Design and construction of a passively Q-switched Nd-YAG pumped UV laser and study its non-linear parameters

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1 Republic of Iraq Ministry of Higher Education and Scientific Research University of Baghdad College of Science Design and construction of a passively Q-switched Nd-YAG pumped UV laser and study its non-linear parameters A thesis Submitted to the Committee of College of Science, University of Baghdad In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Physics By Abdulnabi Hassan Mohsin B.Sc. (Electronic & comm. Eng.)1988 M.Sc. (Laser Technology) 2001 Supervised By Prof. Dr. Baha T. Chiad Prof. Dr. Abbas J. H. Al-Wattar 2013 AD 1434 AH

2 ب سم االله الر حمن الر حيم و ق ل ر ب أ دخ لن ي م دخ ل ص دق و أ خر جني م خرج ص دق و أجع ل ل ي م ن ل د نك س لطانا ن ص يرا ص دق االله الع ظيم سورة الا سراء (ألا ية.( ٨٠ I

3 &الا هداء إلى من بلغ الرسالة وأدى الا مانة.. و ن ص ح الا مة.... إلى نبي الرحمة ونور العالمين سيدنا محمد صلى االله عليه واله وسلم?عبد النبي II

4 Supervisor Certification We certify that this thesis was prepared under our supervision at the Physics Department, College of Science, University of Baghdad, as a partial requirement for the degree of Doctor of philosophy in Physics Science / laser and Molecular. Signature : Name : Dr. Abbas J. H. Al-Wattar Title : Professor Address : College of Science, University of Baghdad Date : / / 2013 Signature : Name : Dr. Baha T. Chiad Al-Khafaji Title : Professor Address : University of Baghdad Date : / / 2013 In view of the available recommendations, forward this thesis for debated by the examination committee. Signature : Name Title Address : Dr. Raad M. S. Al-Haddad : professor Date : / / 2013 : College of Science, University of Baghdad III

5 Examination Committee Certification We certify that we have read this thesis Design and construction of a passively Q-switched Nd-YAG pumped UV laser and study its non-linear parameters as an examining committee, examined the student Abdulnabi Hassan Mohsin in its contents and that, in our opinion meets the standard of a thesis for the degree of Doctor of Philosophy In Physics / Laser and Molecular. Signature: Name : Dr. Nathera A. Ali Title : Professor Date : September, 2013 Chairman Signature: Signature: Name: Dr. Hassan N. Abdul Wahab Name: Dr. Wesam A. Twej Title: Professor Title: Assist. Professor Date: September, 2013 Member Date : September, 2013 Member Signature: Signature: Name: Dr. Sudad S. Ahmed Name: Dr. Wasfe H. Rasheed Title: Assist. Professor Title: Chief Researchers Date: September, 2013 Member Date: September, 2013 Member Signature: Signature: Name: Dr. Baha T. Chiad Name: Dr. Abbas J. H. Al-Wattar Title: Professor Title: Professor Date: September, 2013 Supervisor Date: September, 2013 Supervisor IV

6 Approved by the Dean of College of Science Signature: Name: Dr. Saleh M. Ali Title: Professor The Dean of College of Science Date: / 9 /2013 V

7 ACKNOWLEDGEMENTS At the first, I thank God for his graces that enabled me to continue the requirements of my study and to overcome the difficulties during the courses and research. I wish to acknowledge invaluable assistance during the course of this work to my thesis advisors, and Prof. Dr. Baha T. C. and Prof. Dr. Abbas J. H. for their patience, support, and guidance throughout my research. It has been a great pleasure for me to be one of their students. Their deep understanding of physics with both fundamental and applied science is what has inspired me most. My thanks are extended to Prof. Dr. Raad M. S. the Head of the Department of Physics and to all the staff of the Department of Physics. My thanks also are extended to Prof. Dr. Nathera A. A. the head of the molecular and laser group. My special thanks to my friends and postgraduate students particularly, Mr. Abdulkarim A. A.,, Dr. Wessam A. T., Dr. Mohamed A. H., Dr.Wasfe H. R. and Mrs. Nagam T. A. for their help and support in my research. Finally, I would like to express my extreme love and appreciation to my wife for her moral support, long suffering and patience during my study. 1

8 List of Symbols and abbreviations IR- Infrared SHG - Second harmonic generation SFG- Sum frequency generation THG- Third harmonic generation NLO - Nonlinear optics OPO - Optical parametric oscillation OPA - Optical parametric amplification KTP - Potassium titanyl phosphate (KTiOPO4) BBO - Beta barium borate ( β-bab2o4) KDP - Potassium dihydrogen phosphate LBO - Lithium triborate (LiB3O5) PPLN- Periodically poled lithium niobate (LiNbO3) Nd:YAG - Neodymium-doped yttrium aluminum garnet QPM - Quasi-phase-matching FWHM- full width half maximum MCNWOC- Multi-crystals non-walkoff compensation MCWOC- Multi-crystals walkoff compensation E - Electric field 2

9 P - Polarization ε - Dielectric constant PL -Linear polarization P NL -Nonlinear polarization (1) c - Linear susceptibility (2) c - Second order nonlinear susceptibility s - Conductivity of the media d - Nonlinear coefficient d eff - Effective nonlinear coefficient k - Wave vector cijk - nonlinear susceptibility μ o - Vacuum permeability ω - Angular frequency n - Index of refraction 2 P w - Second Harmonic power p w - fundamental laser power W- Nonlinear crystal width H - nonlinear crystal height λ - Wavelength 3

10 ħ - Plank s constant Ɵ - Phase-matching angle l c - Coherence length r - Walk-off angle l a - Interaction length w - Radius of the beam A - Effective area I - Input intensity I SHG -SHG intensity L c -Crystal length -Harmonic efficiency ΔƟ - Angular acceptance Δλ - Spectral acceptance 4

11 Table of Contents Chapter one Theoretical Part 1.1 Introduction Beam Propagation and properties of Gaussian Beams Nonlinear Optics Three Wave Interactions in 2 nd Order NLO Process Second harmonic generation with plane wave Phase matching Birefringent Phasematching Quasi-Phase Matching Angle Tuning of Birefringent Phase-Matching Condition Spatial walkoff Sum frequency mixing Sum frequency generation conversion efficiency Conversion efficiency enhancement Walk-off compensation Collimated Gaussian beam laser source Type A mixing

12 Type B mixing Historical review Of Optical Harmonic Generation Aim of the work Chapter two Experimental Part Frequency doubling with LBO and BBO nonlinear crystals Introduction NLO crystals properties Lithium triborate (LiB 3 O 5 ) LBO b -Barium Borate crystal (BBO) Experimental setup LBO crystal in SHG experiment BBO crystal in SHG experiment Second harmonic generation with Walk-off compensation Multi-Crystals in Non and walk-off compensation Third harmonic generation at 355nm Third harmonic generation with Walk-off compensation

13 2.9 Temporal and spatial beam profile measurements...76 Chapter three Results and Discussion 3.1 Introduction Nd:YAG laser parameters Second harmonic generation measurements with LBO and BBO crystals Single LBO and BBO experiments Multi crystal SHG experiments SHG with Non walkoff compensation (NWOC) and walk off compensation (WOC)experiments THG harmonic generation measurements THG using Single LBO crystal experiments Multi crystals THG experiments Multi-crystals in SHG and single crystal for SFG Enhancement in SHG stage using LBO-LBO crystals experiments

14 Enhancement in SHG stage using BBO-LBO crystals experiments Single crystal in SHG and Multi-crystals in SFG [ LBO - LBO ] Crystals arrangement in THG experiments SHG and THG wavelengths detections Conclusions Future work Reference 8

15 Abstract An ultraviolet laser at 355nm was designed and implemented by extra-cavity frequency tripling of a passively Q-switched Nd-YAG laser with 1064nm wavelength. Type I critically phase matched b -Barium Borate (BBO) and Lithium triborate (LBO) nonlinear crystals were used for second harmonic generation (SHG) and type II critically phase matched LBO nonlinear crystal was used for sum frequency generation (SFG) to obtain third harmonic generation (THG). With a pumping energy of a 24 mj at 1064nm the maximum second harmonic energy per pulse have been generated were 3.68mJ and 3.14mJ at 532nm for BBO and LBO crystals which corresponds a conversion efficiencies of ( ~15.95% & ~13.81%) respectively. A walk-off compensated configurations in SHG with twin LBO type I crystals and non-twin type I crystals (BBO and LBO) in two configurations nonwalkoff compensation (NWOC) and walkoff compensation (WOC) schemes were achieved. The conversion efficiency enhancement factors for non-twin crystals are (~1.3 & ~1.8), while that for twin LBO crystals are (~1.22 &~ 2.4). A 1.06mJ and 1.176mJ third harmonic energy generated at 355nm UV using two crystals one for SHG and the other for SFG have been obtained which corresponds the maximum conversion efficiencies of (~4.41% and ~4.9%) for BBO-LBO and LBO-LBO crystal arrangements respectively. The maximum third harmonic conversion efficiency enhancement factors obtained due to enhancements in the first stage(shg) for non-twin crystals on WOC schemes were (~1.9 &~2.5 9

16 ),while that for twin crystals on the same scheme were (~1.3 &~1.8) respectively. The maximum third harmonic Conversion efficiency obtained due to an enhancement in the SFG stage using twin-crystal on WOC scheme were 6.1% which gives an enhancement factor of The temporal and spatial beam profiles of the various laser beams generated in the system have been investigated using 2D and 3D image. 10

17 11

18 Chapter Introduction One of the most effective techniques to overcome the spectral limitations of lasers is to exploit nonlinear optics. Nonlinear optics (NLO) is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light. This nonlinearity is typically only observed at very high light intensities (values of the electric field comparable to interatomic electric fields, typically 10 8 V/m) such as those provided by pulsed lasers. The potential of nonlinear optical processes are to provide a mechanism for the generation of new frequency from an already available input frequency. In other words, they provide a convenient technique for frequency conversion of light from an old to a new spectral range. Nonlinear optical processes can take variety of forms. The most important processes in the context of frequency conversion include second harmonic generation, sum-and differencefrequency mixing, and optical parametric oscillation. For light emission over extended spectral band, optical parametric oscillation is the key process of interest[1,2]. This chapter describe the basic concepts of nonlinear optics and relevant fundamental concepts and mathematics required for this thesis are explained. 1.2 Beam Propagation and properties of Gaussian Beams A laser beam of the simplest form is the fundamental or TEM 00 mode. A beam operating in the TEM 00 mode has a Gaussian intensity 12

19 profile where the decrease of the field amplitude with distance r from the axis is given as follows[3]: r E( r) = E.exp - Ł wo ł 1.1 The beam radius denoted as ω, which is commonly called spot size, is given by the radial distance at which the power density drops to 1/e 2 of its maximum value. Hence a Gaussian beam contains 86.4% of its total power within r = ω. The beam radius will have its minimum value at the beam waist denoted by ω 0, r is the radial distance [3]. Figure 2.4 :Illustration of the beam waist ω 0 for a Gaussian beam[3] If a Gaussian TEM 00 laser-beam wavefront were made perfectly flat at some plane, with all elements moving in precisely parallel directions, it would quickly acquire curvature and begin spreading in accordance with[3]: 2 2 Ø pw ø 0 R( z) = Œ1+ œ Œ lz º Ł ł œß 1.2 And 13

20 2 Ø lz ø w( z ) = w Œ 0 1+ œ 2 Œ pw0 º Ł ł œ ß 1/2 1.3 where z is the distance propagated from the plane where the wavefront is flat, l is the wavelength of light,, w ( z ) is the radius of the 1/e 2 contour after the wave has propagated a distance z, and R(z) is the wavefront radius of curvature after propagating a distance z. R(z) is infinite at z = 0, passes through a minimum at some finite z, and rises again toward infinity as z is further increased, asymptotically approaching the value of z itself. The plane z = 0 marks the location of a Gaussian waist, or a place where the wavefront is flat. As R(z) asymptotically approaches z for large z, w( z ) asymptotically approaches the value[4]: w( z ) lz where z is presumed to be much larger than pw / 0 l so that the 1/e2 irradiance contours asymptotically approach a cone of angular radius. 1.3 Nonlinear Optics A light wave consists of electromagnetic fields which change sinusoidally at optical frequencies. When a light wave is incident on a dielectric medium, charged particles in the medium will be displaced from their equilibrium positions and start to oscillate in the applied electric field, forming oscillating electric dipoles. On a macroscopic scale, these oscillating electric dipoles build up in the medium resulting in 14

21 a charge redistribution at optical wavelengths which is described by the polarization P. The polarization can be written as an expansion in powers of the electric field E [5]. pt = Et + E t + E t (1) (2) 2 (3) 3 () e0( c () c () c ()...) (1) Where c is the linear optical susceptibility of the medium and is related (1) 2 to the medium s refractive index n by n c = - 1, 0 e is the permittivity of free space, c (2) (3) is the second-order nonlinear susceptibility, c is the (2) (3) third-order nonlinear susceptibility and so on, c, c. describe the most important optical properties of the medium. For a weak applied electric field E, the charge can follow the field almost exactly and the polarization P is linearly proportional to the applied electric field E. For larger amplitudes of the applied electric field, the relationship between P and E becomes nonlinear, and the c (2) and c (3) terms will be important. In order to demonstrate the theory of nonlinear effects, consider an applied electric field[5,6]: Et ( ) = Ecos( wt) Inserting Eq.(1.6) into Eq.(1.5), we can get[5]: (1) 1 (2) 2 Pt ( ) = e0( c E0cos wt+ c E0(1 + cos 2 wt) (3) 3 p 3 p c E0 (3sin( wt+ ) - sin(3 wt+ )) +...)

