the OPO system needs a complicated layout. Pump wave with pulsed operation typically generated by Q-switched laser is always used to get high gain at generated waves. 2-2 Nonlinear optical crystals for UV light generation Nonlinear optical crystals are considered as a kind of key material for solid laser system development because of their ability to change frequency of laser beam and modulate it in field strength and phase. In the following part of this chapter, important NLO properties called for nonlinear frequency conversion are to be discussed; borate crystals as one kind of useful NLO crystal for UV light generation are to be introduced. 33

41 Chapter.2 Nonlinear optics theory and nonlinear optical crystals Properties required for nonlinear crystals in UV light generation There are several important properties of the nonlinear crystals should be concerned before start to design a frequency converter in UV range, especially for sub-200 nm usage [6]. Firstly, a relatively large effective nonlinear coefficient (d eff ) should be considered. It depends strongly on the geometric symmetry of the crystals, and the phase-matching type achieved in the practical generation. From the expression of generated intensity in equation (2.29), it is obviously found the nonlinear coefficient plays an important part in generation. Wide transparency range either on IR side or UV side is in demand. Because the generation under 190 nm is generally realized by SFG with UV and IR light, it requires the crystal work in either UV range around 200 nm or IR range around 2000 nm. As a useful NLO crystal, it is necessary for the crystal to possess an appropriate birefringence spanning UV and IR, which provides sufficient ability for phase-matching. What is more, since high peak power density is needed in nonlinear wavelength conversion, enough high damage threshold (bulk damage above 100 MW/cm 2 for ns pulse duration) is important for the crystal to sustain high intensity radiation. Otherwise the NLO effect has not chance to be realized in practical use. At last, it is obvious that as a useful NLO material, good physical properties such as, high optical quality, high mechanical properties and stable chemical property are demanded. Also, reliable growth method for achieving bulk crystal is required Useful borate crystals As coherent UV laser is found more and more applications in industry, NLO crystals suited for UV light generation have drawn great attentions. Especially, borate crystals, such as β-bab 2 O 4 (BBO) belongs to anionic group (B 3 O 6 ) 3- ; 34

42 LiB 3 O 5 (LBO), CsB 3 O 5 (CBO), CsLiB 6 O 10 (CLBO) belong to anionic group (B 3 O 7 ) 3- ; and KBe 2 BO 3 F 2 (KBBF) belongs to anionic group (BO 3 ) 3-, can provide large effective nonlinear coefficient and phase-matching ability that are considered effective choice in UV light generation. Beta-barium borate (BBO) BBO is a negative uniaxial crystal belonging to point group 3m, which is grown by top-seeded solution growth (TSSG) technique with flux method. The crystal belongs to anionic group (B 3 O 6 ) 3- that makes the large nonlinear coefficient d 22 theoretically possible [2]. The cutoff wavelength on UV side is locates at 189 nm while on IR side locates at 2500 nm. The crystal has a moderately large nonlinear coefficient, large birefringence and relatively small dispersion. It also features a large temperature tolerance in phase-matching and good physical and chemical properties. BBO has a wide phase-matching range for SHG from 205 to 1500 nm. It is also widely used in tunable optical parameter oscillators and amplifiers besides SFG. However, BBO has too small angular acceptance and large walk-off angle, which limit its application for laser systems possessing larger divergence and for focusing to increase the power density. Also the low damage threshold restricts its application in high power UV light generation such as fourth and fifth harmonic generation of Nd-doped laser. Lithium triborate (LBO) LBO belongs to point group mm2, is grown with flux method with TSSG technique. The crystal belongs to anionic group (B 3 O 7 ) 3- which is an ideal structure from the point view of absorption edge, SHG coefficient and damage threshold. The cutoff wavelength on UV side is locates at 160 nm while on IR side locates at 2600 nm. It has birefringence of about Δn=0.04 (532 nm). LBO is a kind of negative biaxial crystal whose Sellmeier s equations are given as [7]: n , 2 2 x 2 35

43 Chapter.2 Nonlinear optics theory and nonlinear optical crystals n n , 2 2 y (2.64) 2 2 z 2 Nonlinear optical coefficients are d 31 =0.94 pm/v, and d 32 =1.12 pm/v. The effective nonlinear coefficient can be simply expressed as [8]: xy plane: d eff =d 32 cosφ (Type I), yz plane: d eff =d 31 cosθ (Type II), xz plane: θ>v z d eff = d 32 sin 2 θ+d 31 cos 2 θ (Type I), θ<v z d eff = d 32 sin 2 θ+d 31 cos 2 θ (Type II). (2.65) The major advantage of LBO are summarized as follows: (1) it possesses exceptionally low angular sensitivities, wide acceptance bandwidth, small walk-off angles for SHG and THG of Nd-doped laser; (2) it has a widest temperature-tuned NCPM range to SHG from 0.9 to 1.9 μm, and larger effective nonlinear coefficient in these generations than critical phase-matchings; (3) it is also featured by relatively high optical-damage threshold, mechanical hardness, chemical stability, and non-hygroscopicity. The major weakness of LBO comes from small birefringence that hinders the crystal being used from achieving SHG shorter than about 277 nm. Cesium triborate (CBO) CBO belongs to point group 222 and anionic group (B 3 O 7 ) 3-, is grown with flux method or stoichiometric melts with TSSG technique. The cutoff wavelength on UV side is locates at 167 nm while on IR side locates at 3400 nm. It has birefringence of about Δn=0.06 (532 nm). CBO is a negative biaxial crystal whose Sellmeier s equations are given as [9]: n n , 2 2 x , 2 2 y 2 36

44 n (2. 66) 2 2 z 2 Nonlinear coefficient is d 14 =0.86 pm/v. Expressions for the effective nonlinear coefficient in the principal planes of CBO are [10]: xy plane: d eff =d 14 sin2φ (Tpye II), yz plane: d eff =d 14 sin2θ (Type I), xz plane: θ<v z d eff =-d 14 sin2θ (Type II), θ>v z d eff =-d 14 sin2θ (Type I). (2.67) Though the nonlinear coefficients for CBO and LBO are approximately equal, their effective NLO coefficients are quite different due to different crystal symmetry. The CBO can get nearly maximum effect nonlinear coefficient in some UV light generations such as Type II 355 nm (1064 nm +532 nm 355 nm) generation and Type I 266 nm (1064 nm nm 266 nm) generation. This suggests CBO a more effective NLO material for frequency conversion into UV region than LBO. Unfortunately, its application in these generation is not so popular as LBO because of limitation of the high hygroscopy. Cesium lithium borate (CLBO) CLBO is first developed by Osaka University and is also the key research object in this dissertation. LBO belongs to point group -42m and anionic group (B 3 O 7 ) 3-, which is grown with flux method or stoichiometric melts with TSSG technique. The cutoff wavelength on UV side is locates at 180 nm while on IR side locates at 2750 nm. It has birefringence of about Δn=0.05(532 nm). CLBO is a negative uniaxial crystal with Sellmeier s equations as [11]: n o , n e (2.68) 2 37

45 Chapter.2 Nonlinear optics theory and nonlinear optical crystals Nonlinear coefficient is d 36 =0.95 pm/v. The effective NLO coefficients for Type I and Type II processes are given by[12]: d eff =d 36 sinθsin2φ (Type I), d eff = d 36 sin2θcos2φ (Type II). (2.69) CLBO has relatively large effective NLO coefficients in SFG for DUV light especially under 200 nm. CLBO features large angular and temperature bandwidths favorable for stable DUV operation. Compared with BBO, CLBO also has smaller walk-off angles, which make it produce better spatial profile and overlapping of the mixing beams. The second, fourth, and fifth harmonic generations of 1064 nm laser with CLBO have been proved effective, the data of these generations with THG are concluded in Table 2.1. CLBO has remarkable properties particularly in fourth and fifth harmonic generations. Table 2.1. Properties for CLBO in harmonic generation with 1064 nm laser source. Wavelength (nm) (PM Type) (Type II) (Type II) (Type I) (Type I) Phase- matching angle θ (deg.) d eff (pm/v) Δθl (mrad cm) Δλl (nm cm) ΔTl ( C cm) Walk-off angle (mrad) (ω) 35.72(2ω) (ω) (3ω)

46 Potassium beryllium fluoroborate (KBBF) KBBF belongs to point group 32, is grown with flux or hydrothermal method. The crystal belongs to (BO 3 ) 3- group, which make it powerful in phase-matching with large birefringence and achieve transparency down to VUV range. The cutoff wavelength on UV side is locates at 147 nm while on IR side locates at 3400 nm [6]. KBBF is the only kind of NLO crystal that can directly generate UV light under 200 nm with SHG process. For instance, it can be used to realize the sixth harmonic light at 177 nm of Nd:YAG laser with the input third harmonic light at 355 nm. However, because of limitation in the growth technology, KBBF crystal cannot be grown to enough thickness other than a few millimeters. Therefore, it cannot be cut according to phase-matching angles as wishes just like other NLO crystals. In order to achieve phase-matching with KBBF, a prism-coupled device (PCD) [13] should be used to increase the transmittance of the incident light at the surface of the crystal. As shown in Fig.2.16, 177 nm VUV has been successfully demonstrated with the device, which makes the crystal a potential in future application use. Fig Prism coupled device used with KBBF in VUV light generation. Prism is cut with wedge angle which equals to the phase-matching angle of θ PM =68.6. Normal incident light will get through the glass-crystal boundary without obvious refraction, because the refractive indices on the two sides are almost equaled. So the light inputted in the KBBF can meet the phase-matching condition. Generated light will separate with original light due to dispersion in the glass. 39

47 Chapter.2 Nonlinear optics theory and nonlinear optical crystals There is a summary of main parameters of the borate crystals listed in Table 2.2. Table 2.2 Borate crystals to be discuss in this work Crystals Point group Transparent range (nm) Nonlinear coefficient Birefringence Δn Shortest SHG Anionic group (pm/v) (nm) BBO 3m d 11 = (B 3 O 6 ) 3- LBO mm d 31 = (B 3 O 7 ) 5- d 32 =1.13 d 33 =0.256 CBO d 14 = (B 3 O 7 ) 5- CLBO -42m d 36 = (B 3 O 7 ) 5- KBBF d 11 = (BO 3 ) 3- There are two other kinds of crystal used in this research. Here are brief introductions for both of them. Potassium titanyl phosphate (KTP) KTP belongs to point group 32, which is grown with flux or hydrothermal method. The cutoff wavelength on UV side is locates at 350 nm while on IR side locates at 4500 nm [6]. Due to large effect nonlinearity and excellent optical properties, KTP suits for the nonlinear wavelength conversion material in various applications. Especially, SHG can be realized with KTP ranges from CO 2 lasers to Nd:YAG lasers. With large temperature bandwidth in phase-matching process, KTP is employed to achieve QPM by temperature tuning to realize perfect phase-matching. Although KTP is very attractive for various SFG, DFG, and optical parametric applications over its entire transparency range, high power operation with KTP is limited by its low damage threshold. Periodically poled lithium niobate (PPLN) PPLN is made by periodical layout of nonlinear material that utilizes quasi phase-matching in nonlinear wavelength conversion processes. The frequency 40

48 conversions with PPLN use nonlinear coefficient d 33 = 25pm/V which is much larger than the off-diagonal coefficients [14]. With absorption cutoff at about 400 nm, PPLN becomes an efficient choice for SHG of light ranges from 1000 nm to about 2000 nm. Of course, the actual conversion efficiency depend on the properties of the laser beam used (e.g. pulse length, repetition rate, beam quality, and line width). Another common use for PPLN is for building an optical parametric oscillator (OPO) that generate IR light at about nm. The operation wavelengths in this process can be regulated by changing the PPLN temperature or the poled period of PPLN. Because of photorefractive effect occurred can damage the crystal and cause the output beam to become distorted, 5% MgO doping lithium niobate is widely used to make the device for it can significantly increases the optical and photorefractive resistance of the crystal while preserving its high nonlinear coefficient. 2-3 Summary In this chapter, the principle of nonlinear optics is introduced. As the second order nonlinear effect, nonlinear frequency conversion is described from the fundamental to numerical analysis with Maxwell s equations. For generating sufficient output with the nonlinear process, the condition of phase-matching should be fulfilled. Nonlinear optical crystal with birefringence property is fit for the generation, whose phase-matching properties are discussed in detail. As key material for generating new frequencies with solid laser system, NLO crystals are introduced and their important properties that required for UV light generation are discussed. Moreover, as the most popular material for UV light generation in this field, borate crystals used in the dissertation are briefly introduced. 41

49 Chapter.2 Nonlinear optics theory and nonlinear optical crystals References in Chapter 2: [1] R. W. Boyd, Nonlinear Optics (Academic Press, 2010) 3rd ed., Chap. 2. [2] V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 3rd revised edition, 1999). [3] J. Zondy, M. Abed, and S. Khodja, J. Opt. Soc. Am. B 11, 2368 (1994). [4] K. Asaumi, Appl. Opt. 37, 555 (1998). [5] J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962). [6] C. Chen, T. Sasaki, R. Li, Y. Wu, Z. Lin, Y. Mori, Z. Hu, J. Wang, S. Uda, M. Yoshimura, and Y. Kaneda, Nonlinear Optical Borate Crystals: Principals and Applications (Wiley, Germany, 2012) 1st ed., Chap. 3. [7] K. Kato, IEEE J. Quantum Electron. 26, 1173 (1990). [8] D. A. Roberts, IEEE J. Quantum Electron. 28, 2057 (1992). [9] K. Kato, IEEE J. Quantum Electron. 31, 169 (1995). [10] Y. Wu, T. Sasaki, S. Nakai, A. Yokotani, H. Tang, and C. Chen, Appl. Phys. Lett. 62, 2614 (1993). [11] N. Umemura, K. Yoshida, T. Kamimura, Y. Mori, T. Sasaki, and K. Kato, Advanced Solid-State Lasers, OSA TOPS 26, 715 (1999). [12] N. Umemura and K. Kato, Appl. Opt. 36, 6794 (1997). [13] C. Chen, J. Lu, T. Togashi, T. Suganuma, T. Sekikawa, S. Watanabe, Z. Xu, and J. Wang, Opt. Lett. 27, 637 (2002). [14] L.E. Myers, R. C. Eckardt, M. M. Fejer, and R. I. Byer, Opt. Lett. 21, 8 (1996). 42

50 Chapter nm VUV light generation with borate crystals 3-1 Introduction for VUV light generation at 189 nm Although lots of researches have reported the UV generation in the range of 190 nm-200 nm [1-4], however, there is very few record about the generation in 180 nm-190 nm range as far as I know. For example, Kouta et al. reported a generation of 186 nm light based on Ti:sapphire laser with the SFG with the fundamental (774 nm) and the third-harmonic (248 nm) light. The generation was confirmed with a BBO crystal which is cooled to 91K so that the cutoff wavelength shortened from 189 nm to 180 nm [5]. Another 180 nm-190 nm range generation is realized by SFG with fifth harmonic light of 1064 nm laser and IR light of about 1400 nm generated by OPO. Because a large birefringence is not required in such UV+IR form SFG, borate crystals LBO, CBO, and CLBO were all proved to be feasible for the generation until 185 nm [6-8]. However, conversion efficiency of the SFG with these borate crystals has not been investigated, because the experiments in these reports were based on Q-switch laser sources with a pulse repetition of 10 Hz for phase-matching angles measurement use. In order to comply with laser source equipped in practical applications, repetition rates in the tens of kilohertz range are preferable for the generation [9]. Under such circumstance, to ensure sufficient conversion efficiency, the high-repetition rate laser beam should be focused in nonlinear optical crystal to make the peak power density reach the order of 100 MW/cm 2 which is similar to unfocused 10 Hz laser beam. In this research, as shown in Fig.3.1, a laser system of 189 nm light generation by SFG with 213 nm and IR light is built based on a high repetition rate 1064 nm laser source. PPLN, which can provide high conversion efficiency, is used as the OPO material. The generated VUV wavelength is till about 189 nm due to the limitation of the generated range of the PPLN OPO used. Table 3.1 lists the phase-matching properties at 189 nm light generation for the potential borate 43

51 Chapter nm VUV light generation by borate crystals crystals. Among them, CBO is expected to give largest output power according to the effective nonlinear coefficient. With the system, I attempt to make highly efficient VUV generation and unveil the phase-matching property under 190 nm of these borate crystals with a high-repetition rate laser source. Fig.3.1. Scheme for 189 nm light generation. Table 3.1. Property of borate crystals for SFG at 189 nm. Candidate Transmission Phase-matching Phase-matching Effective nonlinear crystal range (nm) type angle* (θ, φ) coefficient d eff (pm/v) LBO [6] Type I in xy plane CBO [7] Type I in yz plane *Phase-matching angles for SFG at nm were calculated with the interacting wavelengths of and nm. 3-2 Experiment for 189 nm light generation In this section, the 189 nm VUV light generation realized by SFG with 213 nm and IR light by borate crystal will be introduced. The description of the whole system will be divided into several parts which contains the demonstration of SHG, OPO, 4HG, 5HG and the final generation setup. The generation results will be summarized in the last part of the section. (90.0, 71.0 ) 0.28 (54.5, 90.0 ) 1.04 CLBO [8] Type I (59.5, 45.0 )

52 3-2-1 Scheme for 189 nm light generation The experimental setup of the 189 nm light generation system is depicted in Fig.3.2. A commercial Q-switched Nd:YAG laser of 1064 nm operating at a 10 khz repetition rate (COHERENT MATRIX 1064) was employed as the fundamental laser source, with a pulse width of 60 ns and a maximum average output of 7 W. The system is built with five stages of nonlinear frequency conversions. First, it is a harmonic generator ranges from the SHG at 532 nm to the fifth-harmonic generation at 213 nm. SHG is realized with LBO, while 266 nm and 213 nm light generations are realized by CLBO1 with SHG2 and by CLBO2 with the SFG1. The crystals selected are best suited for these generations to our knowledge. On the other hand, IR is produced by a PPLN OPO, which pumped with residual 1064 nm light after SHG LBO. At last, the SFG for producing VUV light at around 190 nm is realized by borate crystals. Delay lines are set in light paths of 213 nm and 189 nm light generation to improve the conversion efficiency of SFGs. Fig.3.2. Experimental setup for 189 nm light generation. Cs stand for cylinder lenses while Ls stand for spherical lenses. There are delay lines set in 1064 nm and IR light path for 213 nm and 189 nm light generations. 45

53 Chapter nm VUV light generation by borate crystals SHG with LBO The second-harmonic generation (SHG) is performed using a non-critical phase-matching (NCPM) LBO crystal. It is cut with angles: θ=90, φ=0 and a dimension of mm 3. The oven mounted LBO is heated to 151 C to meet the phase-matching condition along x-axis. The fundamental beam is focused to a radius of about 36 µm. As shown in Fig.3.3, SHG is got with a maximum conversion efficiency of 36.8% with input of 6.39 W. Fig.3.3. SHG measured by the LBO. Green spots stand for output, grey spots stand for conversion efficiency IR light generation with OPO After the SHG part, a PPLN OPO pumped by residual 1064 nm light is employed to obtain IR light generation [10]. As shown in Fig.3.2, the pump light is polarized vertical to the paper tuned by a half-wave plate and focused by a spherical lens (L2). The OPO is operated in quasi-phase-matching mode with three interacting waves polarized parallel for using a large d 33 nonlinear coefficient. The PPLN device used named OPO1-20 which has nine periods range from 29.5 to 31.5 µm, manufactured by Covesion Ltd. It has a length of 20 mm and an aperture of mm 2 for the single period. 46

54 The OPO built here can directly produce IR light with a bandwidth of moderate range that is suited for efficiently interact with common frequency conversion crystals. Further, the IR can be frequency mixed with an harmonic of the pump laser, since the build-up time of the OPO is short enough. The process determining the parameters for resonate cavity shown in Fig.3.4 is critical for OPO s construction. First, the length of linear resonance cavity is set to be 40 mm which is a little longer than the oven mounted PPLN, to make sure the oscillation is stable. The second step is to decide the beam waist and radius of curvature for the concave mirrors (M1 and M2) which formed the resonate cavity. The device OPO1 has specification for generation of signal light from 1410 nm to 2100 nm corresponding to the idler branch from 2100 nm to 4300 nm. To generate VUV around 190 nm, the OPO need to operate at SRO mode to generate IR at about 1677 nm of signal, according to idler of about 2900 nm, where is the center of the OPO oscillation range. The oscillation range is mostly ruled by the transparent and reflection range of the concave mirrors. In this system, it used concave mirrors customized by SIGMAKOKI CO. The mirrors are ordered with high-reflection coating from 2500 to 3200 nm with a center wavelength at about 2850 nm, which corresponds to signal light range of about 1600 to 1850 nm. Otherwise, the coat is transparent at the signal range and also at 1064 nm. Fig.3.4. Sketch for the PPLN OPO operating at SRO mode. It is built by a PPLN and two concave mirrors. Parameters related to resonate cavity is defined in (3.1). R(z) stands for the radius of curvature for the resonate cavity that equals the radius of curvature for 47