22 From Eq.(1.7), it reveals that the polarization contains not only the linear component, but also a d.c. term and nonlinear components at frequencies of 2ω,3ω,..... Thus light waves at new frequencies can be generated through the nonlinear effect. The term c (2) gives rise to a number of interesting optical phenomena such as second harmonic generation (SHG), d.c. rectification, see Figure 1.1, optical parametric oscillation (OPO), and three-wave mixing processes. The term c (3) results in third harmonic generation, two photon absorption, and four-wave mixing, etc. The second harmonic generation will be first on the focus of this thesis, the effects that arise from c (2) will be further derived, although a similar methodology can be applied to third harmonic effects[5]. Figure 1.1: Fourier analysis of the nonlinear polarization [5]. 16

23 1.3.1 Three Wave Interactions in 2 nd Order Nonlinear Process Nonlinear-optical effects belong to a broader class of electromagnetic phenomena described within the general framework of macroscopic Maxwell equations. The Maxwell equations not only serve to identify and classify nonlinear phenomena in terms of the relevant nonlinear optical susceptibilities or, more generally, nonlinear terms in the induced polarization, but also govern the nonlinear-optical propagation effects. We assume the absence of extraneous charges and currents and write the set of Maxwell equations for the various electric fields. For three interacting waves, then, we must seek three coupled amplitude equations each giving the rate of growth or delay of the field at one frequency as a function of the fields at the two other frequencies. In edition we should expect in each of these equations some measure of the phase difference between the polarization wave and the electromagnetic wave. We start by introducing the nonlinear polarization as a source term in the Maxwell s equations and assuming propagation in the Z direction. Moreover to limit the discussion to three interacting traveling waves, we define [7]: E ( z,) t E ( z) e 1 1 -i( w1t-kz 1 ) = 1.8 E ( z,) t E ( z) e 2 2 -i ( w2t-k2z ) = 1.9 Where the subscripts 1 and 2 refer to the various interacting fields. In the simple case of frequency mixing with two incoming plane waves E 1 and E 2 propagating along the z-axis and the assumption of a linear polarization in a single transverse direction. These two incoming fields induce a nonlinear polarization at frequency w=w 1 +w 2 that may be written as: 17

24 w1+ w ( ) de( ) E P z, t z (z) e [ i ( ) t i ( k k ) z ] NL = And we assume that a new field is created at frequency w 3 =w 1 +w 2 with a field: E ( z,) t E ( z) e 3 3 -i ( w3t-k3z ) = 1.11 Using the assumption of the slowly varying amplitude approximation we can derive as a consequence the three coupled wave equations by which the three amplitudes of the waves are coupled [5]: de dz s m 1 m =- E - iw d E E exp( id kz) + c. c i * 1i 1 ijk 3k 2 j 2 e1 2 e1 de dz * 2 j s 2 m0 * 1 m0 * 2 j w2 ijk 1i 3k 2 e2 2 e2 =- E - i d E E exp( id kz) + c. c 1.13 de dz =- s m 1 E - m iw d E E exp - ( i D kz) + c. c k k 3 ijk 1i 2 j 2 e3 2 e3 Where D k = k3 -k2 - k1, s is the conductivity of the media for the various fields d ijk the nonlinear coefficient of the media and c.c. the complex conjugate. The c 2 interaction involves three waves which may either be input or generated within the nonlinear material. There are three kind of interactions, they are sum frequency generation (SFG) or up-conversion; difference frequency generation (DFG) or mixing, and optical parametric generation (OPG). SFG describes the situation where two longer 18

25 wavelengths (lower frequenciesw1 and w 2 ) are mixed with each other to generate a shorter wavelength (higher sum frequencyw 3 ) via the second order nonlinear susceptibility c 2. A schematic description of SFG is shown in Figure 1.2(a). The interaction can be expressed as: w1+ w2 = w3 Second harmonic generation (SHG) is a special case of SFG in which w1 = w2. DFG describes the situation where a higher frequencyw 3 and a lower frequencyw 2 are mixed with each other to generate a difference frequencyw 1 via the second order nonlinear susceptibility c 2.This process generates a longer wavelength. A schematic description of DFG is shown in Figure 1.2(b) and the interaction can be expressed as w3- w2 = w1[5].opg uses a highest frequency (shorter wavelength) w 3 to generate two lower frequencies (longer wavelength) w2, w 1 via the second order nonlinear susceptibility c 2. The generated pairs at frequenciesw 1 andw 2 are determined by the phase matching condition: D k = k3 -k2 - k1 = 0 This process can be thought of as the reverse process of SFG. For historical reasons we refer to w3 as the pump, w 1 as the signal andw 2 as the idler(normallyw 2 < w 1 )[5].When, w2 = w1the process is said to be degenerate. An Optical Parametric Oscillator (OPO) makes use of this interaction. A schematic description of this process is shown in Figure 1.2(c) 19

26 Figure 1.2: The three wave processes. (a) Sum frequency generation; (b) Differencefrequency generation; (c) Optical parametric generation[ 5] 1.4 Second Harmonic Generation With Plane Wave One of the most basic nonlinear optical processes resulting in the generation of a new field component is known as second harmonic 2 generation (SHG). This process is referred to as a c process because it occurs in a material, commonly a birefrigent crystal, with a non-zero second order nonlinear susceptibility. The second harmonic refers to light generated in the crystal at twice the fundamental frequency, or half the wavelength, of the incident field. SHG is a special case of the more general process known as sum frequency generation (SFG), whereby two input fields at frequencies w1 and w2 are combined in a 2 c material to generate a new field component at frequency w3 = w2 + w1[8]. We will first discuss the details of SHG and then continue with description of SFG. The simplest c 2 nonlinear interaction is second harmonic generation (SHG), and it is also one of the most important. Starting out from the coupled wave equations, assuming just a single input field, so E 1 (z) =E 2 (z),a radiation field E 3 (z) may be generated. Under the assumptions: 20

27 - that there is a nonzero nonlinear coefficient d; this implies a certain symmetry of the medium; - that there is no absorption in the medium, so the conductivity term may be neglected; - there is only little production of the wave at w 3, so that the field amplitudes are not affected by the conversion process; The coupled wave equation can be integrated straightforwardly[8]: (2 w) m 2 i Dkz E ( z ) =- i w de ( w) e dz 1.15 (2 w) e Where d is an effective nonlinear coefficient that depends on the direction of propagation and the polarization of the fields with respect to the crystal relative orientation etc. We use the effective nonlinear coefficient d to replace the term d ijk. where the integration is over the length of the medium (and the overlap of light beams) between 0 and L. The integration yields, assuming that E 2 w (0) = 0 : (2 w) m 2 e E ( L ) =-w de ( w) (2 w) e kl -1 Dk i D 1.16 The output second harmonic intensity is proportional to : 2 (2 w) (2 w) wm ( ) * ( ) = ( w) D 2 n e 0 Ł E L E L d E L Sinc kl 2 ł

28 If the beams are written in terms of beam intensities, so of power per unit area A, then it follows that the conversion efficiency for second harmonic generation is: h SHG = P DkL P P Ł 2 ł A (2 w) ( w) w d L Sinc ( w) 1.18 Where P 2w the power of the second harmonic wave, the term A is the effective area which is given by: A w 0 2 = p, 0 w is the Gaussian beam electric field radius, l is the crystal length, h SHG is the second harmonic conversion efficiency and the phase mismatching is given by[8]: 4p D k = k - 2 k = ( n - n ) w w 2w w lw The SHG conversion efficiency in Eq depends on the effective nonlinear coefficient d, the crystal length l, the input intensity power and phase mismatching D k [9]. When D k = 0 the refractive indices of incident fundamental and second harmonic waves are equal, and the power of SHG process is maximal. The characteristic dependence of SHG power on phase mismatch is illustrated in Figure 1.3 Figure 1.3 : Second harmonic output power vs Dk.[9] 22

29 As all useful nonlinear materials have normal dispersion, the refractive indices will differ for the different wavelengths ( n2 w n ). The second harmonic power P 2w will change periodically along the interaction distance l in an un-poled NLO crystal, see Figure 1.4. It should be noted that this analysis does not hold for focused Gaussian beams, where the theory due to Boyd [10] shows a linear length dependence, rather than the quadratic length dependence shown above. w Figure 1.4: The second harmonic power with phase mismatch, P2 w shows a periodic change along the interaction distance l in an un-poled lithium niobate crystal[5]. From the above plot, it can be seen that the P 2w oscillates along the 2 interaction length governed bysin ( D kl / 2). When D kl = p the interaction has occurred over one coherence length. 1.5 Phasematching A factor complicating nonlinear processes have electric fields with different frequencies in general propagate with different phase velocities due to dispersion. In SHG for instance, the fundamental radiation moves with the phase velocity c/ n w and so does the driving polarization. The 23

30 generated field, the second harmonic, however, propagates with a phase velocity of c/ n2 w.thus the driving polarization and the generated wave drift out of phase. The direction of the power flow from one wave to the other is determined by the relative phase between the interacting waves. Therefore, an alternating phase shift results in power flowing back and forth between the fundamental and the second harmonic instead of solely converting power from the fundamental radiation to the second harmonic. The distance, after which back-conversion starts, is typically a few micrometes. If nothing is done to prevent the back-conversion, the maximum generated power will therefore be limited to the power that is obtained within this short region. Efficient conversion requires, however, significantly longer crystals, having typically sizes of several millimeters. Hence it is essential to employ techniques, which prevent the phases of the waves to drift apart, namely to achieve phasematching. Two important methods were achieved for phasematching between the different components exist: birefringent phasematching and quasiphasematching. The first time a nonlinear process showed efficient frequency conversion was birefringence phasematched second harmonic generation[11,12]. Only shortly afterwards quasi-phasematching was suggested independently by Armstrong et. al [13]. and Franken et al [14]. This technique was demonstrated for the first time by the latter group employing a stack of thin plates of quartz, where every second piece was rotated by Birefringent Phasematching The most commonly used method to achieve the momentum conservation hk1+ hk2 = hk3which also can be written as 24

31 + = 1.20 nw n w nw is, to employ birefringent phasematching (BPM). BPM utilizes the fact that the three principal axes in biaxial materials have different indices of refraction. By letting the beams enter at different angles and/or be polarized in different directions, the needed relationship between n 1, n 2 and n 3 can be fulfilled. Fig.1.5 shows BPM for SHG in a uniaxial, negative (n o > n e ) crystal. The fundamental wave is launched at an angle θ relative to the optical z axis. It is polarised in the x-y plane, which results in an ordinary beam. Thus, it propagates with a phase velocity of c/ n w 0, and so does the driving polarization. The second harmonic is then generated as an extraordinary beam. Therefore, its index of refraction is dependent on the angle θ and given by[15]: 1 sin cos 2 2 q q n w ( ) ( ne ) ( n0 ) 2 ( e q ) = This relation describes an ellipse as can be seen in Fig If it is possible to match these two velocities by achieving n = n e the two w 2 w 0 ( q ) beams will propagate through the crystal in phase and the energy will flow from the fundamental wave to the second harmonic[16]. 25

32 Figure 1.5: Birefringent phasematching in a negative uniaxial crystal[16] This means that we should find such direction of propagation of light in the crystal, where the refractive index( n w )for incident light equals the refraction index for second harmonic ( n2 w ). In this case both waves travel together and efficient energy conversion is possible. On Figure 1.6 we can see it graphically. This situation is impossible in isotropic media, since in such media refractive index n is increasing along with frequency w. However, this condition can be satisfied in birefringent (i.e. anisotropic) crystals[9]. Figure 1.6: Phase matching condition in anisotropic crystal.[9] 26

33 This type of phase matching is called birefringent or index phase matching. In anisotropic crystals the refractive index depends on incident field polarization and direction of propagation. The optical axis for this type of crystals is defined as the angle of the beam propagation in relation to the optic axis, θ, does not only control the phasematching condition, but also whether the interaction is denoted critical or noncritical[17]. The ideal case is noncritical phasematching and can in uniaxial crystals only be achieved for θ = 90. All other angles (θ 90 ) result in critical phasematching. The drawback with critical phasematching is a phenomenon called walk-off, which complicates the phasematching process. Thus, for critical interaction the ordinary and the extraordinary beam do not overlap after a certain distance any longer. This, obviously, prevents further energy conversion and reduces the useful crystal length. Another consequence of the walk-off phenomena is that it limits the ability to focus tightly, because narrow beams separate quicker than large ones. However, tight focusing is sometimes necessary in order to increase the intensity. Due to these limitations in the interaction distance, noncritical phasematching is preferred, where energy can flow between the tightly focused beams while propagating through a longer crystal[17]. The refractive index varies with the orientation of the polarization with respect to optical axis. If the polarization is perpendicular to the optical axis, it is known as ordinary polarization. Parallel polarization is known as extra-ordinary. Two types of phase matching in birefringent crystals are possible in principle. Type I: both input waves have the same polarization while an output wave has orthogonal polarization as shown in Figure 1.7 [18]. 27

34 Figure 1.7: type I phase matching Type II: when one wave is an extraordinary ray, the other is an ordinary ray, and the output SH wave could be ordinary or extraordinary ( depending on type of birefringence in a crystal). This situation is shown in Figure 1.8 [18]. Figure 1.8: Type II phase matching The refractive indices of the two waves which can propagate in a crystal at an angle Ɵ to the optic axis are given by the following equation [ 9]: n ( q ) = e n nn o sin ( q) + n cos ( q) o e e

35 where n o is the ordinary refractive index of crystal, n e is the extraordinary refractive index of crystal. Usually nonlinear optical (NLO) crystals are cut normal to Ɵ to match the required orientation. In this case such crystal needs to be rotated around one axis. Because of relatively sensitive angular alignment this technique is called critical phase matching. In case o of q = 90, refractive indices of both waves are almost equal and we can achieve phase matching by temperature tuning (index of refraction is a function of temperature). This type of phase matching is called noncritical. It has an advantage of spatial walk-off due to birefringence being equal to zero. As a result we can focus incident light into the crystal more tightly. Major drawback of this method is the need to maintain the crystal s temperature within specified limits which are usually higher than room temperature. Birefringent phase matching can be achieved when refractive indices for SH and fundamental waves are equal as we can see on Figure 1.6 [16,17] Quasi-Phase Matching Quasi-phasematching (QPM) was devised by Bloembergen et al. [9]. Periodically poled nonlinear crystals with quasi-phase-matching allow the generation of SHG in an efficient and broadly tunable format. These crystals can work with any type of polarization of interacting waves. Quasi-phase-matched materials allow us to reach efficient nonlinear frequency conversion. This method is based on changing of the nonlinearity through artificial structuring of the nonlinear material. As was mentioned earlier, distance over which a relative phase between the two waves shifts by π is called a coherence length. This is also the half period of the growth and decay cycle of the second harmonic. When sign 29

36 of power flow from one wave to the other is dictated by the relative phase between the interacting waves. As a result, the continuous phase slip between these waves caused by their differing phase velocities leads to an alternation in the direction of the flow of power, as shown by curve C (Figure 1.9). In the ideal case ( D k 0 )the second-harmonic field grows linearly with distance in the medium, and as result the intensity grows quadratically, as shown by curve A in (Figure 1.9) [9]. Figure 1.9 : Stepwise build up of second harmonic power a) for perfect phasematching. b)with a periodic phase shift in the coherence length. C) Without phase matching. [9]. QPM comprises repeated inversion of the relative phase between the incident and second harmonic waves after an odd number of coherence lengths. The phase is changing periodically so that on average, the proper phase relationship is maintained for growth of the second harmonic, as shown by curve B (Figure 1.9). One way to invert the phase is to change the sign of the nonlinear coefficient. This changing could be done by two techniques. First, changing the sign of nonlinear coefficient by forming a stack of thin plates of nonlinear crystals with thickness lc which are 30

37 rotated by180 o degrees with respect to each other. The second, more common way to produce it, is by using ferroelectric crystals where we can form this periodic structure by applying a strong electric field across the material [9]. This process is called poling and such materials are called periodically poled. This is schematically presented in Figure Figure 1.10 : A nonlinear crystal with periodically varying nonlinear coefficient d(z) of period L [19] As follows, in periodically poled materials, birefringence is no longer needed to obtain phase matching and materials can be engineered to use their most favorable nonlinear optical coefficient which is dependent on the orientation of the crystallographic axes relative to the propagation direction of the beams Angle Tuning of Birefringent Phase-Matching Condition Since index of refraction in anisotropic crystals depends on propagation direction, crystal (or angle) tilting is normally used to achieve birefringent phase-matching condition. Light polarized 31

38 perpendicular to the plane containing the propagation vector k and the optical axis is said to have ordinary polarization and for this direction n 0 refractive index is called the ordinary refractive index. Light polarized in the plane containing k and the optic axis is said to have extraordinary polarization and experiences a refractive index ne ( q ) that depends on the angle Ɵ between the optic axis and k according to the equation [9]: q 2 cos ( ) = n n n n 2 2 q a 2 2 b a 1.23 Where na is the refractive index when Ɵ=0 and nb is the refractive index when q = 90 o. There are two axis for tilting crystal angles as is shown in Figure 1.11 [9]. Figure 1.11: Crystal angle tilting.[9] Since the NLO crystals are normally cut in the principal crystal plane, conversion efficiency is not sensitive to the angle tilting around b-axis. To 32

39 reach the best conversion efficiency, the crystals should be rotated just around the a-axis Spatial Walk-Off Due to the birefringence of the NLO crystals, the beam of the input laser will separate from the generated beam at a walk-off angle r as shown in Figure Therefore, the spatial walk-off limits the total length of the crystal as well as reduces the harmonics conversion efficiency. Figure 1.12 :Illustration of the walk-off effect[9] The beams will separate or walk off after a distance l a called interaction length with walk off angle r. The interaction length l a can be calculated from the equation: l a w = p 1.24 r Where( w ) is a radius of the beam( (mrad)[9]. m m ) and ( r ) is the walk-off angle 33

40 1.6 Sum Frequency Generation The most effective method to achieve such UV lasers was based on harmonic generation [20-22]. All solid- state fundamental frequency lasers operating in near-infrared (NIR) range are converted into UV frequency by means of nonlinear optical (NLO) crystals. There are two configurations for the harmonic generation: the intra-cavity and the extracavity. For the intra-cavity harmonic generation, it takes the advantages of high efficiency and compact configurations since the NLO crystals were positioned in the oscillator, which results in very high peak power of the fundamental frequency laser. However, the beam quality is always poor for the intra-cavity harmonic generation because of the significant thermal effect of the laser gain medium and the NLO crystals; especially for high-power UV operation [23,24]. Moreover, the design of the thermally stable cavity optics is complex and difficult, and the UV damage of the optical elements in cavity is hard to avoid. The extracavity harmonic generation using NLO conversion is an effective method to achieve high-power high-beam quality UV laser. The stable Q- switching can provide high-stability and high-peak-power fundamental frequency IR source [24], which is beneficial to the generation of efficient UV laser with the NLO conversion. Figure 1.14 Shows the schematic diagram for UV laser production. While it is theoretically possible to accomplish THG directly by frequency-tripling a fundamental beam in a single NLO crystal, in practice THG is produced indirectly. The fundamental beam is first frequency-doubled. This second-harmonic beam is combined with the unconverted remnant of the fundamental beam in a separate crystal. The THG output results from nonlinear "sum frequency mixing". A setup for polarization matching in the frequency conversion is shown in Figure 1.14 as well. 34

41 Nd:YAG BBO I or LBO I LBO II Figure 1.14: Schematic of polarization matching in the frequency conversion[24] In sum frequency mixing, a portion of the fundamental beam is first doubled, then combined in a second nonlinear crystal with the residual part of the fundamental. For SHG, this design uses Type I phasematching, in which the input beams are parallel to the ordinary crystalline axis; Type II phase-matching, in which the input beams have perpendicular polarizations, is then used for sum frequency mixing. On the other hand second-harmonic generation itself can be thought of as a special case of frequency mixing, in which both input beams are identical. In the more general case, a beam of frequency ω 1 combines with a second beam of frequency ω 2 through the second-order susceptibility of a nonlinear crystal to produce a new beam of frequency ω 3. When ω 2 = 2ω 1, then ω 3 = 2ω 1 + ω 1 = 3ω 1, and the output is the third harmonic of the fundamental. In contrast, frequency tripling is a thirdorder effect in which one fundamental beam (the equivalent of three beams at ω 1 ) produces in a single crystal a new beam at ω 3. The problem arises from the requirement that the fundamental beam and the tripled beam stay in phase in the crystal that is, they must be phase-matched[25]. In the quantum picture, phase-matching is equivalent to satisfying the conservation of momentum for the three photons that are converted into one photon with three times the individual energy. As it turns out, the efficiency of THG in an infinite, uniform nonlinear medium is zero, even with perfect phase-matching. This is also the case for most practical nonlinear materials. The frequency-tripled waves generated in different 35

42 regions of the crystal interfere destructively, resulting in net zero THG. Although frequency-tripling is not a practical route to THG, tripling can take place directly in a non-isotropic medium[26]. Unlike second-order nonlinear coefficients, which vanish in some materials because of crystalline symmetry, all materials possess a third-order coefficient. In practice then, the same second-order nonlinear process used for SHG is also used for THG via sum frequency mixing. This is true for commercial systems that produce fourth- and fifth-harmonic output as well. A fundamental beam is first frequency doubled, then either doubled again to obtain the fourth harmonic, or sum frequency mixed for THG, which is then mixed with the SHG beam to produce the fifth harmonic. Producing these harmonics directly is extremely difficult, because the infrared (IR) fundamental has to phase-match with the UV output[27]. Generally, type I frequency-doubler and type II frequency-tripler will be the best design for THG which needs no polarization rotator. However, when a type II KTP crystal is used as frequency-doubler and type II LBO as frequencytripler (see the Figure 1.15), the laser polarizations coming out from KTP are not optimized for THG. Therefore we need to change it into its optimum, a polarization rotator can do it, in which a common 1/2 wave phase retardation plate could only rotate the polarization of 532 nm to a specific angle. However, the linear polarization of 1064 nm will be distorted to be elliptical. The THG-PR rotator is specially designed to maintain the linear polarization of 1064 nm (l plate) and change simultaneously 532 nm (l/2 plate) to the angle you need. The THG-PR can be applied to the following THG various configurations[28]: 1. Type II (SHG) + Type II (THG) 2. Type I (SHG) + Type I (THG) 36

43 3. Type II (SHG) + Type I (THG) Figure 1.15: Sum frequency generation using type II and type II nonlinear crystals [28] 1.7 Sum Frequency Generation Conversion Efficiency The basic physical description of SFG is very similar to SHG. The primary difference is that, in SFG, two input fields at frequencies w 1 and 2 w 2 are combined in a c material to generate a new field component at frequency w3 = w1+ w2. The nonlinear polarization resulting from two input fields, w1 and w2 is derived in the same manner as(1.1.) and is found to be[29]: 1.25 This expression shows that this polarization is able to generate new field components at frequencies 2w 1,2w 2, w 1 + w 2 and w1 -w 2. These frequencies represent the processes of SHG of frequencies w 1 and w 2, 37

44 respectively, SFG and difference frequency generation (DFG). Here in the present work we suggest that the production of harmonics may occur by a cascading process. We mean by cascading that the higher generations are produced by successive pumping of successive NLO crystals starting with a fundamental beam. In the harmonic production by cascading process we expect mixing is possible between the fundamental with the second harmonic for the third in the process called sum frequency generation. Such that the SFG efficiency can be expressed with respect to the fundamental in all cases, thus[30]: h SFG = I d Il I = sinc p eff e0cn1n 2n3ls Ł Dkl ł Conversion Efficiency Enhancement The conversion efficiencies for both second harmonic and that of sum-frequency generation can be enhanced in various ways[31] : - Adjust D k = 0 termed as phase-matching - Focusing of the input intensity - Walk-off Compensation - Double pass, Multi-pass techniques In our project we used an optical system utilizing nonlinear crystals in such a way to overcome the difficulties exhibited with prior critically phase-matched systems and to provide significantly improved performance in such system. This system utilizes a pair of nonlinear crystals in a linear cavity. The crystals in the crystal pair being so aligned as to cause spatial compensation for the walk-off produced,thereby 38

45 achieving a substantial improvement in the frequency-doubling and sumfrequency efficiencies[ 32,33] Walk-off Compensation Frequency tripling of IR lasers has two main non-linear optical methods,either direct or indirect. Although there are many nonlinear crystals that can be used for these two methods, lithium triborate (LBO) crystals are the most common for IR high power lasers[34], owning to their deep UV transparency, large nonlinearity, relatively small walk-off loss, and high growth yield. The LBO crystal for the IR- to- green conversion can have non-critical phase matching(ncpm) condition, while the one used to mix the IR and green to UV cannot. This results in beam walk-off which lowers the conversion efficiency. Walk-off loss can be a serious problem in the UV conversion of low- peak-power IR lasers, which is common in the development of materials processing, thus for high conversion the low peak power beams should be focused in small size, which makes the walk-off loss serious. Several methods to compensate for the walk-off loss have been suggested[35-37]. An experimental results has been achieved according to theoretical models proposed by many authors using various types of nonlinear crystals. According to these studies Alpha Barium Borate crystals are thought to be the best materials for walk-off compensations [34] Collimated Gaussian Beam Laser Source In this section we apply the methods to enhance the harmonic conversion efficiency if the laser source is collimated Gaussian beams, 39

46 where the confocal parameters comparable to the crystal length. We have used a certain crystal arrangement in type A and type B mixing scheme. In type A mixing the two input beams have parallel Poynting vectors, but the product beam walks off from them. In type B mixing the Poynting vectors of the input beams are not parallel, and the Poynting vector of the product beam parallels one of them. Type A includes collinearly phasematched mixing of two o(e) waves to generate an e(o) wave, while type B includes mixing an e and an o wave to produce an e or an o. More generally, any process can be forced to be either type A or type B by tilting the input beams in the appropriate way. For example, tangentially phase-matched sum-frequency generation in a negative uniaxial crystal uses two o input beams, but one is tilted to propagate parallel to the Poynting vector of the product e wave. This is type B, even though both input beams are o polarized. Similarly, mixing an e and an o wave is type A if the e input beam is tilted so its Poynting vector parallels that of the o input beam. Unfortunately these noncollinearly phasematched processes cannot be walk-off compensated by means of crystal segments of alternating walk-off direction except for plane waves, but the discussion below otherwise applies to these situations as well as to collinear phase matching[38] Type A Mixing In this context collimated Gaussian beams have a Gaussian spatial profile and are weakly focused at the center of the crystal, with a confocal length much greater than the crystal length, implying that the phase fronts are nearly planar throughout the length of the crystal. Figure (1.16) illustrates spatial walk-off and two crystal compensation. 40

47 Figure.1.16: Beam behavior in a birefringent crystal for type A frequency doubling in a single crystal (upper) and in two walk-off compensating crystal segments (lower)[38]. Consider first the influence of spatial walk-off on single-crystal mixing efficiency for beam diameters comparable to or smaller than the birefringent walk-off, r L. We assume the input beams have equal widths W in the walk-off direction and heights H in the other transverse direction. Each z slice of the crystal radiates a product field in a Gaussian beam of width W and height H offset in the walk-off direction by - rz relative to that radiated by the Z = 0 slice. The fields from all contributions are equal and combine in perfect phase if D k = 0. The reduction in power due to walkoff can be expressed by the following empirical expressions for the mixing efficiency. For type A sum and difference-frequency mixing of cw Gaussian beams with identical spatial profiles in a single crystal, the product power is given by[38]: P - ( ) d PPL Ø 1 ø = Œ œ WH n n n Œº ( rl/ W) œß eff l

48 where the quantity in braces is a walk-off correction term derived from modeling. For mixing two input beams with identical spatial and temporal Gaussian profiles, the pulse energy is[38] U - ( ) d UU L Ø 1 ø = Œ œ TWH n n n Œº ( rl/ W) œß eff l The subscripts 1 and 2 refer to input light of frequencies w 1 and w 2, and subscript 3 refers to light at the generated frequencyw 1 w 2. Units are millimeters for W, H, and L; seconds for T; nanometers for vacuum wavelength l ; watts for P; joules for U; and pm/v for d eff. The quantities W, H, and T are FWHM irradiance values for the beam widths and pulse duration. For second harmonic generation, half the input power or energy should be assigned to P 1 or U 1 and half to P 2 or U 2 [38,39]. If the crystal is divided into two walk-off-compensating segments of length L/2, in this method of transformation in sequentially placed these crystal parts with spatial compensation of the walkoff i.e. walkoff compensation(woc) enables to solve, partly, the problem of spatial dispersion of media. Its essence is that for non- axial components of radiation the phase difference between two waves resulted in the first crystal may be compensated in the second one which is turned around the axis of radiation at The lower diagram of Fig.1.16 shows this arrangement scheme, the area of the product beam is reduced, and its power is correspondingly increased. It should be evident, based on the product-beam area, that the efficiency can be calculated by replacing r in Eqs. (1.27) and (1.28) with r /2. More generally, cutting the crystal into 42

49 N segments reduces the effective walk-off angle by N, improving the conversion efficiency by the amount indicated by Eqs. (1.27) or (1.28) with r replaced by r / N [39] Type B Mixing Figure 1.17 depicts type B mixing. This diagram illustrates how a large walk-off limits the effective interaction length to l» W / p for two input beams of width W. Figure 1.17: Beam behavior in a birefringent crystal for type B frequency doubling in asingle crystal (upper) and in two walk-off compensating segments (lower)[37] For type B mixing with collinear input beams of identical Gaussian spatial profiles exactly overlapped at the input face of the crystal, the correction terms in Eqs. (1.27) and (1.28) are replaced by : 2 4 Ø º ( rl/ W) + 1.0( rl/ W) ø ß 1 1/

50 Higher efficiency is possible by offsetting the input beams so that walkoff causes them to cross midway through each crystal segment rather than at the input face. The coefficients 0.6 and 1.0 under the radical are then replaced by 0.15 and 0.095, respectively, reflecting an efficiency enhancement greater than three for large walk-off ( r L= W ). A greater mixing efficiency is possible by increasing the width of the beam that walks- off to approximately r L and positioning it to be centered on the other input beam at the crystal center. Modeling indicates that if the beam width (FWHM) is set to the greater of W or 0.6 r L, the efficiency is nearly identical to that for type A mixing, and Eqs. (1.27) and (1.28) apply, with W or T referring to the smaller input beam. In any of these situations, walk-off compensation in N segments can be accounted for by replacing r with r / N [38]. 1.8 Historical Review Of Optical Harmonic Generation The field of nonlinear optics has just entered its fifth decade, and while the early years of the discovery were mostly characterized by studies of the phenomenon itself and the understanding of the basic physics, the last two decades were devoted to high performance novel nonlinear devices and to the development of new phase-matching techniques. It was the invention of the Ruby laser in 1960 that first enabled scientists to explore the behavior of light in optical media at high intensities. Although the birth of the field of nonlinear optics is often taken to be the first observation of second-harmonic generation by Franken et al. in 1961 [40], in fact the rudiments of this field started much earlier. Parts of this early history can be traced back to work performed at 44