55 Chapter nm VUV light generation by borate crystals the two concave mirrors. w 0 is the beam waist size usually located in the center of the cavity. z stands for the position inside the cavity that the center is defined as 0 point. As the center oscillation wavelength is chosen around 2850 to 2900 nm, given a value for R(z), beam waist size could be calculated. Given the waist size, the laser intensity at the waist can be obtained to evaluate the whether the damage threshold of OPO medium is exceeded. After proper value of w 0 and R(z) is get, the next question becomes how to make the waist needed. w R( z) z 1 z (3.1) Inside the OPO cavity, as the pump light and idler light have same confocal parameter during oscillation, the waist size of 1064 nm light can be obtained with w 0 of the idler light (which is also called the eigenmode of the resonate cavity). Therefore, the next step becomes to focus the 1064 nm light with the waist needed. There is also a complicated calculation about q factor for laser beam and will not be discussed here. Fig.3.5. Waist of 1064 nm beam measured in the cavity. It has the same confocal parameter with idler light which make the oscillation of OPO. In our experiment, 100 mm-radius curvature concave mirror is chosen which 48

56 can make the focused 1064 nm beam to a waist needed in the center of the resonate cavity. Fig.3.5 shows the waist size of 1064 nm light measured in the experiment, which is about 130 μm. During the oscillation, the output IR light is tuned from 1610 nm to 1890 nm in the signal branch and corresponding idler branch is from 3140 nm to 2430 nm. The center output wavelength depends on the grating period of PPLN and temperature tuning will change the period slightly. For PPLN, temperatures in the 100 C-200 C range are used in order to minimize the photorefractive effect that can damage the crystal and causes the output beam to be distorted. Since the photorefractive effect is more severe in PPLN when higher energy photons in the visible part of the spectrum are present in the crystal, it is especially important to use the crystal only in the suitable temperature range. (a) (b) Fig.3.6. Signal light wavelength measured by optical spectrum analyzer. The spectral bandwidth for 1474 nm is read as about 4 ns, for 1659 nm is read as about 9ns. In the multi-grating section, the grating period increases from 2950 nm to 3150 nm every other 0.25 μm. OPO exhibits a free-running optical bandwidth without injection seeding. I measured the wavelength of the signal with optical spectrum analyzer (Advantest Q8381A) as shown in Fig.3.6. It is found the spread-width of the spectrum is changed at different signal wavelength according to the property of PPLN. As the optical spectrum analyzer used has a measurement range spreads from about 800 to 1600 nm, the longer part of the signal 49

57 Chapter nm VUV light generation by borate crystals wavelength from OPO in the experiment cannot be directly measured. Nonlinear frequency conversion occurred in the OPO contains not only the OPO process 1/1064=1/signal+1/idler, but also SFG processes such as 1/1064+1/signal=1/red 1, 1/1064+1/idler=1/red 2. When the power is enough for the oscillation, it will be an infinite process. Thanks to the generated by-product red light, measurement of the signal light wavelength that is out of the measurement range of the optical spectrum analyzer becomes possible. For 189 nm light generation, an IR wavelength of nm corresponding to nm light generation is chosen, at the grating period of μm operated at the temperature of 120 C. The free-running spectral bandwidth (FWHM) at the center wavelength was about 2.6 nm. The maximum output power of nm was 450 mw with a maximum conversion efficiency of 17.8% from 1064 nm pump power Fourth harmonic and fifth harmonic generation with CLBO The crystals used in 266 nm and 213 nm light generation are kept at 150 C and used argon gas flow to reduce water impurity [11]. As CLBO is one kind of hygroscopic material, the method is effective for improve the degradation resistance of the crystal in UV generation and extend its life time [12]. Fig.3.7. Conversion efficiency of 4HG by CLBO. Blue spots stand for output while black spots stand for conversion efficiency. 50

58 The 532 nm beam was focused to a waist of 34 μm in radius. The conversion efficiency of the generation is shown monotonically increased with the input power as shown in Fig.3.7. The fourth-harmonic generation is obtained via a mm type I CLBO crystal (CLBO1 in Fig.3.2) with a maximum conversion efficiency of 28.9% at 2.35 W input power. Then, the fifth-harmonic generation was obtained by SFG with the fourth-harmonic light and depleted pump light after the OPO in a mm 3 type I CLBO crystal (CLBO2). The Type I SFG was achieved with both beams polarized horizontally and gave the output vertically polarized. Three cylindrical lenses (f C1 =130 mm, f C2 =100 mm, and f C3 =100 mm) were used in the fourth-harmonic branch to correct the beam shape which deformed due to walk-off effect. The beam pattern involved in the generation approximates round, which is typical configuration for nonlinear frequency generation. Fig Setup for 213 nm light generation. Ls stand for lenses; Cs stand for cylinder lenses. Orange line stand for 1064 nm light path that has a delay path of about 3.9 m arranged into it. L is used in delay path for collimating the beam to a radius under 500 μm in case it diverges. In this step, for the effect of OPO resonance, the 1064 nm pulse s shape got asymmetrically depleted in temporal range. The power from its latter part transferred to OPO and became oscillating power. As the result, the 1064 nm pulse could not cover the 266 nm pulse that the conversion efficiency dived. How to effectively utilize the undepleted leading edge of the 1064 nm pulse has 51

59 Relative light intensity Chapter nm VUV light generation by borate crystals become an issue for lifting the conversion efficiency in this generation. As measure with oscilloscope, the distance between the pulses of 1064 nm and fourth-harmonic is about 13 ns. According to the relation: l=c t (l stands for delay length, c stands for light speed of m/s, t stands for delay time), an optical delay path of 3.9 m was set in 1064 nm light to optimize the temporal overlap of the two pulses. As shown in Fig.3.9, the pulses of the two lights mostly coincide in temporal range when the delay line has been set. The dashed line outlines the original 1064 nm pulse, which implies the origin location of the two pulses before the OPO oscillation and the delay line. Fig.3.9. Adjustment for depleted 1064 nm pulse in temporal range for 5HG by CLBO. Blue line stands for asymmetrically depleted 1064 nm pulse; blue dashed line outlines the original pulse of 1064 nm before it pumps the PPLN OPO, they both depict the 1064 pulse after a 3.9 m delay line is set. Cyan line stands for 266 nm pulse. Obviously, the residual power of 1064 nm contributed for 213 nm light generation is affected by the conversion efficiency of the OPO. As IR power generated from OPO and the residual 1064 nm power left after OPO both share the 1064 nm pump power, how to make the balance of the two parts of power became another issue in the generation. It will be lack of power for either 213 nm or nm light if the balance is poor, that there will be not enough power in the final 189 nm light generation. 52

60 Relative light intensity Relative light intensity Relative light intensity Relative Intensity light intensity (a) (b) (c) (d) Fig Temporal profile of 1064 nm pulse changed in 213 nm light generation. Yellow profile stands for 1064 nm pulse; blue profile stands for 266 nm pulse. The power for 266 nm pulse was fixed at 520 mw; the power for 1064 nm pulse and generated 213 nm are (a) 860 mw, 45 mw; (b) 1020 mw, 62 mw; (c) 1440mW, 100mW; (d) 1800mW, 125mW. (The delay adjustment is not optimal condition in these pictures.) As seen from Fig.3.10, the temporal profile of the 1064 nm pulse increases as its power increased with the conversion efficiency of OPO reduced. The adjustment is achieved by tilting of the concave lens of the OPO to break its optimal oscillation condition during the 5HG. As known from Fig.3.10 (a), the 1064 nm pulse is got depleted in the center part that formed a dip. In order to make the best use of the 266 nm power, which is generated from fundamental laser source with a small total conversion efficiency, the temporal profile of the 1064 nm pulse should be enlarged by reduce the conversion efficiency of OPO, to a great extent to cover the 266 nm pulse (as shown in Fig.3.10(d)). 53

61 Chapter nm VUV light generation by borate crystals At last, the power of nm light is decided to be set at 240 mw, with about 1.6 W power left in residual 1064 nm. The 213 nm output reached, at most, 155 mw with 22.8% SFG efficiency, from input power of the fourth-harmonic light. Also in this generation, for achieving higher conversion efficiency in SFG, it is also need to consider the focusing condition of 266 nm and 1064 nm beams. Fig.3.11 compares two focusing conditions, one is to focus the two beam to the same radius; the other is to focus the 1064 nm beam to the same confocal parameter as 266 nm beam according to (3.2) [13]. The latter configuration is thought to give better performance as the wavefront of the two beams coincide. 2 2 n1w 1 n2w2 2 2 (3.2) 1 2 (a) (b) Fig Sketch for two kinds of focusing condition in SFG to 213 nm. (a) Two beams are focused to the same waist size; (b) 1064 nm beam is focused to the same confocal parameter as the 266 nm beam. I have tried the generation with several focusing conditions for the 1064 nm beam. The results of 213 nm output power shown in Fig.3.12 is measured as the input 266 nm fixed at 680 mw with radius of 44 μm. When the confocal parameter of the 1064 nm beam was set same to 266 nm beam at about 7 cm, the SFG showed the best performance. 54

62 Fig nm output with different focusing conditions for 1064 nm. 266 nm beam was focused at 44 μm in radius while 1064 nm beam was changing. Each group of data are acquired with 266 nm power fixed at 680 mw and the 1064 nm input power changed Summary for 189 nm light generation preparation A summary for the stages prepared for 189 nm light generation, which are adjusted to optimal condition is shown as Fig Fig Summary for 189 nm light generation system. For the DUV light generation, 2.35 W output for 532 nm light is generated 55

63 Chapter nm VUV light generation by borate crystals with conversion efficiency of 36.8% from fundamental laser power. 680 mw output for 266 nm light is generated with conversion efficiency of 28.9% from 532 nm power. At last, 213 nm light was generated by SFG of residual 1064 nm light and 266 nm light, with 22.8% conversion efficiency from 4HG and has an output power of 155 mw. IR light of 1698 nm is generated from OPO with 240 mw output by 9.5% from 1064 nm pump power nm light generation with borate crystals At the final stage, VUV light at around 190 nm was generated by SFG with the fifth-harmonic light and IR in the last borate crystal. Before the generation, a temporal distance between 213 nm pulse and IR pulse after they are generated is measured by oscilloscope with silicon detector. The measurement is similar to the last stage generation so the figure is omitted here. The quantity of temporal distance reads about 10 ns that corresponding to a distance of 3 m in light path. As the same arrangement in 213 nm light generation, a delay line was set in the path of IR. As shown in Fig.3.14, IR is focused by a lens with f L6 =200 mm after the delay line. Two cylinder lenses with f C4 =100 mm and f C5 =130 mm to used focus 213 nm beam which is deformed due to walk-off effect. Both of the beams have vertical polarization direction for the Type I phase-matching plane and the generated light polarized horizontally. After the SFG to 189 nm light generation borate crystal, a 60 dispersion prism was used to disperse VUV light from other lights. Fig Setup for 189 nm light generation. C4 and C5 stand for cylinder lens and L6 stands for lens used for focusing. The borate crystal is set on a rotating stage for angle tuning. Generated light is dispersed by a 60 dispersion prism after the crystal. 56