51 The Institute of Optics, and research in nonlinear optics has thrived at the Institute ever since. The earliest report of a nonlinear optical effect known to the author is that of G. N. Lewis, who in 1941 reported saturation with increasing excitation strength of the fluorescence intensity of the organic dye fluoresce in a boric acid glass host [41]. In fact, the author with his students Mark Kramer and Wayne Tompkin became very much intrigued by this material system. One of the most interesting applications of the first laser was the investigation of the nonlinear interaction between light and matter,thus it was not long after Franken s experiment that Armstrong et al. [42] published the classic paper in which he investigated the microscopic origins of the nonlinear susceptibilities and the interactions between light waves in a medium with such nonlinear susceptibilities. Experimental observations of NLO processes such as, second harmonic generation (SHG) and sum-frequency generation (SFG), all of which will be discussed in subsequent chapters, resulted in the rapid growth of NLO as an important area of scientific research. An important step in laser technology was the ability to produce a pulsed output. Early laser pulse generation was achieved with Q- switching, which uses an electro-optic modulator, such as a Kerr cell, to generate pulses of much greater intensity than the previous continuouswave (CW) output. The typical pulse durations of early Q-switched lasers were on the order of several 10 s of nanoseconds, the first pulses being around 120 ns in duration [43]. Pulses in the picosecond domain were achieved with the development of modelocking [44], which has remained the standard method of laser pulse generation. This technique produces pulses by locking the laser cavity s longitudinal modes in phase so that 45

52 once every cavity round trip, they constructively interfere to generate a pulse shorter and more intense than with Q-switching alone. The first experimental investigations of third harmonic generation (THG) in crystals with cubic nonlinearity were performed back in [45] ; the authors of these investigations confined themselves, however, only to a determination of the nonlinear susceptibilities of third order of different crystals, and to a determination of the synchronism conditions. The theory of THG, which was developed in approximately the same years [46, 47], did not go beyond the frame of geometrical optics of homogeneous beams. In such an approximation (essentially for plane unmodulated waves), an analysis was made of the dependence of the process of frequency tripling on the detuning of the wave vectors, the attenuation of the waves in the medium, the self-action of the waves (nonlinear detuning), and the reaction of the harmonic on the pump. Results of a theoretical and experimental investigation of third harmonic generation in media with an inversion center are reported. THG in isotropic and anisotropic media is considered in the quasi-optical approximation. A frequency tripler for a single-mode laser with an output power of 1 MW/cm 2 is described[47]. In the 1970's the thermal effects on the phase matching in a nonlinear optical crystal have been studied [48]. The nonlinear optical properties of the nonlinear crystals have been determined in many techniques [ 49, 50]. New nonlinear optical crystals families had appeared like HCOOLi.H 2 O,HCOONa and HCOOLi 0.9 Na 0.1..H 2 O crystals,[51,52]. The operation of harmonic generation with crystal temperature control offers significant advantages in controlling the phase matching of the nonlinear crystals. 46

53 In the 1980's W. Seka et al produced an efficient conversion from to 0.35 micron by third harmonic generation in two type II KDP crystals was reported. Energy conversion efficiencies of up to 80% have been measured under conditions applicable to large glass laser systems. A new tripling scheme used for these experiments requires a minimum of optical components and is insensitive to exact crystal alignment and laser beam divergence. A convenient scaling law allows tripling optimization for many different laser conditions[53]. R. Craxton achieved a comparison of three schemes ("angle-detuned," "polarization-mismatch," and "polarization-bypass") permitting high efficiency frequency tripling of 1 μm laser radiation. The overall characteristics of each are examined in terms of sensitivity to input intensity, polarization angles, and mismatch angles. The "polarization-mismatch" scheme is favored for tripling current high-power 1 μm Nd:glass laser radiation with KDP crystals. All schemes permit the tripling of some shaped pulses without substantial degradation in efficiency[54]. During the processes of harmonic generation using both intra-cavity and extra-cavity scheme conversion is conceptually simple and elegant, many difficulties appeared like optical damage to the nonlinear crystal caused by the high electric fields necessary for nonlinear conversion. Another limitation for achieving high harmonic generation has been the poor beam quality in the intra-cavity configuration of the pump sources themselves [55]. The first problem had been overcome because new nonlinear crystals with high damage thresholds had been developed, for example KTP, BBO, and LBO [56]. The KTP crystal had been shown to be especially useful optical material. Its large nonlinear optical coefficient combined with a high optical damage threshold make it 47

54 particularly attractive for frequency doubling and parametric generations [57-59]. In mid 1980's the second problem had been overcome because diode pumping had provided a new generation of efficient high power solid state lasers with single transverse mode outputs and a high degree of pulse to pulse stability which is especially efficient for extra-cavity scheme [55].In the 1990's many designs and applications had been developed in production and enhancements of SHG and THG processes and UV lasers productions. A more than 1 m w of tunable continuouswave radiation at 369 nm has been generated by sum-frequency mixing of the radiation from a 1310-nm diode laser with the radiation from a 515-nm argon-ion laser in a beta-bab(2)o(4) crystal has been obtained by Sugiyama K et al [60]. In the same year J.J. Zondy design a theoretical model for type I and type II second harmonic generation,the results obtained show the beam walkoff between the pump polarization waves in type-ii interaction may be regarded as an additional absorption in a type-i interaction experiencing the same walkoff angle and also for type-i SHG, the criterion of optimum focusing becomes meaningless in type-ii coupling as the walkoff angle or the crystal length increase[61]. I. V. Tomov et al demonstrated an experimental results on the cubic nonlinear susceptibility of barium metaborate for the generation of phase-matched third-harmonic generation (THG) of µm pump radiation. The various processes that are responsible for THG was achieved for types I and II phase matching. THG power of 50 µw is recorded with an average pump power of 800 mw of 1-kHz repetition rate picosecond pulses[62]. After two years Jean-Jacques Zondy et al studied second harmonic generation using a pair of two identically cut KTP crystals in a critically 48

55 phase-matched. A single-pass increase as great as times the conversion efficiency of a single crystal is obtained [63]. The high harmonic conversion efficiencies due to zero phase mismatching was the great demand for a new nonlinear crystals and the discovery of the nonlinearity that in its principle of operation depends on periodic poling gives higher results on these efficiencies[64]. K. Kintaka et al proposed and first demonstrated an LiNbO 3 waveguide device with cascading quasi-phase-matched second harmonic generation and quasiphase-matched sum-frequency generation for generation of a third harmonic wave. Ultraviolet light of 355 nm wavelength, which was the shortest value ever reported for LiNbO 3 waveguide wavelengthconverters, was obtained with Nd:YAG laser light[65]. G. C. Bhar et al studies a Tunable ultraviolet radiation in the nm region that has been generated with beta barium borate crystals by type I sum-frequency mixing. A conversion efficiency of 21% at nm has been obtained with input power densities as low as 28 MW/cm 2 for the fundamental and 2.4 MW/cm 2 for its second-harmonic radiation [66]. D. Taverner et al investigated the pulse energy conversion of SHG and THG using the more practical, all solid-state source, MOPA-pumped, Q-switch source. In the initial experiments two PPLN samples 1 and 2 and the Q-switch laser operating at reduced output a maximum SH conversion efficiency of 62% has been obtained. On the other hand the maximum THG conversion efficiency of 15% was obtained. The reduced efficiency results is mainly due to the Gaussian temporal profile of the fundamental pulses which gives low SH conversion in the pulse wings[67]. At the beginning of the third millennium, the problem of finding the optical beam that generates the sum or difference frequency with the greatest possible efficiency in homogeneous crystals with second order 49

56 nonlinearity is tackled and solved[68]. In the same year a multicrystal means of compensating for the thermally induced phase mismatch encountered in the generation of high average power UV radiation is described by S. Wu et al. The concept is experimentally tested with a Nd:YAG laser 4th harmonic generator based on two β-bab 2 O 4 (BBO) crystals. Single versus two crystal results demonstrate that this design compensates for the thermally induced phase mismatch, effectively increasing the interaction length of nonlinear optical crystals during harmonic generation under high loading[69]. J. Yu-Lei et al obtained a maximum of 310 mw average output power at 355 nm by extracavity frequency tripling with a BBO crystal in a Q-switched Nd:YVO 4 laser with 11.2 W of laser diode pump power. The single pass frequency conversion efficiency (infrared-to-ultraviolet) is 14.3%. The power stability of the ultraviolet laser is better than 1% in 30 min[70].a generation of deep ultraviolet radiation at 210nm by type-i third harmonic generation is achieved in a pair of BBO crystals with conversion efficiency as high as 36% has been obtained by G. C. Bahar et al [71]. An experimental results has been demonstrated for an intracavity type I sum frequency mixing of 1.06m m and 532nm in YCOB crystal. Three type II phase matching KTP crystals with different lengths were used to generate 532nm from 1.06m m. The maximum ultraviolet output power of 1305mW was obtained with 15mm KTP crystal for continuous operation, while the maximum ultraviolet average output power of 124mW was obtained with a 10mm KTP crystal for Q-switched operation[72]. An experimental developments in material sciences have generated hope that it will be possible to devise optical media where the difference in group velocity between the fundamental and third harmonic may be 50

57 strongly suppressed. Under these circumstances both pulses would travel together over a long distance. This would lead to an enhancement of the generation process, and hence strong focusing and/or using ultra-short pulses might not be crucial. This is very beneficial for the efficiency of third harmonic generation, even increasing it by a factor of two or more[73]. Zhipei Sun s team achieved a laser that is operated in Q- switched mode at 1.3micron fundamental and internally frequency tripled using two LiB 3 O 5 (LBO)crystals. A 4.3W average power at 440nm was demonstrated at 3.5kHz[74]. An experimental results of 17.7 W average power output at 355nm by the third harmonic generation of 1064nm light has been achieved by Wu Yi- Cheng and his team. A CBO type II phase matched crystal is used. The THG energy conversion efficiency with CBO is twice as large as that with LBO[75]. After one years Haibo Peng et al designed High-power, quasi-continuous wave blue laser output is obtained by intracavity frequency-tripling of a µm Nd:YAG laser with two LiB 3 O 5 (LBO)crystals. A 7.6 W average power at nm was demonstrated at 5 khz[76]. C. X Wang et al reported a high power UV generation with TEM 00mode output powers in excess of 30W in Q- switched end-pumped Nd:YVO 4 and side pumped Nd:YAG lasers using extra-cavity sum frequency generation in LBO. With this system arrangement a 32W output power at 355nm have been achieved[23]. Fu-qiang et al obtained an experimental results for third harmonic generation at 355nm with an output power of 1.32W is achieved at the incident pump power of 27.5W, corresponding to an optical-to-optical efficiency of 4.8%[77]. X. Ding and his team reported a blue-violet laser obtained by intracavity frequency-doubling of an all-solid-state Q- switched tunable Ti:sapphire laser, which was pumped by a 532nm intracavity frequency-doubled Nd:YAG laser. A (BBO) crystal was used for frequency-doubling of the Ti:sapphire laser. At an incident pump 51

58 power of 22W, the tunable output from 355nm to 475nm was achieved, involving the maximum average output of 3.5W at 400nm with an optical conversion efficiency of 16% from the 532nm pump laser to the blueviolet output[78]. Liu Huan achieved a laser diode-end-pumped Nd : YVO 4 in an intra-cavity frequency-tripled quasi-continuous 355 nm laser. The efficient second and third-harmonic generation is generated by two lithium triborate (LBO) crystals. An average 355 nm laser with output power of 245 mw was obtained at a pump power of 6.76 W, a pulse repetition rate of 20 khz and the highest optical-to-optical efficiency of 3.62 %[79]. X. Ya et al demonstrated a high repetition rate extra-cavity third harmonic generation of 355nm at high beam quality. A 30.2 W TEM 00mode 355nm UV laser was obtained with two stage amplifier MOPA laser, and the optical to optical(1064nm to 355nm) conversion efficiency was up to 30%[80]. Bin Li et al developed a high efficiency extra-cavity third harmonic generation at 355nm a Q-switched Nd:YAG diode pumped laser has been used with an input pump power of 25W, average power of 3.2W third harmonic radiation at 355nm was obtained the optical to optical (1064nm to 355nm)conversion efficiency was up to 47.4%[81]. An experimentally demonstrated compensation of the second harmonic radiation walk-off with respect to beam of initial frequency has been done by V. V. Kiyko and his team, as a result the third harmonic conversion efficiency within sequentially placed LBO crystals was increased in the order more than three times[82]. The development of compact conversion efficiency optical tripler which generates a beam with small divergence and high angular stability is currently a topical problem. In the past, many efforts had been made to increase the optical 52

59 conversion efficiency for both doubler and tripler as well as the optical beam quality. Thus a passively Q-witching of solid state laser with a saturable absorber can provide a reliable pulsed operation with the benefits of high stability, inherent compactness, and low cost. In this way an experimental results was developed using a passively Q-switched laser to perform the extra-cavity harmonic generations, the maximum average output power at 355nm was 1.62W for an incident IR power of 6.2W[83]. The high power UV lasers based in harmonic generation have been in the great demand for many applications because of the low maintenance cost and the stability. Thus the search for new nonlinear crystals is so demanded for this purpose, L.R. Wang et al investigated a third harmonic of a Nd:YAG laser with nonlinear crystal La2CaB ( ) 10O LCB 19 a maximum output power of 31.6 W at 355nm is obtained [84]. A great progressing on finding new nonlinear crystal researches nowadays is focusing on finding new high quality, good chemical and thermal stability NLO crystals for UV light generation and their optical properties evaluation. A CsB O ( CBO ), ( 3) 8 Na La O BO (NLBO) and CsLiB O ( ) 6 10 CLBO can be applied in THG conversion fields, LBO is widely used in THG effect study after many years research because it has a good THG conversion efficiency, high pumping energy, small spatial walk-off angle and large size of crystals[85]. C.Jung et al achieved a theoretical and experimental study of a novel walk-off compensation method for efficient UV beam generation. A 30% enhancement in the UV beam generated was achieved by using an alpha barium borate crystal as a walk-off compensator in which the power of the generated UV beam increased 1.9 times[86]. Y.J. Huang et al achieved an experimental results which employed the 53

60 optimized high power Q-switched laser without parasitic lasing to achieve highly efficient extra-cavity harmonic generation. At pump power of 44W,the output powers at 355nm and 532nm as high as 6.65W and 8.38W was obtained. The optical to optical conversion efficiencies from 1064nm to 355nm and 808nm to 355nm are up to 38.2% and 15.1% respectively[87]. H Chen and his team demonstrated a novel 355nm ultraviolet (UV) laser operating at ultrahigh repetition rate from 300 khz to 1 MHz. For 400 khz the corresponding conversion efficiency as high as 41.6% [88]. 1.9 Aim Of The Work The experiments discussed in the body of this thesis were performed using an experimental technique to generate the 2 nd and 3 rd harmonics of a passively Q-switched Nd:YAG laser system at 532nm and 355nm, respectively. Pulses on the order of nanoseconds have been previously used in the lab to generate these wavelengths, however the current Nd:YAG laser system produces pulse duration of 12 ns. The high average power and high beam quality are important for various demands in both scientific and industrial applications in many fields such as material microprocessing,optical printing, optical treatment, spectroscopic analysis and scientific research in general compared with traditional gas lasers such as HeCd (325nm) or N 2 (337nm) lasers the most obvious advantage of all solid state UV lasers are the long lifetime, high efficiency and compact size. All these demands makes the headlines of this project. The goal of this project is: 54