64 The prism used here is made of fused quartz which was chosen to prevent absorption of the VUV. The distance between the output face of the borate crystals and power meter was about 50 mm. Power loss of VUV included reflection at the surface of the crystals, and absorption in air was not taken into account. The generation was conducted in air ambient with no cell and no temperature tuning for the crystal sample. The oxygen in the air is thought to present an elevating absorption rate as VUV wavelength is below 190 nm. The setup used in the experiment is designed in the view of simplicity that no vacuum chamber or nitrogen gas flowing is allocated to keep oxygen away. During the generation, turn the rotating stage mounted crystal carefully and to observe the glass sheet placed beside. Fluorescence will be produced when illuminated by the VUV light to confirm the generation. The measure method for phase-matching angle of the crystal is shown in Fig First to measured the external angle and calculate the internal angles according to (3.3), where n DUV and n IR stand for refractive index in the crystal. The average of internal angle for DUV and IR light is termed as deviation angle (ϕ) that the phase-matching angle is set to be the sum of cut angle of crystal sample and deviation angle in this dissertation. Fig Measurement for calculating phase-matching angle inside the crystal. The DUV and IR light have the same external angle; internal angle of them is calculated with Snell s equation. 57

65 Chapter nm VUV light generation by borate crystals DUV DUV sin internal external arcsin, n DUV IR IR sin internal external arcsin, n IR DUV IR ( ) / 2. (3.3) external external nm light generation results and discussions In this section, the 189 nm VUV light generation results with borate crystal of CBO, LBO and CLBO that listed as candidates in Table 3.1 are shown. High efficiency generation is also challenged with these crystals Phase-matching angles for LBO and CLBO In the measurement for phase-matching angles, a CLBO crystal cut at θ=60.2 and φ=45 is used, which has a size of mm 3. For LBO crystal, two samples with size of mm 3 cut at θ=70, 80 and φ=90 and two samples with size of mm 3 cut at θ=65, 75 and φ=90 are prepared. LBOs used in the experiment are purchased, while the CLBOs used are grown in Mori laboratory from Osaka University. Each sample used is polished and not coated. The 189 nm light generation is realized with both LBO and CLBO that is justified with fluorescence which is marked with red circle in Fig The generation results with each LBO sample and CLBO are concluded in Table 3.2. Fig.3.17 shows the experimental results that indicating the relationship of the phase-matching angles for LBO and CLBO and the wavelengths generated with this system. Phase-matching angles are measured by changing the wavelength of IR while 213 nm is fixed. The measured phase-matching angles of nm by SFG with nm and nm were φ=72.7 for LBO and θ=60.2 for CLBO. It is found that the measured Type I phase-matching angles of θ for CLBO are in good agreement with the theoretical curve. On the other hand, the 58

66 measured φs for LBO in the x-y plane are slightly larger than the theoretical curve and the difference is growing greater towards shorter wavelength side. This can be explained as the phase-matching angles in the process of approaching 90, deviation between larger wavelength occurred in Sellmeier formula and is getting larger and larger that resulted in such difference. 189 nm 213 nm Fig nm VUV light generation by CLBO judged with fluorescence. The picture captures the beam spots on glass sheet after the 189 nm, 213 nm, 1698 nm, and other residual light are dispersed by the prism. 189 nm spot is the on the first place of the left side marked with red circle. The brightest one in the picture is the spot of 213 nm light. Wavelength (nm) IR Table 3.2. Phase-matching measurement with LBO and CLBO. VUV Phase-matching angle of LBO (deg.) Calculated Measured Phase-matching angle of CLBO (deg.) Calculated a a a, b b b, c c, d d Measured LBO samples: a: φ=65, b: φ=70, c: φ=75, d: φ=80 and θ=90. 59

67 Chapter nm VUV light generation by borate crystals Fig Phase-matching angles for LBO and CLBO at around 190 nm. Red line stands for calculated curve for phase-matching angles of CLBO with Sellmeier formula from Ref. 8; red dots stand for measured phase-matching angles of CLBO. Green line stands for calculated curve for phase-matching angles of LBO with Sellmeier formula from Ref. 6; green dots stand for measured phase-matching angles of LBO. The wavelength of VUV is calculated with wavelength of IR which is measured by optical spectrum analyzer Phase-matching angles for CBO Two samples with size of mm 3 cut at φ=70, 77.5 and θ=90 for CBO are used in the measurement. The CBO is grown from a self-flux solution with a composition of 74 mol% B 2 O 3 [17]. Fig.3.18 shows the measured phase-matching angles with CBO at around 190 nm SFG. It was predicted to obtain the highest output power among candidate crystals according to effective nonlinear coefficient as the calculated result is shown in Table 3.1. However, while phase-matchings are realized at about 190 nm range, there is no SFG obtained at 189 nm. The measured phase-matching angles are quite different from the theoretical curve calculated with the reference [7]. 60

68 Table 3.3 CBO samples used in measurement for phase-matching angles. Wavelength (nm) Phase-matching angle (deg.) IR VUV Calculated Measured a b b LBO samples: a: φ=70, b: φ=77.5, and θ=90. [7] [15] Fig Phase-matching angles for CBO at around 190 nm. Red dashed line stands for theory value calculated with Sellmeier formula from Ref. 7; purple line stands for theory value calculated base on Ref. 15. Blue dots stands for measured values. The wavelength of VUV is calculated with wavelength of IR which is measured by optical spectrum analyzer. However, such result is found to comply with the discovery made by Kagebayashi [14] that there are difference between the calculated values and theoretical curve about phase-matching angles of CBO in VUV light generation at 193 nm by the SFG with DUV and IR. It seems that Sellmeier formula of CBO [7] have a deviation in UV range concluded from these results. On the other hand, in Fig.3.18, there is another calculated curve of CBO closed to the experimental results of the SFG with 213 nm and 1698 nm light. 61

69 Chapter nm VUV light generation by borate crystals In this measurement, each sample used is polished and not coated. The results of measurement with each sample are concluded in Table 3.3 where the calculated phase-matching angle is based on equations (3.4). It is calculated from Sellmeier formula developed by H. Shimatani from Mori laboratory, Osaka University [15]. The equations are given as n x , n y , (3.4) 2 n 2 x , where λ is in micrometers. Otherwise, phase-matching angles calculated from the two sets of Sellmeier formula are found almost identical in the visible range and begin to separate in the near-uv range. It could be confirmed that the latter Sellmeier formula used have better accuracy in depicting the CBO crystals grown Mori laboratory, Osaka University. It can be assumed that the differences in phase-matching angle caused by the refractive index change of the crystal resulted from different growth conditions. The CBO utilized in previous researches was grown from stoichiometric melt [16]; in recent researches, CBO used is grown from a self-flux solution, because it is a better way to obtain large-sized and inclusion-free crystals [17] nm light generation with CLBO and LBO The generation of 189 nm light is shown as in Fig In this generation, a minimum beam waist of w=32 μm is set for 213 nm, which located in the center of the crystal. At the same time, the IR of nm is collinearly focusing into the crystal to the beam waist of w=105 μm, approximately corresponding to the same confocal parameter of about 70 mm as the DUV light. During the generation, the IR power was maintained at 220 mw while the input of the

70 nm changed from 0 to 155 mw. Fig Parameters for 189 nm SFG. As a result of the generation, a notable output of VUV was achieved by a CLBO with size of mm 3. Fig.3.20 shows the output power as a function of the input fifth-harmonic power. The 189 nm light output power increased monotonically as the input power increased. A maximum output power of 11.4 mw was achieved at an input power of 155 mw. The corresponding SFG efficiency was 7.3% from the fifth-harmonic power, and the generation efficiency from the source laser was 0.16%. Near the maximum input power, saturation behavior was observed. This could be caused by water impurity in CLBO [11] for the generation was in air ambient and a promotion is expected with a dehydration process before and during the generation. On the other hand, under the same generation condition with CLBO as shown in Fig.3.19, LBO showed output of less than 1 mw even by using the longest sample with a length of 20 mm. The great difference of the two crystals could be explained according the information given by Table 3.1 and Fig The calculated value for effective nonlinear coefficient of LBO is about 44% of CLBO. According to equation (2.29), the output of SFG is directly proportional to the effective nonlinear coefficient. Furthermore, as the measured phase-matching angles for LBO are larger than the calculated values, its effective nonlinear coefficient will get further smaller. Therefore, it is estimated that the output of LBO is about 15% of CLBO, which has a good accordance with the 63

71 Chapter nm VUV light generation by borate crystals experimental result. Fig nm output generated by CLBO. 3-4 Perspective From the phase-matching property of CLBO shown in Fig.3.21, as the SFG achieved shorter wavelength to about nm, the effective nonlinear coefficient increases to the maximum value d 36 as the phase-matching angle rises toward θ=90 as given in equation (2.69). Consider the actual phase-matching angles approach 90 faster than calculated values and UV absorption edge of the crystal becomes larger and larger under 190 nm, it is expected the generation range could possibly reach 185 nm with high conversion efficiency. To achieve VUV light generation with shorter wavelength, the output of OPO should be tuned to about 1400 nm which is the shortest edge for the signal that can be generated by MgO:PPLN as the specification. Furthermore, the according idler wavelength which should be reflected during the OPO oscillation has beyond the reflection range of mirrors coated with normal material. My experiments with customized mirrors have failed to produce the short wavelength IR and the reason is not well understood. 64

72 Fig Perspective for VUV light generation with CLBO. The generation is expected to be extended to the range in the blue round. Therefore, new scheme for achieving 185 nm VUV light generation with other types of OPO is considered. A reasonable alternative is to use KTP OPO which can produce shorter wavelength IR than PPLN with phase-matching in xz plane. With the method, pump light is changed to 532 nm light, and the scheme for the generation is shown as Fig However, because the OPO and fourth harmonic generation stage share the power of 532 nm light, such scheme will need large conversion efficiency in the first SHG stage. Fig Scheme for VUV light generation based on KTP OPO. 65

73 Chapter nm VUV light generation by borate crystals 3-4 Summary A high-repetition-rate, all-solid-state laser system for 189 nm VUV light generation is built based on a 1064 nm Nd:YAG laser. The generation is realized by SFG with 213 nm light (5HG) and IR in a borate crystal. In the system, 266 nm and 213 nm UV light generation is produced by CLBO crystals while IR light is produced by PPLN OPO. As the result, with this laser system, 189 nm VUV was demonstrated by LBO and CLBO successfully. The phase-matching property for LBO and CLBO around 190 nm was found have good accordance with the theory value. On the other hand, the VUV light generation with CBO was not realized until the generated wavelength extended to 190 nm, which is inconsistent with the theory prediction. The new phase-matching property for CBO around 190 nm was found to have better agreement with new Sellmeier formula. It could be explained by the different growth method of the CBO crystals. An output of 11.4 mw at 189 nm was generated with CLBO of 15 mm length. CLBO is considered suitable for VUV light generation until 185 nm given its phase-matching property and short absorption range. With high power laser source, a practical level output of 189 nm light could be expected with the scheme. 66

74 References in Chapter 3: [1] J. Sakuma, K. Moriizumi, and H. Kusunose, Opt. Express 19, (2011). [2] K. Deki, J. Sakuma, Y. Ohsako, N. Kitatochi, T. Yokota, M. Horiguchi, Y. Mori, and T. Sasaki, Proc. Conference on Lasers and Electro-Optics, CPD4 (1998). [3] Y. Urata, T. Shinozaki, Y. Wada, Y. Kaneda, S. Wada, and S. Imai, Appl. Opt. 48, 1668 (2009). [4] H. Masuda, K. Kimura, N. Eguchi, and S. Kubota, Advanced Solid-State Lasers, OSA TOPS 50, 490 (2001). [5] H. Kouta and Y. Kuwano, Opt. Lett. 24, 1230 (1999). [6] K. Kato, IEEE J. Quantum Electron. 26, 1173 (1990). [7] K. Kato, IEEE J. Quantum Electron. 31, 169 (1995). [8] N. Umemura, K. Yoshida, T. Kamimura, Y. Mori, T. Sasaki, and K. Kato, Advanced Solid-State Lasers, OSA TOPS 26, 715 (1999). [9] J. J. Jacob and A. J. Merriam, Proc. SPIE 5567, 1099 (2004). [10] L. E. Mayers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, J. Opt. Soc. Am. B 12, 2102 (1995). [11] T. Kawamura, M. Yoshimura, Y. Honda, M. Nishioka, Y. Shimizu, Y. Kitaoka, Y. Mori, and T. Sasaki, Appl. Opt. 48, 1658 (2009). [12] K. Takachiho, M. Yoshimura, Y. Takahashi, M, Imade, T, Sasaki, and Y. Mori, Opt. Mater. Express 4, 559 (2014). [13] G. D. Boyd and and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968). [14] Y. Kagebayashi, K. Deki, Y. Morimoto, S. Miyazawa and T. Sasaki, Jpn. J. Appl. Phys. 39, 1224 (2000). [15] H. Shimatani, Master s Thesis, Graduate School of Engineering, Osaka University, Osaka (2009) [in Japanese]. [16] T. Saji, N. Hisaminato, M. Nishioka, M. Yoshimura, Y. Mori, and T. Sasaki, J. Cryst. Growth 274, 183 (2005). [17] Y. C. Wu, T. Sasaki, S. Nakai, A. Yokotani, H. G. Tang, and C. T. Chen, Appl. Phys. Lett. 21, 2614 (1993). 67

75 Chapter nm VUV light generation by borate crystals 68

76 Chapter nm VUV light generation with borate crystals 4-1 Introduction In order to develop the next generation inspection laser source with solid-state system, it is focused on the generation of VUV light in 170 nm-180 nm range. In this section, examples for the VUV light generation are to be introduced and difficulties in generation of the range are to be discussed. As our plan for generating VUV light at 179 nm, a new system based on two OPOs is designed Introduction for VUV light generation in 170 nm-180 nm range There are lots of difficulties in sub-180 nm VUV light generation with nonlinear frequency conversion. One of the biggest of them is lacks of NLO crystals which have enough birefringence and transparency in the range. KBe 2 BO 3 F 2 (KBBF) and RbBe 2 (BO 3 )F 2 (RBBF) crystals which have extensive transmission range and large birefringence are considered suitable NLO medium for the generation. The nm light generation by direct SHG from the third harmonic light of 1064 nm at nm has been demonstrated with these crystals [1, 2]. Because KBBF belongs to (BO 3 ) 3- anionic group, it tends to be grown in a layer structure that cannot be cut with the phase-matching angle. The VUV generation by KBBF is now realized using an optical contacted prism coupled device (PCD), showing potential for future use [3]. Besides, as reported several years ago, a UV generation until nm light has been realized based on a 200-fs system pumped by Ti:sapphire amplifier [4]. It is generated with SFG using fourth harmonic generation and parametrically generated IR by LBO. However, the phase-matching is made based on femtosecond system that is not as practical as nanosecond laser source. There has been no other report in this range so far to my knowledge. Therefore, in order to make VUV light generation in the range of 170 nm-180 nm, proper NLO crystal and original system design are of the same importance. 69

77 Chapter nm VUV light generation by borate crystals As commercially used nonlinear optical crystals, CLBO and BBO do not have enough transparency under 180 nm for UV generations. LBO and CBO are featured with absorption edges below 170 nm, however, their birefringence do not allow simple generation like KBBF to get direct SHG from nm [5, 6] Scheme for 179 nm light generation As an alternative method to approach the wavelength wanted, another group of SFG with DUV and IR light making the generation to 179 nm (198.8 nm nm ~179 nm) is found [7, 8]. CBO and LBO are considered fit for the generation. The design of the new scheme for 179 nm light generation is as shown in Fig.4.1. It uses a 198 nm DUV light [9] that coincide with the inspection laser source in practical service. The merit of the design is that utilization of OPO makes DUV wavelength adjustable to accommodate the phase-matching properties of the crystals in the last stage. By tuning the output wavelength of KTP OPO, the generated DUV ranges from nm to nm. Fig.4.1. Scheme for 179 nm VUV light generation with LBO. The generation is realized from SFG of nm DUV and 1797 nm IR light based on two OPOs. In the final SFG process of the generation, LBO and CBO showed phase-matching possibility and CBO seems to give larger output as effective 70

78 nonlinear coefficient shown in Table 4.1. In this research, the VUV generation at 179 nm is tried to unveil the phase-matching property of the two borate crystals in the range. Candidate crystal Table 4.1. Property of borate crystals for the generation. Transmission range (nm) yz plane *Phase-matching angles for SFG at 179 nm were calculated with the interaction of nm and nm light. 4-2 Experimental setup for 179 nm light generation This section will introduce the stages in the system for the 179 nm light generation, including SHG part, KTP OPO and intracavity LBO SHG part, PPLN OPO part, and 198 nm SFG part. At last, there will be a brief summary of the generation results of all the stages. Phase-matching angle (300K) LBO 160~2600 φ=74.1, Type I, xy plane CBO 167~3400 θ=50.1, Type I, Setup for DUV and IR light generation Effective nonlinear coefficient d eff (pm/v) Ref. As shown in Fig.4.2, a commercial Q-switched neodymium doped yttrium orthovanadate (Nd:YVO 4 ) 1064 nm laser (HIPPO H10-106QW, Spectra Physics) is employed as the fundamental laser source. It delivers linear polarized beam with M 2 <1.2, up to 11.5 W output at repetition rate of 15 khz with a pulse width of 8 ns. The system is composed of 7 stages of nonlinear wavelength conversion, divided in tunable DUV light generation part, tunable IR light generation part and the final VUV light generation part. The IR light is realized with a PPLN OPO. The DUV part is based on a compact implementation of the KTiOPO 4 (KTP) OPO with intra-cavity LBO SHG [10]. As a popular material in UV light generation, CLBO crystal is used to generate 244 nm by SHG and 199 nm by 71

79 Chapter nm VUV light generation by borate crystals SFG that also plays important role in the generation. There are delay lines set in light path of 1064 nm and IR for temporal adjustment. Fig.4.2. Experimental setup for 179 nm light generation. Ls stand for spherical lenses; Ms stand for mirrors in KTP OPO and intracavity LBO SHG setup; CMs stand for mirrors in PPLN OPO; and Cs stand for cylindrical lenses. There are delay lines set in light paths of 1064 nm and IR SHG with improved conversion efficiency In the first step, the SHG of 1064 nm was performed by a type I noncritical phase-matching (NCPM) LBO with AR coating for 1064 and 532 nm. The LBO is housed in oven, kept at 151 C with a stability of ±0.1 C, to satisfy the non-critical phase-matching along x axis. At first, a LBO with size of mm 3 was used for the SHG in this system. After that, the ratio between SHG power and residual 1064 nm power is set about 2:1. Consider about the whole system, the SHG power will then be generated to DUV light while the residual 1064 nm power will be generated to IR light. For there are two more steps of nonlinear frequency conversion in the SHG branch, and each step has about 40% conversion efficiency, it will lead to too small DUV power compared with IR power for the last step SFG. 72

80 The direct method to improve the balance of the power of DUV and IR to lift the efficient of the system is to increase the conversion efficiency of the SHG process. As the SHG output given by equation (2.29), a simple method is to use a longer crystal to realize the goal, because the conversion efficiency is proportional to crystal length s square, compared with focusing the fundamental beam to a thinner radius that may cause damage in the crystal. The theory for determining the focusing condition is given by Boyd and Kleinman [11]. For there is no walk-off in this NCPM SHG, the optimal confocal parameter (2nπw 2 0 /λ) of the beam has a simple relation with the length of the crystal. LBO 25 mm LBO 10 mm Fig.4.3. Compared the conversion efficiency of two SHG LBOs with different optimal focusing conditions using the same Nd:YVO 4 laser source. LBO with length of 25 mm is used with 1064 nm focused to radius of 85 μm while for 10 mm-length LBO is 54 μm. In the experiment, the length of LBO is changed from 10 mm to 25 mm as long as it can be covered with the oven. The corresponding proper waist radius of 1064 nm has changed from 54 μm to 85 μm. The SHG was generated with a maximum conversion efficiency of 62.5% as shown in Fig.4.3 compared with 10 mm-long LBO. The improvement was not as large as the square of the crystal length s ratio may be resulted from the loss occurred as the laser propagates 73