61 1- Generation of a 532nm and 355nm pulses of various energies in order to obtain the optimum and the maximum harmonic conversion efficiencies for SHG and THG in visible and UV regions respectively. 2- An improvement in the spatial interaction length of the interacting waves using a walkoff and non walkoff compensation techniques for twin and non-twin nonlinear crystals will be presented in order to study the enhancements in the specified conversion efficiencies for both second and third harmonic generations. 3- Obtain the temporal and spatial beam profiles of laser pulses for various crystal arrangements schemes for SHG and THG will be presented and discussed. The performance of the various setups and the results of the pulse energy and characterization measurements will be presented by which the whole description of many nonlinear parameters and techniques used to characterize the generated second harmonic generated and UV pulses such that the optimum design configuration for both SHG and THG will be presented. 55

62 56

63 Frequency Doubling With LBO And BBO Nonlinear Crystals 2.1 Introduction In the present work we suggested a model to find an efficient method for the generation of second and third harmonics of Nd:YAG laser operating on 1064nm wavelength based on cascading technique. The model involves optimization parameters that can be manipulated to enhance the efficiency. In our project is to study experimentally the possibility of finding UV laser light from laser light interaction with certain nonlinear crystals. The justification for such effort is based on the fact that UV laser is needed for many applications especially in molecular studies of many materials. This UV laser can be found from the halide excimers (ArF, XeCl and KrF).The drawbacks of these lasers are, that they use corrosive gases and need high voltage discharges as well as regular maintenance in addition to the fact they are bulky in themselves[83]. Also obtaining UV lasers from direct a solid state material is so difficult since their upper state lifetime is very short. Hence the powerful technique we present here provides maintenance free and compact size laser source. This technique is the cascading harmonic generation of higher orders using extra-cavity configuration. In addition to what mentioned above we carried out experimental work for enhancements of harmonic generation either in SHG stage or in SFG stage on a non-walk-off (NWOC) and walk-off (WOC) compensations schemes. This chapter outlines the experimental arrangement setups used to achieve second harmonic generation as a first stage followed by sum frequency generation stage for UV laser production based on cascading techniques as well as the harmonic generation enhancements schemes. 57

64 2.2 NLO Crystal Properties This section reviews some nonlinear crystals that have been used in our project for the design of the SHG and SFG Lithium Triborate (LiB 3 O 5 ) LBO Lithium triborate (LiB 3 O 5 or LBO) is a biaxial crystal with wide spectral range,and it is one of the most popular crystals especially for high average power SHG owing to wide acceptance angle and small spatial walk-off. However, the effective nonlinear coefficient of LBO, which is d eff = 0.85pm/V, limits it s SH conversion efficiency. The second drawback of this crystal is the hydrophobic [106] properties. Some optical properties of LBO crystal are listed in Tables 2.1. Table 2.1: Optical and nonlinear optical properties of LBO crystal[89] Transparency Range SHG Phase Matchable Range Therm-optic Coefficient (/ C, λ in μm) Absorption Coefficients Acceptance angle Temperature Acceptance Spectral Acceptance nm nm (Type I) nm (Type II) dn x /dt=-9.3x10-6 dn y /dt=-13.6x10-6 dn z /dt=( λ)x10-6 <0.1%/cm at 1064nm <0.3%/cm at 532nm 6.54mrad cm (φ, Type I,1064 SHG) 15.27mrad cm (θ, Type II,1064 SHG) 4.7 C cm (Type I, 1064 SHG) 7.5 C cm (Type II,1064 SHG) 1.0nm cm (Type I, 1064 SHG) 58

65 1.3nm cm (Type II,1064 SHG) Walk-off Angle NLO Coefficients 0.60 (Type I 1064 SHG) 0.12 (Type II 1064 SHG) d eff (I)=d 32 cosφ (Type I in XY plane) d eff (I)=d 31 cos2θ+d 32 sin2θ (Type I in XZ plane) d eff (II)=d 31 cosθ (Type II in YZ plane) d eff (II)=d 31 cos2θ+d 32 sin2θ (Type II in XZ plane) b -Barium Borate Crystal (BBO) The other NLO crystal used to generate the second harmonic of the fundamental wavelength in the present experimental work is a b -barium borate crystal ( b - BaB2O4 or BBO). This crystal is a negative uniaxial crystal and it has an effective nonlinear coefficient of d eff = 2.09pm/V and also it has wide spectral range. Table (2.2) shows some of optical and NLO properties of borate crystals. Table 2.2: Optical and Nonlinear Optical Properties of BBO[89] Transparency Range nm SHG Phase Matchable Range nm (Type I) nm (Type II) Therm-optic Coefficient (/ C) dn o /dt=-16.6x10-6 dn e /dt=-9.3x10-6 Absorption Coefficients <0.1%/cm at 1064nm <1%/cm at 59

66 532nm Acceptance Angle 0.8mrad cm (θ, Type I, 1064 SHG) 1.27mrad cm (θ, Type II, 1064 SHG) Temperature Acceptance 55 C cm Spectral Acceptance Walk-off Angle 1.1nm cm 2.7 (Type I 1064 SHG) 3.2 (Type II 1064 SHG) NLO Coefficients d eff (I)=d 31 sinθ+(d 11 cos3φ- d 22 sin3φ) cosθ d eff (II)= (d 11 sin3φ + d 22 cos3φ) cos2θ 60

67 2.3 Experimental Setup In the present experiment a Q-switched Nd:YAG laser has been used which consisted of a high peak power oscillator with excellent gain medium for efficient 1064nm wavelength especially for operation at stable high peak power Q-switched laser. A xenon flash lamp was used to pump the Nd:YAG laser rod as a laser medium of (f =4mm) 6mm and a 1% of Nd ions concentration. Both the front and the rear face of the rod are antireflection coated (AR) at 1064nm wavelength. To achieve high peak power laser pulses of short duration, a passive Q-switch is used in this system. It involved the inserting of a retard prism of 100% reflectivity to the 1064 nm wavelength placed as a rear mirror of the laser cavity. Its front face is coated with a BDN-II chemical dye material which has a high absorption at the wavelength 1064 nm and can be saturated with a very short (12-30 ns) relaxation time. Therefore, it will act as a passive Q - switch. The power supply for driving the Nd:YAG laser represents the electrical part of this system. It consists of the following unit: a- Charging and PFN unit, b- Ignition (trigger) unit Figure 2.1 shows HV power supply block diagram, while Figure 2.2 shows the entire circuit diagram. There are two primary sections, a DC to DC step-up inverter, and a trigger circuit for the xenon flash tube in the laser head. 61

68 DC To HV Trigger 24 AC Transform Transform Voltage control Figure 2.1: HV switch mode power supply The inverter circuit is composed of four transistors, Q 1 through Q 4. Q 1 and Q 2 form a push-pull multivibrator with a frequency of about 880 Hz. The outputs at the collectors of Q 1 and Q 2 are approximately square waves with a 180 degree phase difference. The square wave outputs directly drive the gates of power MOSFETs Q 3 and Q 4, resulting in an AC square wave signal driving the primary of TR 1, the step-up ferrite transformer, which is a standard 24V CT,5A to 750 V unit. The output of TR 1 is fed into a half wave rectifier, which consists of D 1 and D 2 resulting in a charging voltage of about V across C 5. The trigger circuit consists of Q 5, C 6, R 1, R 6, R 13, U 2 (SCR) and TR 2 the trigger transformer. Initially, U 2 is non-conductive (off) and a sample voltage from the main capacitor (C 5 ) charges the capacitor C 6 to 150 V through R 13. When a trigger current is applied to either as a single pulse or as a train of pulses with 1 Hz fed from a pulse generator the gate of U 2, it turns on, rapidly dumping the charge from C 6 into the primary of the trigger transformer TR 2, which then steps the pulse up to approximately 10 kv. The 10 kv pulse is applied to the trigger electrode of the xenon flash tube; the pulse provides enough ionization of the xenon gas to allow the tube to fully conduct, pulling the energy from the main capacitor C 5. 62

69 U 2 turns off as C 7 discharges, and the tube ceases conducting once the anode to cathode voltage falls below about 50 volts, preparing the circuit for another firing cycle. Resistor R 12 helps guarantee lamp commutation (shut-off), but may be omitted to obtain higher speed strobes (the circuit can easily operate over 3 Hz even with R 12 in place). A charging control is accomplished in this circuit which consisted of a voltage comparator U 4 (LM 324). This IC if feed with two voltage samples one directly from the low voltage DC supply (24v) which represents the reference voltage while the other one is from the main high voltage. When the HV sampled exceeding that of the reference voltage the comparator output initialize the relay through transistor Q 6 this intern stops the charging current of TR1. 63

70 Figure 2.2: Power supply for driving the Nd:YAG laser The Nd:YAG laser source has a typically an arbitrary polarization. The state of polarization of the beam is very critical in configuring the experimental layout regarding the NLO crystal orientation because unpolarised emission can be a significant disadvantage giving lower than expected conversion efficiencies because the laser can lase in a nonphase-matched polarization. Using a linear polarizer the direction of the polarization is determined to be parallel to the plane parallel to the front plane of the NLO crystal. 64

71 2.4 LBO Crystal In SHG Experiment Figure 2.3 shows the optical setup for second harmonic generation, while the photograph of the same optical setup is depicted in Figure 2.4. A type I ( o o e ) critical phase-matching (CPM) LBO crystal was used as the frequency doubling crystal, and it was cut at θ 90,φ 19.6 with dimension of mm, and the temperature of the crystal was at room temperature. This crystal and all others were provided by the ATOM Optics Company LTD. Both the entrance and the exit surfaces of the LBO crystal were antireflection (AR) coated at 1064 nm and 532 nm wavelengths. Although this crystal has a high damage threshold (15 Gw/cm 2 for λ 1064 nm, pulse duration 0.1 ns), but unfortunately the AR coatings on the crystal surfaces are not, this compel us to use a laser beam intensity not exceeding the damage threshold of the AR coating which is of the order 850Mw/cm 2. For this purpose a multifocusing lens have been used to focus the laser beams in the various nonlinear crystals. P L 1 L 2 Nd:YAG LBO 1064nm x 1 x 2 x 3 F Figure2.3: Second harmonic generation arrangement where P is linear polarizer, L 1 &L 2 are lenses and F is 532nm narrow band filter 65

72 Nd:YAG polarizer Lenses Crystal 532nm Joulemeter Figure 2.4: A photograph of experimental setup for SHG On the other hand the nonlinear crystal mounting and alignment is achieved by using a crystal mounts that are made from aluminum and Teflon. They were used for safe and convenient handling of nonlinear crystals. A two nonlinear crystal mounts have been constructed in this research. They are independent, although of course they are coupled through the optical interaction. Nominally each crystal used was housed inside a Al cylinder fixed on xy-holder and then on micrometer translation stage with the x-y screws and crystal rotation. The orientation of the optimum phase matching angle is determined, and then by a micrometer translation the position of the optimum pumping spot size is realized. The design philosophy was to stabilize the crystal angle according to the incident IR laser beam polarization and measure data at a perfect phase matching of the crystal according to measurements. The fundamental laser beam(1064nm) of the oscillator is focused in the non- 66

73 linear crystal by a (AR coated) collimating lenses system consisted of a fixed focal length(300mm) plane convex lens L 1 and a set of various focal lengths L 2 ( from )mm plane convex lens. With this optical arrangement we obtain a various beam waists inside the nonlinear crystals of the order (0.33-1) mm and a higher laser beam intensity inside the NLO crystal is a achieved as well. The spot of the generated second harmonic of 1064nm is measured using a slit. The slit is scanned through the spot to measure its size. This focusing scheme is necessary when using a nonlinear crystal with a lower nonlinear coefficient (LBO) crystal when compared with Potassium Titanyl Phosphate (KTP) crystal. For instance the later has a higher nonlinear coefficient such that we don t need high beam focusing for SHG production. The separation among the various optical equipments of the system are (x 1 =x 2 =6cm, x 3 =30cm, x 4 is varied from 5cm to 15cm and x 5 =6cm). The orientation of the LBO crystal is determined according to the phase matching angle of the crystal and the polarization of the fundamental laser measured after the polarizer. A higher fundamental laser beam intensity as well as the precise rotation for NLO leads a good phase matching between the interaction wavelengths and produces higher SH generated energies and conversion efficiencies. The SH generated energies and the corresponding conversion efficiencies have been measured experimentally using a digital energy-meter provided by Genetc incorporation LTD which has a maximum measurable energy range of 3J and the spectral range from 0.19 to 20 m m measurements have been done in two steps:. These First when the infrared pumping energy of the laser source is kept constant at its maximum value and a variation in the second lens focal 67

74 length has been done which represents variations in a laser beam waist inside the LBO crystal. Second when the infrared pumping energy is varied from (4mJ to 24mJ ), while the beam waist inside the LBO crystal is kept at its minimum value (0.33 mm).that gives the maximum SH generated energies and maximum conversion efficiencies. For the separation between the SH generated wavelength (532nm) and the fundamental wavelength (1064nm) two methods have been used: The first one is by using (532nm) narrow band pass filter with a band width (10nm). The filter had more than 99.9% reflectivity at 1064 nm and 94.5% transmission at the 532 nm The 5.5% loss of green radiation at the dielectric filter was taken into account when estimating the total amount of generated second harmonic. The second method was by using a dispersive element such as a BK7 prism. 2.5 BBO Crystal In SHG Experiment The experimental setup depicted in Figures (2.3&2.4) for LBO NLO crystal were repeated for BBO crystal. Also a type I ( o o e ) critical phase-matching (CPM) BBO crystal has been used as the frequency doubling crystal but, it was cut at θ 90,φ 11.6 with dimension of mm, and the crystal was at room temperature. Although BBO crystal has a high damage threshold, but still we were suffering from the lower threshold damage of the NLO crystal AR coating. Therefore the same focusing scheme and beam waist variations inside BBO crystal have been used. Additionally the same procedures for obtaining the second harmonic generated energies and their 68

75 corresponding conversion efficiencies have been used. Eventually the same measuring equipments for LBO crystal have been used for BBO crystal as well. 2.6 Second Harmonic Generation With Walk-off Compensation There are two important multi-crystal arrangements, multi-crystals without walk-off compensation (MCNWOC) and other is multi-crystals with walk off compensation (MCWOC). These two schemes have been used in this research for SHG enhancement. The first NLO crystal was either BBO or LBO type I, while the second crystal was always LBO type I. The optical arrangements of these two crystals system has been discussed separately using either [LBO-LBO] or [BBO-LBO] crystals arrangements. Figure 2.5 (a & b) shows the general type I crystals arrangements on NWOC and WOC schemes respectively. The crystals in each pair being so aligned as to cause the second crystal to compensate for the walk-off produced by the first crystal, thereby achieving a substational improvement in SH generated energies and their corresponding conversion efficiencies Multi-Crystals In Non And Walk-off Compensation The multi crystals arrangements and orientations for NWOC and WOC were depicted in figure 2.5 (a & b). While the general schematic and experimental diagrams for multi crystal NWOC and WOC SHG setups are shown in figures ( ). 69