81 Chapter nm VUV light generation by borate crystals through the crystal. It is noted that all the data presented in this experiment are not corrected for the absorption losses of the crystals and the reflection losses at the crystal surfaces KTP OPO and intra-cavity SHG After that, a singly-resonant OPO and intra-cavity SHG to access 489 nm with 532 nm pulse is constructed as shown in Fig.4.4. The resonator is a L-shaped standing wave cavity formed by three mirrors, contains a mm 3 KTP serving as OPO material, as well as a mm 3 LBO for intra-cavity SHG of OPO signal. The physical length of the cavity is about 30 mm that slightly exceeds the sum length of the two crystals. The Type II KTP was cut at θ=90 and φ=59 with AR coat at 978 nm. While the Type I LBO was cut at θ=90 and φ=17.6 with 978/489 AR coating. The waist of the pump light of 145 μm, is positioned on the surface of M nm pulse Depleted pump pulse Pump pulse (a) (b) Fig.4.4. Details for KTP OPO and intra-cavity SHG LBO. (a) shows the setup for the cavity which is formed by concave mirror M1; two dichroic mirrors M2 and M3; reflection mirror M4. (b) shows pulses involved in the generation observed with oscilloscope. Cyan curve stands for pump pulse; pink curve stands for depleted pump pulse; blue curve stands for generated 489 nm pulse. 74

82 The OPO is built on the wavelength relation: 532 nm (pump) 978 nm (signal) nm (idler). The process for the generation is like: 532 nm pump pulse passes through curved end mirror M1 (radius of curvature of 500mm); the signal light at 978 nm of OPO is reflected by dichroic flat folding mirror M2; the signal and its SHG are retroreflected by end flat mirror M3. As seen from Fig.4.4, depleted pump pulse still has considerable power left after the oscillation of the OPO. For utilizing the residual power of the pump pulses passed through M2, a double-pass pumping retroreflected structure is set with M5, making it pump the OPO for another time. Also there is distance observed between 489 nm pulse and depleted pump pulse which means the buildup time of OPO. To make the pulses coincide, an optical delay about 400 mm that is of the order of the buildup time of the OPO was set [11]. A lens with f=400 mm is used in delay line for collimating the depleted beam to make sure it can return with origin beam shape. The difference of 489 nm output between single pass and double pass with delay configuration is show in Fig.4.5. The oscillation threshold decreased and the output increased after the improvement. As the result, generation efficiency of the 489 nm from the 532 nm pump power of 6 W reached 9.3%. Double pass Single pass Fig.4.5. Compare the output generated with single pass configuration and double pass with delay line configuration. Black squares stand for double pump; red circles stand for double pump with delay line. 75

83 Chapter nm VUV light generation by borate crystals The whole conversion process is in the air condition at room temperature, which brings a problem that the generation becoming unstable. It is mainly because of the poor temperature tolerance, which means birefringence of LBO is easily changed by thermal effect. As LBO heated with beams, the oscillation mode of the cavity changed and output power dived. TEM 00 mode turning into TEM 10 or TEM 20 mode can also be observed from 489 nm beam pattern. For the resonate cavity built has limited space for cover an oven to keep the crystal constant temperature, the adjustment of the system should be done with low power to keep stable of generation made by the LBO. Then, nm was generated as the SHG of 489 nm via a mm 3 type I CLBO (CLBO1) cut at θ=78.1. In order to correct the walk-off in 489 nm light, a pair of cylinder lens was employed to focus it to a 38 μm radius circular waist in the CLBO crystal nm was generated with a maximum conversion efficiency of 35.7% PPLN OPO for IR light generation To generate tunable IR light at around 1800 nm, a PPLN OPO pumped by residual 1064 nm light was employed. The 20-mm-long PPLN with a multi-grating section is set in a 40-mm-long linear resonance cavity. The PPLN used here is same to the Chapter 3 as OPO1-20 that produced by Covesion Ltd. The cavity is formed by two concave mirrors (M1 and M2 with radius of curvature of 100 mm) with high-reflection coating for the wavelength from 2300 to 2800 nm, roughly corresponding to the idler branch of the singly resonant OPO. Consequently, the signal wavelength of the OPO spreads from 1770 to 1970 nm. The wavelength is tuned by the grating period of PPLN and its temperature, exhibits broad free-running optical bandwidth of about 3.5 nm without injection seeding. The grating period is chosen to be 29.5 μm and certain temperature is set for generating the IR wavelength from 1797 nm to 1903 nm corresponding to VUV light generation from 179 nm to 180 nm. With the 1064 nm input focused to 160 μm radius, PPLN OPO gave the maximum conversion efficiency of 23.7% 76

84 with 2.9 W input as shown in Fig.4.6. After conversion efficiency of SHG raised and for adjustment of balance between IR light and residual 1064 nm light after the OPO, the output power of nm is set at 350 mw with a conversion efficiency of 16.5% output Conversion efficiency Fig.4.6. IR output property of OPO in 179 nm light generation system. Black points stand for output power; Red points stand for conversion efficiency. In the experiment, compared with the PPLN OPO built in 189 nm light generation system, this OPO seems more easily to start oscillation. There are two reasons concluded: One is the laser source used in 179 nm has a shorter pulse-width that can produce larger peak power to promote the oscillation; the other is the oscillating idler wavelength here is about 2600 nm that has the best reflection property of the AR coat of the concave mirror building the OPO, so the oscillation in this case is promoted nm DUV light generation Then, DUV light generation of nm was obtained by SFG with the nm light and depleted pump light at 1064 nm after the OPO in a mm 3 type I CLBO (CLBO2) cut at θ=78.1. The nm was focused by a cylindrical lens pair to a waist with radius of 36 μm and collinearly combined 77

85 Relative light intensity Relative light Intensity intensity Chapter nm VUV light generation by borate crystals with 136 μm radius waist 1064 nm beam. Such sizes make two beams the same confocal parameters of about 60 mm, which leads to optimal nonlinear conversion efficiency. In this stage, from the effect of parametric oscillation, the 1064 nm temporal pulse shape was asymmetrically depleted, so it looks like faster than the nm pulse as shown in Fig.4.7. To effectively utilize the undepleted leading edge of 1064 nm pulse, an optical delay path of 1.9 m was set to optimizing the temporal overlap with nm pulse. With the output properties shown in Fig.4.7, SFG efficiency for the DUV light generation was, at most, 25.3% from input power of the nm. 6 ns (a) (b) Fig.4.7 Adjustment of nm and 1064 nm pulses in temporal range observed by oscilloscope. Red line stands for nm pulse; blue line stands for 1064 nm pulse. (a) The two pulses do not coincide; (b) The two pulses got coincide after the delay line set nm output Conversion efficiency Fig nm DUV light generated with SFG by CLBO. Purple spots stand for output, black spots stand for conversion efficiency. 78

86 CLBO crystals used in this system were grown in our laboratory by solution stirring top-seeded solution growth [12]. They are polished on two sides without coating. While with excellent optical properties and crystal quality, they suffered from hygroscopic issues that hinder long-term operation potential. In our experiment, operating at 150 C with argon gas flow is used as a solution to reduce water impurity inside the crystal [13] Summary for 179 nm VUV light generation system A summary for the system is shown as Fig.4.9. All of the stages were adjusted to optimal condition for the final 179 nm light generation. 6 W output of 532 nm light with was generated with conversion efficiency of 62.5% from fundamental laser power. 560 mw output of 489 nm light was generated with KTP OPO and intra-cavity LBO SHG with total conversion efficiency of 11.2% from 532 nm pump nm light with output of 200mW was generated from 489 nm by 35.7%. IR of 1797 nm was generated from OPO with 350 mw output by 16.5% from 1064 nm pump power. 198 nm DUV light was generated by SFG of residual 1064 nm light and nm light, with 30% conversion efficiency from nm and has an output power of 60 mw. Fig.4.9. Summary for 179 nm light generation system. 79

87 Chapter nm VUV light generation by borate crystals SFG for 179 nm VUV light generation In the final stage of conversion, a minimum beam waist of w=29 μm is set for nm DUV, while collinearly focused IR is set with a beam waist of w=114 μm, approximately corresponding to the same confocal parameter of the DUV light of about 60 mm. The input power of DUV was kept at 60 mw and IR at 350 mw. VUV light at around 179 nm was generated by SFG with the DUV light and IR in the last borate crystal. There was also an optical delay path of 2.2 m set to synchronize the arrival time of both pulses. A 60 dispersion prism made from fused quartz was used to disperse VUV light from the DUV light after the SFG. The distance between the output face of the final borate crystals and power meter was about 8 cm. As absorption of 179 nm in air was not predicted large in such short distance, the final generation was kept in air ambient at room temperature for the scheme investigation. For the VUV light generation, two mm 3 samples cut at φ=80, 85 and θ=90 and three mm 3 samples cut at φ=65, 70, 75 and θ=90 for LBO, two mm 3 samples cut at θ=70, 77.5 and φ=90 for CBO are prepared. The CBO sample was grown from a self-flux solution with a composition of 74 mol% B 2 O 3 [14], while the LBO sample was purchased commercially. All of the samples are polished on both sides without coating. As the theoretical phase-matching angles listed in Table 4.1, CBO seemed to be a promising choice for the generation with a larger effective nonlinear coefficient [8] nm light generation result As the result of our experiment, as a candidate crystal, CBO did not satisfy phase-matching for the final SFG at 179 nm, despite the theoretical calculation [8]. Furthermore, there was no SFG obtained at around 180 nm with the sample that is against the calculation based on another reference [15]. In Chapter 3, the measurement in 190 nm range light generation with CBO has a deviation from calculated value, which is still an evidence for a published Sellmeier formula [15]. In this generation, as the wavelength became shorter, the birefringence 80

88 property is considered changed even larger that make the deviation become too large to predict phase-matching. In the case of LBO, 179 nm light is confirmed by fluorescence as shown in Fig The output was estimated to be less than 0.1 mw which could not be measured by our detector in air ambient. The main reason attributed for the low output power is the small effective nonlinear coefficient in the generation, which is the same as the case in 189 nm light generation with LBO. The absorption of oxygen and other optical units is also considered to have impact for such result. In further research, to generate detectable output power in VUV, chamber could be employed to contain the final stage and make an environment of vacuum or Nitrogen gas. Also optical units without much loss in VUV range should be choose more carefully. 179 nm nm Fig nm light generation observed with fluorescence on glass sheet. 179 nm spot is in the dashed circle on the left while nm spot is bright and on the right. As shown in Fig.4.11, phase-matching angles of φ for LBO around 180 nm were taken while tuning IR wavelength with DUV fixed at nm. The observed slope is roughly the same as that of the calculated curve. The data for measurement is also concluded in Table 4.2. However, the observed values in phi are approximately 5 more than those of the calculated curve. As wavelength of IR used in SFG and generated VUV are at edge of the transmission curve of the crystal, it is suspected that there is also a deviation occurred in birefringence 81

89 Chapter nm VUV light generation by borate crystals property of LBO. Therefore such deviation in the experiment is still reasonable. Table 4.2 LBO samples used in measurement for phase-matching angles. Wavelength (nm) Phase-matching angle (deg.) IR VUV Calculated Measured a a a a, b a, b b b, c b, c c c, d 80.1 LBO samples: a: φ=65, b: φ=70, c: φ=75, d: φ=80 and θ=90. Fig Phase-matching property of LBO measured at around 180 nm. The measurement was taken with scanning of IR with DUV fixed at nm. 82

90 4-4 Summary I built a high-repetition-rate, all-solid-state laser system for 179 nm VUV light generation based on a 1064 nm Nd:YVO 4 laser. The generation is realized from SFG with nm DUV and 1797 nm IR light in a borate crystal. In the system, nm DUV light generation is based on a KTP OPO and intracavity SHG with LBO. As the result, 179 nm VUV light is demonstrated by LBO successfully. The output is hardly be detected except observation with a fluorescence. Phase-matching properties for LBO around 180 nm were investigated with the system. The weak output can be explained with small nonlinear coefficient of LBO in the generation. By using CBO, generation at 179 nm and 180 nm is not achieved with the system, which is not accordance to the theory prediction. It could be attribute to the birefringence of CBO has changed so much in VUV range that the deviation is not predictable. 83

91 Chapter nm VUV light generation by borate crystals References in Chapter 4: [1] C. Chen, G. Wang, X. Wang, and Z. Xu,, Appl. Phys. B 97, 9 (2009). [2] C. Chen, S. Luo, X. Wang, G. Wang, X. Wen, H. Wu, X. Zhang, and Z. Xu, J. Opt. Soc. Am. B 26, 1519 (2009). [3] C. Chen, J. Lu, T. Togashi, T. Suganuma, T. Sekikawa, S. Watanabe, Z. Xu, and J. Wang, Opt. Lett. 27, 637 (2002). [4] F. Seifert, J. Ringling, F. Noack, V. Petrov, and O. Kittelmann, Opt. Lett. 19, 1538 (1994). [5] C. Chen, Y. Wu, A. Jiang, B. Wu, G. You, R. Li, and S. Lin, J. Opt. Soc. Am. B 6, 616 (1989). [6] Y. Wu, T. Sasaki, S. Nakai, A. Yokotani, H. Tang, and C. Chen, Appl. Phys. Lett. 62, 2614 (1993). [7] K. Kato, IEEE J. Quantum Electron. 26, 1173 (1990). [8] K. Kato, IEEE J. Quantum Electron. 31, 169 (1995). [9] Y. Kaneda, N. Peyghambarian, K. Miyazono, H. Shimatani, Y. Honda, M. Yoshimura, Y. Mori, Y. Kitaoka, and T. Sasaki, Proc. Conference on Lasers and Electro-Optics, CThW4 (2008). [10] Y. Kaneda, N. Peyghambarian, K. Miyazono, H. Shimatani, Y. Honda, M. Yoshimura, Y. Mori, Y. Kitaoka, and T. Sasaki, Opt. Lett. 33, 231 (2008). [11] G. D. Boyd and D.A. Kleinman, J. Appl. Phys. 39, 3597 (1968). [12] T. Sasaki, Y. Mori, and M. Yoshimura, Optical Materials 23, 343 (2003). [13] T. Kawamura, M. Yoshimura, Y. Honda, M. Nishioka, Y. Shimizu, Y. Kitaoka, Y. Mori, and T. Sasaki, Appl. Opt. 48, 1658 (2009). [14] Z. Wang, D. Rajesh, M. Yoshimura, H. Shimatani, Y Kitaoka, Y. Mori, T. Sasaki, J. Cryst. Growth 318, 625 (2011). [15] H. Shimatani, Master s Thesis, Graduate School of Engineering, Osaka University, Osaka (2009) [in Japanese]. 84

92 Chapter 5. Research about 355 nm UV light generation with CLBO 5-1 All-solid-state 355 nm laser In this section, 355 nm UV (as the third-harmonic generation, THG) light realized SFG of 1064 nm and 532 nm light by different kinds of borate crystals is introduced. Although considered as a useful tool in UV light generation, CLBO has not been used in 355 nm light generation so far. I try to explain the merit of the utilization of CLBO in the generation nm UV light generation with borate crystals As 355 nm UV is achieved through sum-frequency generation (SFG) with 1064 nm and 532 nm light, the material used as the nonlinear frequency conversion media is of significant importance. As one type of nonlinear optical (NLO) crystal suitable in this field, borate crystals are featured with relatively large nonlinear coefficients, short absorption edges, and high laser-induced damage thresholds [1, 2]. With borate crystals LBO, BBO, and CBO, highly efficient 355 nm light generation has been discussed in a number of previous reports. In the example for CBO, Kitano et al. showed 3 W output with a large total conversion efficiency of 30% [3]. 355 nm light generation by BBO was also verified in ps system many years ago [4]. LBO is most commonly used for the application for its high quality and small walk-off angle in the generation [5, 6]. It has been reported employed in commercial lasers [7]. In these generations, Type II phase-matching is used for the simplicity in the setup of laser system CLBO s outlook for 355 nm UV light generation Since developed in the 1990s, CLBO has drawn significant attention due to its potential uses in high average power harmonic generation, particularly in UV 85

93 Chapter 5. Research about 355 nm UV light generation by CLBO range [8-12]. Kojima et al. showed a 20 W 266 nm light generation by CLBO [8]. After that, 42 W output of 266 nm UV by CLBO was reported by Nishioka et al. [9]. Katsura et al. reported 10.2 W output of 213 nm UV achieved with SFG by CLBO [10]. Sakuma et al. has implemented research about 266 nm and 213 nm CW laser generations, they used Brewster-cut CLBO with external resonant cavity for promoting generation efficiency [11, 12]. Furthermore, in longer wavelength range, there is also a report about a 12.5 J second-harmonic generation by Type II CLBO based on a diode-pumped Nd:glass laser [13]. Table 5.1 compares the THG properties of LBO and CLBO in Type I and Type II phase-matching. Phase-matching angles are calculated by SNLO [14] based on Ref. 15 (LBO), 16 (CLBO), while effective nonlinear coefficients are calculated based on Ref. 17 (LBO), 18 (CLBO). As can be seen in this table, CLBO appears to be a promising THG media because of its superiority to LBO in terms of effective nonlinear coefficient in Type II phase-matching. Table 5.1. THG Phase-matching properties for LBO and CLBO. PM angle 423 K Effective nonlinear Temperature range (K cm) Walk-off (mrad) (θ, φ) (deg.) coefficient d eff (pm/v) LBO Type I (ooe) (90, 36.1) Type II (oeo) (49.7, 90) CLBO Type I (ooe) (39.0, 0) Type II (eoe) (48.8, 45) (ω), 36.8(3ω) Phase-matching angles are calculated by SNLO based on data come from Ref. 15 (LBO), 16 (CLBO). Effective nonlinear coefficients are calculated based on data come from Ref. 17 (LBO), 18 (CLBO). According to equation (2.29), as the output intensity is in direct proportion to 86

94 the square of effective nonlinear coefficient, larger conversion efficiency could be expected with CLBO. Also, it has a larger temperature range, which means the generation will not be affected by non-uniform temperature distribution significantly during the generation. However, 355 nm light generation by CLBO has not been previously demonstrated due to its large walk-off angle (in both Type I and Type II phase-matching) and its result of a separation between the interaction beams. If compensation for this walk-off issue were to be achieved, a substantial increase of the output power could be expected. There have been many previous reports exploring ways to circumvent the conversion efficiency limitation that results from walk-off in Type II phase-matching [19, 20]. One conventional scheme involves using a twin-crystal configuration, where two identically cut crystals are mounted with their optical axes symmetrically crossed [19]. Here, partial walk-off compensation is used to enhance output by increasing the effective interaction length in comparison to that of a single crystal. For example, Zondy et al. presented a report on second harmonic generation (SHG) of 1.3 μm and 2.53 μm light by twin-ktp at, in which a single-pass increase of times the amount of single-crystal output was achieved [19]. This method can be utilized in both Type I and Type II phase-matching. Another effort aimed at Type II phase-matching walk-off compensation involves the use of a non-collinear phase-matching configuration [21-23]. A wedged cut structure is considered an especially effective solution for achieving this walk-off compensation method [23]. It makes oblique incident beams on wedged cut surface refract to meet the non-collinear phase-matching condition. Asaumi geometrically analyzed compensated walk-off in Type II SHG of 1064 nm by KTP and LBO, and demonstrated significant power enhancement [21]. Furthermore, Yan et al. recently investigated a wedged cut LBO designed for Type II 355 nm light generation and provided an algorithm for use in determining the optimal wedge angle [23]. In this research, in an attempt to achieve highly efficient 355 nm light generation and inspired by the non-collinear phase-matching method, I designed 87

95 Chapter 5. Research about 355 nm UV light generation by CLBO a walk-off compensated prism-coupled device based on Type II CLBO. To accomplish this, I performed 355 nm light generation with collinear and non-collinear phase-matching and then tested the output enhancement made possible by the new device. 5-2 Method for walk-off compensation In this section, I will introduce the method realizing non-collinear phase-matching for walk-off compensation in 355 nm light generation by CLBO. Similar to the example given section of a Type II SHG, principle for collinear and non-collinear phase-matching for the THG (THG will be used as a term in this section for simplicity) will be briefly discussed, and it will become easy to understand why non-collinear phase-matching can overcome the shortcoming of collinear phase-matching. Then, for achieving non-collinear phase-matching that is not so usual in UV light generation, a wedged-cut structure is needed for it has the ability to combine the beams Poynting vector while keeping their wave vector separated. At last, for the walk-off angle for CLBO is too large for achieving non-collinear phase-matching, a prism-coupled structure is designed as the solution Principle for non-collinear phase-matching Fig.5.1 (a) shows a commonly used collinear phase-matching for Type II (eoe) THG in a negative uniaxial crystal. The phase-matching condition is expressed with wave vector relations as: k ( ) k k ( ). (5.1) ( ) (2 ) (3 ) e PM o e PM It also can be written with a refractive index as: n ( ) 2n 3 n ( ). (5.2) ( ) (2 ) (3 ) e PM o e PM In the plane determined by the z and x (or y) axis of the crystal, the wave vector 88