76 a b Figure 2.5: Type I NLO crystals arrangements on NWOC (a) and WOC (b) schemes P L 1 L 2 F Nd:YAG 1064nm Type I Type I x 1 x 2 x 3 x 4 X6 Figure 2.6: The schematic diagram of a multi-crystals in NWOC arrangement, where P is linear polarizer,l 1 &L 2 are lenses, F is 532nm filter According to this scheme a two type I ( o o e ) critical phasematching (CPM) crystals were used as the frequency doubling are either on non walk-off compensation (NWON) or walk-off compensation (WOC) arrangement. The two crystals were either twin or different(nontwin),but with the same dimensions of mm, and the two crystals were at room temperature. The front and rear crystals surfaces have AR coating at 1064nm and 532nm wavelengths. The two nonlinear crystals were arranged for non walk-off and walk-off compensation respectively. In the present configurations the two crystals are placed on separate rotational mount. Also the optical axis of both crystals was arranged as shown in figures 2.6 and 2.7 (i.e. crystals in the same 70

77 direction for NWOC and crystals in opposite direction for WOC configuration respectively).the same focusing lenses arrangements for the previous setup and as a result the same beam waist inside the NLO crystals have been used. The various optical equipments of the system are separated by the distances (x 1 =x 2 =6cm, x 3 =30cm, x 4 is varied from 5cm to 15cm, x 5 =6cm and x 6 =1mm). The SH generated energies and their corresponding conversion efficiencies are obtained using the same previous method and are sketched in figures mentioned in the next chapter. P L 1 L 2 F Nd:YAG 1064nm Type I Type I x 1 x 2 x 3 x 4 X6 Figure 2.7: The schematic diagram of a multi-crystals in WOC arrangement, where P is linear polarizer, L 1 &L 2 are lenses and F is 532nm transmission filter 2.7 Third Harmonic Generation At 355nm The crystals arrangement for THG and the polarization matching in frequency conversion process are shown bellow depicted in figure 2.8 o (1064 nm) o(1064 nm) e(532 nm) e (532 nm) o(1064 nm) o(355 nm) 71

78 While the experimental setup is shown schematically in Figure 2.9. The photograph for THG experimental setup is depicted in figure The scaled incident IR power from the laser source was focused by the same set of (AR)-coated lenses. The same method of smallest beam waist inside the NLO crystals has been achieved and then was delivered into the extra-cavity harmonic generation module. The THG module was composed of a type I critically phase-matched NLO crystal which was used as frequency doubling followed by a type II critically phase matched 0 crystal. The first crystal was cut at ( 90 0 used and cut at ( 90 0 q =, j = q =, j = 11.6 ) if BBO crystal was ) if LBO crystal was used,but both have the same dimensions of 3 3 5mm, while the second LBO crystal was 0 cut at ( q =, j = 90 ) with the same dimensions. Both faces of the SHG crystal were AR at 1064nm and 532nm while the THG crystal faces were AR at 1064nm, 532nm, and 355nm. Since we were using critically phase matched crystals, both were kept at room temperature. The various optical equipments of the system are separated by the same distances mentioned previously. We were attempting to get the optimum phase matching of both crystals through using an angle tuning of both crystals separately. w 1 (1064nm) w 1 (1064nm) w 3 (355nm) Nd:YA G Type I Type II w 2 (532nm) Figure 2.8: Schematic diagram of polarization matching in the frequency conversion 72

79 P L 1 L 2 F 1 Nd:YAG Type I Type II 1064nm Joulemeter x 1 x 2 x 3 x 4 X6 Figure 2.9: The schematic of the experimental setup for THG, where P is linear polarizer, L 1 &L 2 are lenses and F 1 and F 2 are 532nm and 355nm transmission filters The similar procedure for obtaining the SH generated energies and their corresponded conversion efficiencies was once again repeated for SFG and as a result THG light 355nm was produced. The configurations were carried out for obtaining data for two NLO crystals LBO and BBO namely : a- [LBO][LBO] b-[bbo][lbo] The high intensity laser beam is achieved and focused using the same previous method. Using the same equipments for various measurements. The THG energies and the system conversion efficiencies have been obtained and sketched in figures mentioned in the next chapter. The UV light at 355nm produced is separated using a narrow band UV transmission filter with band width of 15nm. 73

80 Nd:YAG polarizer Lenses Crystal 532nm 355nm Joulemeter Figure 2.10: A photograph of experimental setup for THG 2.8 Third Harmonic Generation With Walk-off Compensation There are various configuration schemes for THG enhancements that can be carried out either in SHG stage which represents the first stage in the NLO crystals system or in the second (SFG) stage. For simplicity we summarized the crystal arrangements that have been used in this project for THG enhancements in figure In this figure two SHG NLO crystals have been used. They can be either twin or different(non-twin) crystals (i.e. two identical LBO crystals or one BBO and the other was LBO crystals). Both of them in these schemes are type I and were with dimensions of 3 3 5mm. They are arranged either on NWOC or WOC schemes in this case we have an enhancements in the first stage (SHG). While for SFG and as a result THG was obtained only one LBO 0 type II crystals have been used. It was cut at ( q =, j = 90 ) with the dimensions of mm. If we want harmonic enhancements in the 74

81 second (THG) stage we use two identical LBO type II crystals with the same cutting angle and dimension as in the first case. Once again they are arranged on NWOC or WOC schemes. Both faces of the SHG crystal are AR at 1064nm and 532nm while the THG crystal faces were AR at 1064nm, 532nm, and 355nm. Since we were using critically phase matched all crystals were kept at room temperature. If we want enhancements in the THG, the same procedure mentioned above for focusing the IR beam onto the NLO crystal module and same beam waists inside the various crystals is achieved. Also a good optical beam alignment and phase matching in both stages were carried out, then the various data for SH and TH generated energies and their corresponding conversion efficiencies were measured as in the above articles and sketched in figures mentioned in the next chapter. 75

82 SHG THG A Nd:YAG MC-NWOC in SHG B Nd:YAG MC-WOC in SHG Nd:YAG C MC-NWOC in THG D Nd:YAG MC-WOC in THG Figure 2.11: Crystal arrangements for MC-NWOC& MC-WOC (A, B) in SHG stage, while(c, D) MC-NWOC & MC-WOC in THG stage. 2.9 Temporal And Spatial Beam Profile Measurements The temporal pulse profile of the fundamental laser beam, SH generated beam and TH generated beam were measured with a 100MHz oscilloscope and a Thorlab Si fast photodetector (DET 36A) which has a 1ns rise time and covers the 200nm to 2600nm wavelength range. While the spatial beam profiles for the fundamental and the harmonic generated beams radiation produced ware characterized by the auto trigger mode of a BEAMAGE-CCD12 CCD camera from Gentec Co. which has a standard wavelength range of 350nm to 1150nm. The second harmonic and third harmonic generated wavelengths in the produced beams are 76

83 confirmed using a Fisher Scientific Co. monochromator in an automatic scanning mode which includes a mechanism to change the wavelength selected by the monochromator. The data were recorded due to the resulting changes in the measured quantity as a function of the wavelength. The monochromator covers the wavelengths of UV and visible ranges. Figure 2.12 shows the photograph of this system. Figure 2.12: A photograph of the monochromator 77

84 78

85 3.1 Introduction A sub-nanosecond uv laser source has big demand in such fields like spectroscopy, micromachining, fluorescence imaging, and data storage. Most often uv light is produced by multi-stage cascading of pulsed laser sources based on Nd 3+ -ion or Yb 3+ -ion doped gain media that oscillate in the near-ir range. For creating compact and relatively small source of UV light suitable for broad type of applications a passively Q-switched pulsed Nd:YAG laser operating at 1064 nm with 1Hz repetition rate was chosen. It delivers 12 ns duration pulses with 70 mj energy. A type I nonlinear crystals of LBO and BBO were chosen for frequency doubling while for sum frequency generation type II nonlinear crystals of LBO were chosen for frequency tripling. An energy enhancement in a so called non-walkoff (NWOC) compensation and walkoff compensation(woc) has been achieved separately in both SHG and THG stages. The second harmonic generation (SHG) and sum frequency generation processes were optimized for (THG) production. The main goal of this work was to study the characteristics of these crystals under similar experimental conditions and to select the most efficient configuration for this task. Different focusing conditions were used during the experiments. In this work we measured the second harmonic and third harmonic output energies as a function of beam waist variations inside the nonlinear crystals and the incident fundamental IR source energy variations at a critical phase matching conditions at room temperature. 79

86 3.2 Nd:YAG Laser Parameters To get high efficient third harmonic generation, the fundamental and the second harmonic laser intensities must be high. Generally, efficient frequency tripling depends on the fundamental and second harmonic energies in a ratio of 1:1 for the extra-cavity configuration. In this scheme the second harmonic intensity is efficiently high which is necessary for efficient third harmonic generation. Two major requirements are important for this source. First, the laser output power must be stabilized. Second, the laser must provide enough power to allow for efficient laser intensity requirements for harmonic generations. The last requirement but not the least important is the robustness and compactness of the set up. Thus the characteristics of the passively Q- switched Nd:YAG laser operating at 1064nm wavelength output pulsed energy firstly investigated under the situation of single shot and 1Hz operation in order to decrease possible influence on the polarization state of thermally induced birefringence in the saturable absorber. The results have been obtained for 5 times system operations. The electrical pumping energy is provided by a variable switch mode power supply that has been designed to give a variable DC voltage of ( V). This voltage was used for charging the pulse forming network (PFN) of the laser flash lamp driving circuit with energy of ( J). Additionally this power supply provides the preionization voltage of 10KV for the lamp. The output radiation of the fundamental laser source has a typically an arbitrary polarization and this was verified using two crossed polarizes that were rotated around their axis by varying the azimuth angle of the polarizes across the laser beam. Thus to ensure the linear polarization of the fundamental laser beam that satisfied the polarization dynamics of the nonlinear crystal used for harmonic generation, the radiation was 80

87 incident on the extracavity polarizer with a transmission of 38 %. The output linearly polarized infrared energy can be varied from 7 to 26.6 mj. At first the scaled infrared output is collimated for the optimum focusing conditions to the efficient SHG were investigated using IR coated plano-convex lens with a focal length of 30cm,then a several lenses were used with different focal lengths covering the range (50,60,70,80,100,110 and 150cm ). The beam waist obtained inside the nonlinear crystals module was from (0.33-1) mm. To optimize the operational conditions for the infrared laser source the data obtained for IR energy is measured directly before the nonlinear crystal module was 24mJ which corresponding a 2 Mw output power. Thus, the pulsed-wave operation of this source has been investigated. The output energy as a function of the electrical pumping energy is presented in the Figure 3.1. At first, the fundamental laser energy increases with the electrical pumping energy, until it reaches the maximum laser energy. Then, the fundamental energy begins saturation after an input of 7.3 J as shown in Figures 3.1 and 3.2. A further increase of the pumping energy makes a slight increase of the output IR energy. The main reason in gain medium saturation is due to high pumping intensities,which can make this effect significant leading to reduce gain and increased thermal input. This effect adds to the thermal loading due to the difference in energy between the pump and the signal photons being taken up by non-radiative decay. Thermal load can have a detrimental effects on the laser material and its output such as increased thermal population of the lower laser level, lensing, aberrations, birefringence and even stress induce fracture. As a result the pulse duration of the output laser pulse becomes wider when the pumping energy is more increased. Wider pulse widths leads to a lower peak output power. 81

88 The conversion efficiency of the laser source is shown in Figure 3.2. The maximum IR energy of the source was determined directly from the source was 70.1 mj which corresponding to an optical conversion efficiency of %. The conversion efficiency starts increasing until it reaches the maximum value at pumping input energy of 7.3 J, and then starts decreasing due to the same reason mentioned above. The temporal pulse profile of the fundamental pulse is shown in Figure 3.3. In this figure the laser pulse duration measured at full width half maximum(fwhm) is 12 ns. While the spatial beam profile for the fundamental laser beam is depicted in Figure 3.4. As it can be seen, in the 2D and 3D profiles the laser operated on a single longitudinal mode (TEM 00 ) centered at 1064 nm wavelength. IR (o/p) energy,mj Electrical pumping energy,j Figure 3.1: The relation between the electrical pumping energy and the IR output energy of the Nd:YAG laser source 82

89 IR efficiency,% Electrical pumping energy, J Figure 3.2: The relation between the electrical pumping energy and the Nd:YAG laser source conversion efficiency Figure 3.3: Temporal profile of the IR pump pulse at 1064nm 83

90 Figure 3.4: Spatial beam profile of the fundamental laser beam at 1064nm 3.3 Second Harmonic Generation Measurements With LBO And BBO Crystals Single LBO And BBO Experiments Referring to Figures (2.3) and (2.4), in chapter two, they show the block diagram and the photograph for second harmonic generation setup using LBO and BBO crystals that were used in this work. The nonlinear interaction between the fundamental beam and the SH generated beam is achieved by the birefringent configuration, and the case that has been described here is denoted as (ooe), where o stands for ordinary beam and e for extraordinary beam. The configuration in which both input beams are of the same polarization i.e. (ooe) or (eeo) is referred to as type I phase matching. During this configuration the collinear input beam was focused onto the NLO crystals. At the first the relation between the second lens focal length and second harmonics energy generated has been studied such that for each measurements the maximum input 84

91 infrared energy was used. Therefore the resultant setup allowed for variation of the spot size inside the crystals. The results are shown in Figure 3.5. It is clear in these curves that the second harmonic generated energy is highly depends on the focal length of second lens (i.e. the beam waist variation inside the crystals). The maximum SH generated energies for LBO and BBO crystals are (~3.75mJ) and (~ 4mJ ) respectively. These values were measured using a 50 mm focal length of the second lens. This corresponds to a beam spot size radius of 0.33 mm inside the crystals LBO BBO 3.5 SHG(523nm) energy,mj Lens focal length, mm Figure 3.5: SHG energy versus lens focal length for the LBO and BBO crystals Referring to eq.(1.18) the SH generated energy is inversely proportional with the beam spot size inside the NLO crystal. Thus the curve shows that increasing of the focal length of the second focusing lens decreases the laser intensity inside the NLO crystals and this in 85

92 turn reduces the output harmonic generations. Also the curve shows that the energy of harmonic generation produced by BBO crystal is more than that of LBO crystal and the main reason is because the BBO crystal has a higher nonlinearity than LBO crystal. To determine the relation between the infrared incident energy and the second harmonic generated energy, first of all at the lowest pumping energy level, the position of the crystals was optimized with respect to the input pumping beam waist in order to get the highest SH output energy. Next, the fundamental energy was gradually increased while recording the SH energy. The position of the crystal was fixed during this measurement BBO LBO 3.5 SHG (532nm) energy,mj IR incident energy,mj Figure 3.6: Second harmonic output energy at 532 nm as a function of incident energy with 50 mm focal length of second focusing lens for LBO and BBO crystal From Figure 3.6 we see and expect the dependence of the SH energy on the input pumping energy. The maximum SH generated energy 86