96 (k) of second-harmonic light (2ω) is shown as a quarter circle (ordinary wave) with a solid line, while fundamental light (ω) and third-harmonic light (3ω) are shown as a quarter ellipse (extraordinary wave) with a dished line. The phase-matching angle θ PM is decided in the manner of k when the ellipse of the ω plus the circle of the 2ω crosses the ellipse of the 3ω. The wave vectors of the incident waves, as well as the resultant wave, dispose in the same direction. As ω and 3ω are extraordinary waves, their associated Poynting vectors (S) are offset by walk-off angles of ρ (ω), ρ (3ω) clockwise from the respective wave vectors. The walk-off angles in the figures are shown larger than actual size so that this can be seen clearly. In such situations, all Poynting vectors in the generation are pointed in different directions, thereby resulting in a progressively reduced overlap between the beams as they traverse the crystal. This leads to a shorter effective interaction length and, ultimately, lower conversion efficiency. (a) (b) Fig.5.1. Collinear (a) and non-collinear (b) phase-matching configurations illustrated in x(or y)-z wave vector plane for type II (eoe) THG by a negative uniaxial crystal. Improving the conversion efficiency of this process requires walk-off compensation in order to extend the effective interaction length of the incident beams. For this purpose, consideration may be given to aligning the Poynting vector directions. As shown in Fig.5.1 (b), by rotating the wave vector of ω counterclockwise at a certain angle and rotating the wave vector of 2ω clockwise slightly, the Poynting vectors of ω and 2ω become parallel, thus allowing 89

97 Chapter 5. Research about 355 nm UV light generation by CLBO optimal overlap of the two energy flows to be maintained throughout the length of the crystal, while the deviation between them and 3ω decreases as well. When the vector sum of ω and 2ω is equal to 3ω, the non-collinear phase-matching configuration for walk-off compensation is established. The mathematical expression of refractive index for the configuration is shown as: n ( )sin( ) 2 n ( )sin( ) 3 n ( )sin( ), (5.3) ( ) ( ) ( ) (2 ) (2 ) ( ) (3 ) (3 ) (3 ) e e e n ( )cos( ) 2 n ( )cos( ) 3 n ( )cos( ), (5.4) ( ) ( ) ( ) (2 ) (2 ) (2 ) (3 ) (3 ) (3 ) e o e n ( ) Tan( ) Tan( )[ ]. (5.5) ( ) ( ) ( ) (2 ) e 2 ( ) no θ (ω), θ (2ω) and θ (3ω) are the phase-matching angles for the three waves measured from the z axis, which are shown in Fig.5.2. Equations (5.3) and (5.4) are for non-collinear phase-matching condition in Type II THG, while (5.5) is for the collinear energy flow of ω and 2ω. Fig.5.2. Phase-matching and walk-off angles of non-collinear phase-matching configuration for type II (eoe) THG by a uniaxial crystal. Effective walk-off for THG after the compensation will get smaller than the walk-off angle for the collinear phase-matching. Table II compares phase-matching and walk-off angles for the waves of Type II THG in collinear and non-collinear phase-matching. It is found that the θ (2ω) for the two conditions were almost the same. As shown in Fig.5.2, the Poynting vector direction of ω is θ (ω) +ρ (ω), which is equal to 2ω, thus making them parallel. The effective walk-off for 3ω in non-collinear phase-matching equals θ (3ω) +ρ (3ω) -θ (2ω) =1.4 (26.2 mrad, the value counted with mrad has a higher accuracy here), which is smaller than ρ (3ω) in collinear phase-matching. 90

98 Table 5.2. Calculated phase-matching and walk-off angles for collinear and non-collinear THG by Type II CLBO (at 150 C). θ (2ω) (deg.) θ (ω) (deg.) ρ (ω) (deg.) (mrad) θ (3ω) (deg.) ρ (3ω) (deg.) (mrad) collinear non-collinear Values for non-collinear phase-matching are calculated based on data come from Ref Method for achieving non-collinear phase-matching Theoretically, the non-collinear configuration is available with usual device by input the lasers into the crystal with a small angle. However, as the laser beam is commonly adjusted with µm level, it is hard for adjusting even with high-precision equipment for the experiment. Therefore, look for special technique seem to be the only way for the research. Similar to the case of LBO discussed in [23], an effective approach for achieving such non-collinear phase-matching is adopted which involves using a crystal with its input surface cut at a wedge angle α as shown in Fig.5.3. Here, the crystal is cut with its z-axis oriented at angle θ. 2ω with an ordinary polarization is selected to propagate at a direction parallel to the crystal s edge for ease of alignment. Therefore, θ is chosen to be equal to θ (2ω) in order to meet the phase-matching condition for THG. The ω and 2ω beams enter the crystal s wedged cut surface at an oblique angle of ψ 0 relative to the line perpendicular to the surface. After occurrence of the refraction effect, they propagate at angles ψ (ω) and ψ (2ω) inside the crystal relative to the line perpendicular to the surface. The angles on either side of the interface satisfy Snell s law, so a smaller amount of ω will be refracted than 2ω because it has a smaller refractive index. As the amount of separation between refractive beams (ψ (ω) -ψ (2ω) ) equals the walk-off angle ρ (ω), the compensation condition will be fulfilled. 91

99 Chapter 5. Research about 355 nm UV light generation by CLBO Fig.5.3. Scheme of wedged cut structure for achieving non-collinear phase-matching in type II (eoe) THG by negative uniaxial crystal. Fig.5.4. Relation of compensated walk-off angle and wedged cut angle. Blue line stands for the range that the wedge angle is small, light can be directly input on the wedged-cut surface; red line stands for the range that total reflection is happened, so there is no direct way to input the laser. The optimal wedge angle for compensation for CLBO is in the dashed line circle which is not available. The wedge angle is calculated to be α=50.2 for CLBO based on data given in Table II. In Fig.5.4, the relationship between the wedge angle and, accordingly amount for the compensated angle is shown. For fully walk-off compensation, blue line expresses range that incident angle at wedged cut surface is smaller than 90 degrees, while red line expressed the opposite range. Unfortunately, the α desired is in red line range, which means the incident 92

100 angle ψ 0 necessary for achieving the desired refractive angle will be over 90 on a wedged cut surface. This is caused by the CLBO s large walk-off angle, which is about 4 times of LBO s. It is easy for LBO to use the configuration to compensate the walk-off as described in [23], while the incident angle is not going to be achieved in the case of CLBO. In order to make the refraction with a relative small incident angle for achieving the same compensation effect, consideration may be given to inputting the beam from the media with a refractive index closer to the CLBO Prism-coupled device structure for non-collinear phase-matching In order to solve this problem, I adopted a structure with a prism attached to the wedged cut surface of crystal, as shown in Fig.5.5. This structure is derived from an optical contact prism-coupled device based on the KBe 2 BO 3 F 2 (KBBF) crystal used for achieving phase-matching in nm UV light generation [24]. The prism used in this design is made of fused-quartz, which has a similar refractive index to CLBO and high transparency from 1064 to 355 nm. As a result, the incident beam only needs to be slightly refracted on the surface in order to achieve the non-collinear phase-matching desired. (The deviation between ω and 2ω in Fig.5.5 equals the actual angle, which differs from the figures above.) Cut angle β of the prism also should be selected so that it is equal to incident angle ψ 0 while making sure a normal incident angle is present on the surface between the prism and outside. In this condition, no separation will occur between ω and 2ω as they propagate through the prism collinearly. How to attach the prism to the crystal tightly is a task for the configuration. Thanks to the optical-contact technique, the two materials can be attached each without any other assistant. The risk of laser-induced damage on combined surface seems to be an issue in high power practical use. Also, cares should be given to make sure the prism not separate from the crystal during the generation. 93

101 Chapter 5. Research about 355 nm UV light generation by CLBO Fig.5.5. Scheme of prism-coupled device on one side. The device is fabricated by attaching the fused quartz prism to the CLBO crystal with optical-contact technology. When the chosen CLBO cut with θ equals the phase-matching angle of 2ω at θ (2ω) =49.0, given the refractive index for ω, 2ω in fused-quartz (n (ω) FQ=1.450, n (2ω) FQ=1.461), α=ψ (2ω) =58.6 is calculated as the wedge angle and β=ψ 0 =61.0 as the prism cut angle. The sample prism-coupled device created is shown in Fig.5.6. The device is based on a CLBO crystal with dimensions of h w l= mm 3, and is cut with θ=49.0 and φ=0, and then fabricated with a wedge angle and prism cut angle of α=β=58.6. For fabrication convenience, the device is made into a cuboid, and there is a small deviation in the prism cut angle from the calculated result. The fused quartz prisms are attached to the CLBO crystal via the optical-contact technique provided by Kogakugiken. Fig.5.6. A prism-coupled device sample fabricated with CLBO and fused quartz. CLBO crystal used has a dimension of h w l= mm 3. CLBO is cut with θ=49, φ=0 ; the device is fabricated with α=β=

102 5-3 Experiments for 355 nm light generation In this section, 355 nm light generation is tested with LBO, CLBO and the new-designed device. From the generation result, walk-off compensation effect of non-collinear phase-matching configuration is to be discussed Setup preparation for 355 nm light generation The experimental setup for THG is shown schematically in Fig.5.7. As can be seen in this figure, a Q-switched neodymium-doped yttrium orthovanadate (Nd:YVO 4 ) laser (HIPPO H10-106QW, Spectra Physics) is employed as the fundamental laser source. This laser delivers linear polarized beam with M 2 <1.2, maximum output of 11.5 W at repetition rate of 15 khz with a pulse width of 8 ns. After the laser source, a polarizer and half wavelength plate set is installed for adjusting the power and polarization direction of the output. Fig.5.7. Experimental setup for 355 nm light generation. The system is based on a commercial Nd:YVO 4 laser. Ls stand for spherical lenses. In the first step, SHG was performed by a mm 3 x-cut Type I non-critical phase-matching (NCPM) LBO at 151 C with anti-reflection (AR) coating for 1064 and 532 nm. Fundamental light is focused to a 170 μm radius waist into the LBO. The maximum conversion efficiency of SHG is 55% at an input of 9 W. In the second step, residual fundamental light and second-harmonic light with orthogonal polarization directions are separately focused by lens pairs 95