93 for BBO and LBO crystals are (~3.68mJ) and (~3.14mJ) respectively, which occur at IR input energy(~24mj). Also this curve shows the harmonic energy generated for BBO crystal is more that that of the LBO crystal and this is because of the higher nonlinearity of the BBO crystal with respect to that of the LBO crystal as we previously said. From these measured values of the second harmonic generated energies we can figure out the harmonic conversion efficiencies for both crystals which is presented in Figure BBO LBO 13 SHG(532nm) efficiency % IR incident energy, mj Figure 3.7: The measured Second harmonic conversion efficiency at 532 nm as a function of the incident energy with 50 mm focal length of second focusing lens, for LBO&BBO crystals Figure 3.7 shows that at the beginning the harmonic conversion efficiency for both crystals are highly increased due to increasing in the pumping energy, but when the pumping energy reach (~12 mj ) in both 87

94 crystals beyond this point a further increasing of the pumping input energy produces only a slight variation of the harmonic efficiencies. The main reason for this is that,at a higher pumping energy both crystals begins to saturate. This harmonic efficiency saturation is due to the depletion of the pumping input energy. Also the fundamental laser pulse duration at higher pumping levels becomes wider and this in turn will minimize the peak laser energy production (i.e. the over all laser intensity is minimized ), and according to eq. (1.18) in which the harmonic generation conversion efficiency is strongly dependent on the incident laser intensity we saw that this condition for harmonic generation is violated. One more thing is shown in this figure is that the harmonic conversion efficiency with BBO crystal is more than that of LBO crystal, this is because BBO crystal has a higher nonlinearity than that of LBO and according to eq.1.18 the harmonic conversion efficiency is highly depends on the nonlinear parameter of the nonlinear crystal. The maximum harmonic conversion efficiencies are (~13.81%) and (~15.95%) for LBO and BBO crystals respectively. But for BBO crystal after it reached the maximum value it is then starts decreasing and the main reason for that is due larger walkoff angle between the interacting waves is for BBO crystal is larger than that for LBO crystal and this will minimize the interacting length between the different waves which in turn minimizes the harmonic conversion efficiency as well as BBO crystal has a smaller acceptance angle compared with LBO crystal. The temporal pulse profile of the second harmonic generated pulse is shown in Figure 3.8. In this figure the laser pulse duration measured at full width half maximum(fwhm) is (10 ns).while it s spatial beam profile is depicted in Figure

95 Figure 3.8: The temporal pulse profile of the second harmonic generated for LBO and BBO crystals at 532nm Figure 3.9 : The spatial beam profile for the second harmonic generation for LBO and BBO crystals at 532nm The elliptical spot shape produced for the second harmonic generation is due to the dispersion effect in the nonlinear crystals. 89

96 3.4 Multi Crystal SHG Experiments Two experimental approaches have been done using multi-crystals in nonwalk-off and in walkoff compensation schemes for SHG SHG with Non Walkoff Compensation (NWOC) And Walk Off Compensation (WOC) Experiments Referring to Figures (2.6) &(2.7) in chapter two, which show the block diagrams for multi crystals on nonwalk-off compensation (MCNWOC) and walkoff compensation (MCWOC) schemes for second harmonic generation. In MCNWOC scheme both the NLO crystals optical axes are arranged in the same direction, and each crystal is cut in type I critically phase matching. The fundamental laser beam is incident onto the first NLO crystal after focusing using the same focusing lens system as before, then onto the second NLO crystal, beam waist inside the nonlinear crystals module covers the range (0.33mm 1mm). Two experimental procedures have been done and the results are recorded for [LBO-LBO] and [BBO-LBO] arrangements. Figure 3.10 shows the behavior of the SH generated energy as a function of the focal length of the second lens in the lens system for [LBO-LBO] twin crystals arrangements on NWOC and WOC schemes. This Figure shows a decreasing of SH generated energy with increasing of second lens focal length. This reduction in the energy is due to the reduction in infrared laser intensity inside the NLO crystal module because of the wider beam waist produced by the focusing lens system. The maximum second harmonic energy generated measured at 50mm focal length lens for LBO-LBO in NWOC and WOC schemes are (~4.58 mj)&( ~9mJ) respectively, which corresponding to a harmonic conversion efficiencies of (~19% )&( ~37.5%). Also this figure shows 90

97 that the SH generated energy and the corresponding conversion efficiency for the WOC scheme is higher than that of NWOC scheme. This is because of walkoff angle produced between the interacting waves in the first crystal is corrected by the second crystal on WOC scheme and as a result increasing in the interaction length between the different waves which in turn increasing the SH generated energy output and the corresponding harmonic conversion efficiency. The ratio between the second harmonic generated energy after enhancement relative to that obtained without enhancement (enhancement factor) using single crystal for the two schemes are ( 1.22)&(2.4) respectively. The same procedure has been done for [BBO-LBO] no twin crystals arrangement also on the two different schemes NWOC and WOC. The results obtained for [BBO- LBO] crystals arrangement are presented in Figure LBO - LBO NWOC LBO - LBO WOC 8 SHG(532nm) energy, mj Lens focal length, mm Figure 3.10: SHG energy versus lens focal length for the[ LBO][LBO] on NWOC and WOC schemes 91

98 8 7 BBO-LBO NWOC BBO-LBO WOC SHG(532nm) energy,mj Lens focal length, mm Figure 3.11: SHG energy versus lens focal length for the[ BBO][LBO] on NWOC and WOC schemes This Figure shows a decrease in SH energy generated with an increasing in second lens focal length. This reduction is due to lower laser intensity because of the wider beam waist produced by the focusing lens system. The maximum second harmonic energy generated measured at 50mm focal length lens for BBO - LBO on NWOC and WOC schemes are (~5.2mJ) & (~7.2mJ) respectively which corresponding to a harmonic conversion efficiencies of (~21.6% ) & ( ~30%). Also in this Figure the SH generated energy and the corresponding conversion efficiency for the WOC scheme is higher than that of NWOC scheme. This is because of the crystals arrangement and walkoff angle produced between the interacting waves in the first crystal is corrected by the second crystal and the result is increasing the interaction length between the different waves which in turn increasing the SH generated energy output and the corresponding harmonic conversion efficiency. The enhancement factor for the two schemes were (1.3)&(1.8) respectively. 92

99 For the same configurations used for twin and non- twin crystals (i.e. [LBO-LBO] on NWOC and WOC as well as [BBO-LBO] in NWOC and [BBO-LBO] in WOC ) the relation between the incident infrared energy and output SH generated energy is presented in Figures 3.12 and Since the setup for these two arrangements is the same the discussion is contained both of them. In these Figures we note the steadily increasing of the SH generated energy with increasing of the infrared pumping input energy. For LBO crystal with one more additional type I LBO crystal is added according to NWOC scheme the maximum SH generated energy at 50mm lens focal length obtained is (~3.75mJ ) while that of WOC scheme is (~7.5mJ ),their corresponding harmonic conversion efficiencies of (15.6%) and (31.25%) respectively. On the other hand for BBO crystal the addition of type I LBO crystal gives a maximum SH energy of (~5.1mJ) for NWOC while that for WOC is (~7mJ ) with corresponding harmonic conversion efficiencies of (21.25%) and (29.16%) for the two schemes respectively. 8 7 SHG(532nm)energy, mj LBO-LBO NWOC LBO-LBO WOC IR incident energy, mj Figure 3.12: Second harmonic output energy at 532 nm as a function of the incident energy with 50 mm focal length second focusing lens for LBO-LBO on NWOC&WOC crystals arrangements 93

100 8 7 SHG (532nm) energy,mj BBO-LBO NWOC BBO-LBO WOC IR incident energy, mj Figure 3.13: Second harmonic output energy at 532 nm as a function of the incident energy with 50 mm focal length second focusing lens for [BBO-LBO] on NWOC&WOC crystals arrangements For the same configurations used above {i.e. [LBO-LBO] on NWOC and WOC as well as [BBO-LBO] on NWOC and WOC },the relation between the incident infrared energy and the SH conversion efficiency is presented in Figures 3.14 and During the procedure of measurement the beam waist inside the NLO crystal module was also fixed at 0.33mm and the variation in the incident pumping energy is accomplished. 94

101 35 30 SHG (532nm) efficiency % IR incident energy,mj BBO-LBO NWOC BBO-LBO WOC Figure 3.14: The measured Second harmonic conversion efficiency at 532 nm as a function of the incident energy with 50 mm focal length second focusing lens, for [LBO-LBO] on NWOC & WOC schemes 35 SHG (532nm) efficiency % BBO-LBO NWOC BBO-LBO WOC IR incident energy,mj Figure 3.15: The measured Second harmonic conversion efficiency at 532 nm as a function of the incident energy with 50 mm focal length second focusing lens, for [BBO-LBO] on NWOC & WOC schemes 95

102 First of all for [LBO-LBO] on NWOC scheme the harmonic conversion efficiency starts increasing with increasing of the pumping energy until the pumping input energy becomes high enough that makes the NLO crystal module to become saturated, hence any successive increasing in the pumping doesn t produce more increasing of the harmonic conversion efficiency. Also the depletion of the fundamental wave can be considered as the main reason for the harmonic energy saturation and reduction. The depletion of the fundamental beam during [LBO-LBO] WOC is so clear in Figure 3.14,since for this scheme the walkoff angle generated in the first crystal is eliminated by the second crystal. On the other hand the two crystals according to these schemes appears as one crystal with a double length. The increasing in crystal length was an important factor in increasing the overall second harmonic efficiency. According to this result the interaction length of the interacting waves will be the longest such that the maximum conversion efficiency is achieved and this will deplete the fundamental beam during propagation. For [LBO-LBO] on NWOC since the nonlinear crystals are arranged such that their optical axes are on the same direction, the walkoff angle generated in the first crystal is not corrected by the second one rather it is increased,therefore the short interaction length created between the interaction waves produces less conversion efficiency. The same reasons are applied for [BBO-LBO] NWOC and [BBO-LBO] WOC schemes as well, since the conversion efficiencies for these schemes exhibit the same behaviors with increasing of the pumping energy. The enhancements in the harmonic conversion efficiencies are listed in Table

103 Table 3.1: Second harmonic generation efficiency enhancement for [LBO-LBO]& [BBO-LBO]]crystals arrangements with NWOC and WOC schemes Crystal arrangement NWOC WOC [LBO-LBO] [BBO-LBO] Figure 3.16 shows the temporal beam profile for the second harmonic generated pulse for multi crystals in two different arrangements for NWOC and WOC. In this figure the laser pulse duration measured at full width half maximum(fwhm) is(10 ns). While Figure 3.17 shows the spatial beam profile for the obtained pulses on these schemes. Figure 3.16: Temporal profile of the second harmonic generated pulse for [LBO- LBO] &[BBO-LBO] on NWOC and WOC schemes 97

104 Figure 3.17: spatial beam profile for the second harmonic generated pulse at 532nm for [LBO-LBO]&[BBO-LBO] on NWOC and WOC schemes 3.5 THG Harmonic Generation Measurements 3.5.1THG Using Single LBO Crystal Experiments This section covers the sum frequency generation which represents the second stage in third harmonic generation at 355nm wavelength of the Nd:YAG laser operating at 1064nm wavelength. The first setups that has been used in this project for third harmonic generated uses a type I LBO or BBO crystal for SHG followed by type II LBO crystal, while the second setups uses either the multi crystal in SHG on non-walkoff compensation (NWOC) and walkoff compensation (WOC) or THG on multi crystal (NWOC ) and (WOC). Referring to Figures (2.9) and (2.10), in chapter two, where they show the block diagrams for third harmonic generation using type II LBO crystal at critically phase matching technique. The crystals arrangements and configurations has been used in which both input beams are of the same polarization either (ooe) or 98

105 (eeo) i.e. collinear beams are incident onto the first crystal module then the second harmonic generated beam as well as the residual of the fundamental beam are mixed into the second crystal module. The collinear input beam was focused onto the NLO crystal by the same focusing lenses used in the first stage of SHG. Thus we can estimate the beam waist inside the nonlinear crystal modules which covers the range (0.33-1mm). At the first the relation between the second lens focal length and third harmonic generated energy has been studied either using a single LBO crystal as a type I or BBO crystal for SHG whereas for THG we use a single LBO type II crystal such that for all measurements the maximum infrared input energy was used. The results are shown in Figure It is clear in this figure that the third harmonic generated energy is highly depends on the focal length of second lens and the beam waist variation inside the crystals [BBO] [LBO] [LBO] [LBO] THG(355nm) energy, mj lens focal length mm Figure 3.18: THG energy versus lens focal lens for the[ LBO][LBO] and [BBO][LBO] crystals arrangements 99

106 The maximum third harmonic generated energies for [LBO-I][LBO- II]and [BBO-I][LBO-II] crystal arrangements were (~1.176mJ)(~1.06mJ) respectively. These values were measured using a 50 mm focal length for the second lens. This corresponding to a beam spot size of 0.33 mm inside the crystal modules. It is clear in this figure that the laser intensity reduction in both crystals due to beam waist increasing which gives a less TH generated output energy. And also we notice that the TH generated energy for [LBO][LBO] crystals arrangement is larger than that of [BBO][LBO]. The main reason is that, since the LBO crystal has a small walkoff angle generated between the interacting waves inside the nonlinear crystal and in [LBO][LBO] crystals arrangement we use two nonlinear crystals from the same kind( i.e. twin LBO crystals),it means that the total walkoff angle generated in both crystals will be smaller than that was generated in the other crystal arrangement (i.e. [BBO][LBO] ) because BBO crystal has a walkoff angle larger than that of LBO crystal. Thus the total interaction length between the interacting waves for [LBO][LBO] is longer than that of [BBO][LBO] crystal arrangement. The maximum third harmonic energy generated measured at 50mm focal length lens for [LBO][LBO] and [BBO][LBO] crystal arrangements are (~1.176 mj)&(~1.06 mj) respectively which corresponding to a third harmonic conversion efficiencies of (~4.9 % )&( ~4.41 %) respectively. For the previous crystals arrangements used the relation between the incident infrared energy and output third harmonic generated energy is presented in Figure In this figure we note the steadily increasing of the third harmonic generated energy with increasing in the infrared pumping input energy. The energy generated with [LBO][LBO] crystals arrangement is larger than that of [BBO][LBO] for the same reason mentioned in the previous 100

107 measurements. The investigation of the previous figure carefully give one more thing ; that at lower pumping energy the harmonic energy generated by the crystal arrangement [BBO][LBO] is greater than that of [LBO][LBO],this is due to that the higher nonlinearity of BBO crystal which is translated as higher harmonic generation, but at a higher pumping energy,the total walkoff angle generated with [BBO][LBO] is greater than of the other and as a result the process of harmonic generation is reversed and become as the harmonic generation for [LBO][LBO] is larger than that of [BBO][LBO] crystals arrangements THG (355nm) energy,mj [LBO] [LBO] [BBO] [LBO] IR incident energy,mj Figure 3.19: Third harmonic generated output energy at 355 nm as a function of the incident energy with 50 mm focal length second focusing lens for [LBO][LBO] &[BBO][LBO] crystal arrangements From the same previous crystal arrangements we can also figure out the relation between the incident infrared energy and the third harmonic conversion efficiency which is presented in Figures During the 101

108 procedure of measurements also the beam waist inside the NLO crystal module is fixed at 0.33mm and the variation in the incident pumping energy is accomplished. 6 5 THG(355nm) efficiency, % [LBO] [LBO] [BBO] [LBO] IR incident energy, mj Figure 3.20: The measured third harmonic conversion efficiency at 355 nm as a function of the incident energy with 50 mm focal length of second focusing lens, for [LBO][LBO]&[BBO][LBO] crystals arrangement At the lower pumping energy Figure 3.20 gives a steadily increasing in harmonic conversion efficiency for both crystal arrangements used for third harmonic generation. At this range of pumping energy the third harmonic conversion efficiency for [BBO][LBO] crystal arrangement is greater than that of [LBO][LBO] until the pumping input energy reached (16.6 mj ) the third harmonic conversion process is reversed. The main reason for this is the larger walkoff angle for BBO crystal on that of LBO crystal. Also this figure indicates that at higher pumping energy the crystal arrangement [BBO][LBO] becomes more saturated than the other one. The main reason for that is the higher nonlinearity of the BBO 102

109 crystal which means a higher harmonic generation can be obtained with BBO crystal compared with that obtained with LBO crystal. Figures 3.21 shows the temporal beam profile for the third harmonic generated pulse for single crystal and for two crystals (LBO and BBO). In this Figure the laser pulse duration measured at full width half maximum (FWHM) is (8 ns). While Figure 3.22 shows the spatial beam profile for the obtained pulses on these schemes. Figure 3.21: Temporal profile of the pump pulse for third harmonic generated pulse at 355nm for both crystals arrangements Figure 3.22: Spatial beam profile for the third harmonic generated pulse at 355nm for both crystals arrangements 103

110 3.5.2 Multi Crystals THG Experiments Two experimental approaches have been done either using multicrystals in second harmonic generation(shg) followed by single crystal for sum frequency generation(sfg) or single crystal for SHG followed by multi-crystals in SFG. On the other hand the multi-crystal arrangements constitutes either nonwalk-off compensation (NWOC) or walkoff compensation (WOC) schemes Multi-crystals In SHG And Single Crystal For SFG Enhancement In SHG Stage Using LBO-LBO Crystals Experiments Referring to Figure (2.11) A & B in chapter two, which show the block diagrams for multi crystals on nonwalk-off compensation (MCNWOC) and walkoff compensation(mcwoc) schemes for second harmonic generation followed by sum frequency generation process. In MCNWOC scheme the optical axes of both the NLO crystal are arranged in the same direction while for the MCWOC the optical axis of the second crystal is reversed by relative to that of the first crystal. The first NLO crystals module contained two crystals either arranged as LBO-LBO on NWOC or WOC, while the second NLO crystals module contained only one LBO crystal. After focusing using the same focusing lens system as before the infrared laser beam is incident first onto the first crystals module and then onto the second crystals module. The beam waist inside the nonlinear crystals modules covers the range (0.33mm - 1mm). The experimental procedures that has been done and the results are recorded for [LBO-LBO][LBO] on NWOC and WOC arrangements schemes. Figure 3.23 shows the relation between the third harmonic 104

111 generated energy as a function of the focal length of the second lens in the lens system for [LBO-LBO][LBO] crystal arrangements on NWOC and WOC schemes. This Figure shows a decreasing in third harmonic generated energy with increasing of lens focal length. This reduction in energy is due to the reduction in infrared laser intensity propagating through the crystals modules. For the WOC scheme the third harmonic generation is larger than that of NWOC scheme because the crystal module for SHG is responsible for energy enhancement since the two crystals behave as a one NLO crystal and it s length equals the length of both. According to eq.(1.26)in which the third harmonic efficiency is directly proportional with the crystal length. And using two crystals means doubling crystals length, which means using a single crystal,but with a double length. The maximum third harmonic energy generated for these two schemes are(~1.4mj) and (~2.1mJ) respectively. All data recorded in this curve are taken at constant pumping energy at a beam waist covers the range (0.33mm-1mm) [LBO-LBO] [LBO]NWOC [LBO-LBO] [LBO]WOC THG (355nm) energy, mj Lens focal length, mm Figure 3.23: THG energy versus lens focal lens for the[ LBO-LBO][LBO] on NWOC and WOC schemes 105

112 The relation between the incident infrared energy and output third harmonic generated energy for this crystal arrangement is presented in Figure THG (355nm)enegy, mj [LBO-LBO] [LBO]NWOC [LBO-LBO] [LBO]WOC IR incident energy,mj Figure 3.24: Third harmonic generated output energy at 355 nm as a function of the incident energy with 50 mm focal length second focusing lens for [LBO-LBO][LBO] on NWOC &WOC crystal arrangements In Figure 3.24 the curves of the third harmonic energy increases steadily with the increasing of the infrared pumping input energy, but the output energy obtained from the crystal arrangement at WOC is larger than that of NWOC. The main reason is that, the two crystal arranged on NWOC translates the propagation of energy as it passes through a single crystal it s length represents double that of single crystal, it doesn t mean that the third harmonic energy generated is doubled, actually it doesn t, since the total walkoff angle for both crystal are added which in turn minimizes the interaction length between the interacting waves, thus the energy enhancement for NWOC will be less. While crystals arrangement on WOC gives more harmonic energy enhancement because the crystals arranged in such a way that during the waves propagation the walkoff 106

113 angle generated in the first crystal is corrected in the second one such that the total third harmonic energy generated on both crystals may be considered that is generated from single crystal with double length. The maximum third harmonic energy generated with NWOC and WOC schemes are (~1.52mJ) and (~2.1mJ) respectively. For the same crystal arrangements we can figure out the relation between the incident infrared energy and the third harmonic conversion efficiency which is presented in Figures According to eq.( 1.26 ) mentioned in chapter one and the results obtained in Figure 3.25, it is clear that the third harmonic efficiency depends on the pumping input energy level which in turn play a role in increasing of the fundamental laser intensity. At the lower pumping energy the rate of increasing of the third harmonics efficiency is more than that at higher pumping energy. Also this Figure indicates that the third harmonics efficiencies for [LBO-LBO][LBO] on WOC is more than that of the other in NWOC crystals arrangement. The main reason for that is the total walkoff angle in first crystal module scheme is smaller than of the second one and this gives a longer interaction length during the waves propagation. As a result a higher third harmonics efficiency is obtained from the first scheme compared with that obtained form the second. Figures 3.26 shows the temporal beam profile for the third harmonic generated pulse at 355nm for [LBO-LBO][LBO] on NWOC&WOC schemes. In this Figure the laser pulse duration measured at full width half maximum(fwhm) is(9ns). While Figure 3.27 shows the spatial beam profile for the obtained pulses on these schemes. 107

114 10 [LBO-LBO] [LBO]NWOC [LBO-LBO] [LBO]WOC 9 THG (355nm) efficiency % IR incident energy, mj Figure 3.25: The measured third harmonic conversion efficiency at 355 nm as a function of the incident energy with 50 mm focal length second focusing lens, for [LBO-LBO][LBO] NWOC & WOC crystals arrangement Figure 3.26:Tempral beam profile for the third harmonic generated pulse at 355nm for [LBO-LBO][LBO] on NWOC&WOC schemes 108

115 Figure 3.27: Spatial beam profile for the third harmonic generated pulse at 355nm for [LBO-LBO][LBO] on NWOC&WOC schemes Enhancement In SHG Stage using BBO-LBO Crystals Experiments Referring to the Figure (2.11) A & B again. which show the block diagrams for multi crystals on nonwalk-off compensation (MCNWOC) and walkoff compensation (MCWOC) schemes for second harmonic generation followed by sum frequency generation process. In NWOC scheme BBO and LBO crystals are arranged such that their optical axes are in the same direction first, then the optical axis of the second crystal is reversed by relative to the first crystal for WOC scheme. For third harmonic generation the crystals are arranged in two crystal modules one contained BBO and LBO crystals arranged for SHG and the other contained just one LBO crystal for THG. The first NLO crystals module arranged either [BBO-LBO ] on NWOC or WOC, then the first crystal module followed by LBO crystal for third harmonic generation. Focusing should be done on the incident infrared beam before the NLO crystals 109

116 models. A beam waist covering the range (0.33mm 1mm) is obtained using the same focusing lens system as before. The experimental procedures that has been done and the results were obtained for [BBO- LBO][LBO] crystals arrangements for both NWOC and WOC schemes. Figure 3.28 shows the relation between the third harmonic generated energy as a function of the focal length of the second lens in the lens system for [BBO-LBO][LBO] on NWOC and WOC schemes [BBO-LBO] [LBO]NWOC [BBO-LBO] [LBO]WOC THG (355nm) energy, mj Lens focal length,mm Figure 3.28: THG energy versus lens focal length for the[ BBO-LBO][LBO] on NWOC and WOC schemes This Figure shows the same behavior as in the pervious case. There is just one note that should be mentioned here which is the maximum third harmonic energy generated in this crystals arrangement. The maximum third harmonic energy generated for these two schemes are(~1.96mj) and (~2.55mJ) for NWOC and WOC respectively. All the data recorded in this 110

117 curve are taken at constant pumping energy at a beam waist covers the range (0.33mm-1mm). The relation between the input pumping energy and the output third harmonic energy generated and the corresponding harmonic conversion efficiency can be summarized in Figures 3.29 and [BBO-LBO] [LBO]WOC [BBO-LBO] [LBO]NWOC 2.5 THG (355nm) energy, mj IR incident energy, mj Figure 3.29: Third harmonic generated output energy at 355 nm as a function of the incident energy with 50 mm focal length second focusing lens for [BBO-LBO][LBO] on NWOC &WOC crystal arrangements There is a steadily increasing of the TH generated energy with increasing of the pumping input energy and this is in agreement with eq.(1.26) derived in chapter one. We can deduce from Figure 3.30 that the third harmonic efficiency variation is the same at lower and higher pumping energy although that the [BBO-LBO][LBO] in WOC exhibits a slight saturation at the end of this curve. The main reason for that is; since [BBO- LBO] crystals are arranged on WOC the net walkoff angle 111

118 generated in both crystals is small, although the BBO crystal has acceptance angle smaller than that of LBO crystal, but the total interaction length created in both crystal will be longer that makes the interacting waves highly contributes to the harmonic generation which makes crystals saturated THG (355nm), efficiency % [BBO-LBO] [LBO] NWOC [BBO-LBO] [LBO] WOC IR incident energy, mj Figure 3.30: The measured third harmonic conversion efficiency at 355 nm as a function of the incident energy with 50 mm focal length second focusing lens, for [BBO-LBO][LBO] on NWOC & WOC crystals arrangement On the other hand at higher pumping energy the harmonic efficiency for the crystal arrangement with WOC will be higher than that with NWOC scheme this is due to walkoff angle correction in the second crystal. The third harmonic generated energy enhancements using the walkoff angle correction in SHG to that obtained using only one crystal in the first stage can be summarized in Table

119 Table 3.2: Third harmonic generated energy enhancement in different schemes Crystals arrangement NWOC WOC [LBO-LBO][LBO] [BBO-LBO][LBO] Figures 3.31 and 3.32 show the temporal and spatial beam profile for the third harmonic generated pulse after using crystals arrangements for third conversion efficiency enhancement. The THG laser pulse duration measured at FWHM is 9ns. Figure 3.31: Temporal beam profile for the third harmonic generated pulse at 355nm for [BBO-LBO][LBO] on NWOC&WOC schemes 113

120 Figure 3.32: Spatial beam profile for the third harmonic generated pulse at 355nm for [BBO-LBO][LBO] on NWOC&WOC schemes Single Crystal In SHG And Multi-crystals In SFG [LBO-LBO]Crystals Arrangement In THG Experiments Referring to Figure (2.11) C & D in chapter two, which show the block diagrams for multi crystals on nonwalk-off compensation (MCNWOC) and on walkoff compensation(mcwoc) schemes using twin LBO crystals for third harmonic generation proceeded by LBO crystal used for SHG. Again on NWOC scheme both crystals are arranged such that their optical axes are in the same direction while for the MCWOC the optical axis of the second crystal is reversed by relative to the first crystal. The first NLO crystals module contained only one LBO crystal. while the second NLO crystals module contained two LBO crystals either arranged in [LBO-LBO] on NWOC or WOC. After focusing using the same focusing lens system as before the infrared laser beam is incident first onto the first crystals module then onto the second 114

121 crystals module, the beam waist inside the nonlinear crystals modules also covers the range (0.33mm - 1mm). Figure 3.33 shows the relation between the third harmonic generated energy as a function of the focal length of the second lens in the lens system for [LBO][LBO-LBO] crystal arrangements on NWOC and WOC schemes [LBO] [LBO-LBO]NWOC [LBO] [LBO-LBO]WOC THG (355nm), energy mj Lens focal length, mm Figure 3.33: THG energy versus lens focal length for the[ LBO][LBO-LBO] on NWOC & WOC schemes This Figure shows a decreasing of third harmonic generated energy with increasing of lens focal length. This reduction in energy is due to the reduction in infrared laser intensity propagating through the crystals modules. There is a slight difference between the energy obtained by NWOC compared with that obtained from the WOC scheme. The reason for that is ; according to crystals arrangement for energy enhancement in the second stage, which means enough energy for both 1064nm and 532nm should be provided, but the lower nonlinearity of LBO crystal produces less second harmonic energy which will be not quit enough for production of a high energy enhancement in the next stage. 115

122 THG (355nm) energy, mj [LBO] [LBO-LBO]NWOC [LBO] [LBO-LBO]WOC IR incident energy,mj Figure 3.34: Third harmonic generated output energy at 355 nm as a function of the incident energy with 50 mm focal length of second focusing lens for [LBO][LBO- LBO] on NWOC &WOC crystal arrangements The same interpretation and discussion are valid for the next two Figures 3.34 and 3.35 which show the relation between the incident IR energy and the output third harmonic generated energies and the corresponding third harmonic conversion efficiencies respectively for both NWOC and WOC schemes. 116

123 7 6 THG (355nm) efficiency,% [LBO] [LBO-LBO]NWOC [LBO] [LBO-LBO]WOC IR incident energy, mj Figure 3.35: The measured third harmonic conversion efficiency at 355 nm as a function of the incident energy with 50 mm focal length of second focusing lens, for [LBO][LBO-LBO] on NWOC & WOC crystals arrangements The enhancement factors in the third harmonic generation using the walkoff angle correction can be summarized in Table 3.3 Table 3.3: THG energy enhancement for twin and different crystals Crystals arrangement NWOC WOC [LBO][LBO-LBO] Figures 3.36 and 3.37 show the temporal and spatial beam profiles for the third harmonic generated pulse, after using crystals arrangements for third harmonic conversion efficiency enhancement in the second stage (THG stage ) using [LBO][LBO-LBO] on NWOC and WOC 117

124 crystals arrangements. The UV laser pulse duration measured at full width half maximum(fwhm) is (9 ns). Figure 3.36: Temporal beam profile for the third harmonic generated pulse at 355nm for [LBO][LBO-LBO] on NWOC&WOC schemes Figure 3.37: Spatial beam profile for the third harmonic generated pulse at 355nm for [LBO][LBO-LBO] on NWOC&WOC schemes 118