Characterization of Terahertz Radiation Generated in an Organic Crystal

Transcription

1 Characterization of Terahertz Radiation Generated in an Organic Crystal Master Thesis By Åsa Bengtsson Supervisor: Prof. Jörgen Larsson Assistant Supervisor: Dr. Carlito Ponseca Division of Atomic Physics Faculty of Engineering, LTH October 17, 2016

2 Abstract The terahertz region of the electromagnetic spectrum is an important research area allowing insights into fundamental science such as inter-molecular interactions, and with applications in the environmental, medical and security field. Using femtosecond lasers, it is possible to design compact and efficient terahertz generation schemes, resulting in few-cycle broadband pulses. This master thesis is concerned with generating terahertz radiation through optical rectification in the organic crystal DSTMS. This crystal has a high second order nonlinear coefficient and is phase matched for a 1500 nm pump laser. Terahertz radiation was successfully generated, with a maximum energy of 3.75 µj, corresponding to a generation efficiency of 0.71% at a pump laser energy of 530 µj. The theoretical background of this process, as well as the practical work is presented in this thesis. i

3 Acknowledgements I would like to thank my supervisor Jörgen Larsson for the opportunity to carry out such a fun and interesting masters degree project, and for all the guidance and useful insights along the way. A big thanks also to my assistant supervisor Carlito Ponseca for sharing his knowledge and experience in terahertz science. Finally, I would like to thank everyone in the Ultrafast X-ray Science group at the department of Atomic Physics and MAX IV for always being there with support, encouragement and helpful discussions. ii

4 Popular Science Summary Generating terahertz light using a laser and a crystal. Terahertz light can interact with matter and cause molecules to vibrate and undergo structural changes. This can be used to investigate phenomena that are tiny in space, and occur on an extremely small time scale. Terahertz light must however first be generated, and this can be done by using intense laser light propagating through a crystal. Light can be used as a tool to measure and investigate our surroundings. Different kinds of light can be used to explore different phenomena, and a vast quantity of different techniques have been developed. Light can be used to measure properties that are impossible to access in other ways. For example, extremely short distances can be measured using light, because the wavelengths of light itself can be very short, and work as mini yardsticks. Light can also interact with different materials in a way that enables us to analyze them. Measuring with light involves finding the right wavelength for what you want to measure, and figuring out the right technique to do it. The electromagnetic spectrum includes all different wavelengths of light, and stretches from the very long radiowaves, with wavelengths that are hundreds of kilometers long, to the very short gamma rays, with wavelengths at merely picometers (10 12 m). In addition to wavelengths, one can also describe light by its frequency. There is a specific part of the electromagnetic spectrum called the teraherts band, which is comprised of light with frequencies around Hz, or 1 THz. This light typically has wavelengths of a couple of tenths of mm. Terahertz frequencies are useful in a number of different applications. A key feature of terahertz light is that it is highly absorbed by water. This means that terahertz frequencies are well suited to use in both medical and environmental research, where water content is an important aspect. Terahertz light can interact with materials in a number of different ways. It can cause molecules to start vibrating, and induce electronic and structural changes in the material. These changes can then be observed by using a different kind of light, for example x-rays. These kinds of experiments, where light is used to poke and observe materials, are powerful investigative tools in science, and are part of what will be done at the new MAX IV facility in Lund. In order to use terahertz light, one must first generate it. This has been the focus of a degree project at the Atomic Physics Division at Lunds University. There are many ways of generating terahertz light, and methods differ in efficiency as well as properties of the generated light. One method is using a laser to illuminate a crystal. When very intense light, like the light from a laser, interacts with matter a number of strange, so called nonlinear, effects occur. One of these is that light of a certain frequency can convert into light of a different frequency. The underlying mechanism is that laser light will cause the polarization in the crystal to oscillate over time, and these oscillations act as a source of electromagnetic radiation. Typical efficiencies (how much of the input laser energy is converted into terahertz light) of this kind of generation method are between a few tenths of per mille and a few percent. Using the short pulse laser at the FemtoMAX beamline at MAX IV, and an organic crystal called DSTMS, terahertz light was successfully generated at the relatively high efficiency 0.71 %. iii

5 Contents 1 Introduction THz science Terahertz generation using femtosecond lasers Aim of project Theory Nonlinear optics Terahertz generation Phase matching Crystal optics DSTMS Useful equations Method Equipment Laser system DSTMS crystal Detection Building the setup Measurements Final setup and measurements Additional notes Results Summary Discussion and conclusions Future work Appendix Wavelength scan Microtech Pyroelectric Detector

6 1 INTRODUCTION 1 Introduction This thesis presents the results of a diploma project performed in the Ultrafast X-ray Science group at the Division of Atomic Physics at Lund University. The purpose of this master degree project has been to generate terahertz radiation using optical rectification in an organic crystal. The experimental work has been carried out at the FemtoMax beamline at the MAX IV facility. An introduction to the field of terahertz science and the motivation for this project, as well as specific goals, are given below. 1.1 THz science Terahertz science is the science concerning the specific part of the electromagnetic spectrum called the terahertz band, usually considered to be THz. The full electromagnetic spectrum, including the terahertz band, can be seen in figure 1. The terahertz region can also be expressed in wavelengths and energies, which is presented in table 1. There are a number of features that make terahertz radiation interesting. For example, vibrational states and inter-molecular interactions in organic molecules take place within this energy region. Terahertz radiation is also highly absorbed in water, which enables atmospheric research. The high absorption in water can also be utilized in the medical field, as water content is often an important factor in biological systems. Many materials, such as paper and fabric, are largely transparent to terahertz, in contrast to optical wavelengths, which in combination with a high reflectivity for metals makes it suitable for security applications. For example, concealed weapons and explosives could be detected using terahertz radiation. [2] Especially interesting for researchers is the possibility to use terahertz frequencies to investigate structural dynamics of solids. Terahertz radiation can induce lattice vibrations, spin waves and phase transitions in matter. These effects can then be observed using for example x-ray pulses. Performing so called pump-probe experiments using terahertz radiation and x-rays can thus be an important investigative tool. [1] 2

7 1.2 Terahertz generation using femtosecond lasers 1 INTRODUCTION There exists a multitude of generation and detection possibilities. Broadband pulses as well as continuous waves can be produced in a number of ways, for example in electron accelerators, and through frequency conversion in nonlinear crystals. Electron accelerators offer a high intensity, whereas laser based systems are more easily available, and can be made relatively compact [2]. More specifically, femtosecond lasers can be used in table-top schemes to generate broadband terahertz pulses. This is of interest at the FemtoMAX beamline at the MAX IV facility, where terahertz radiation generated by the femtosecond laser can be used in combination with x-rays to perform pump-probe experiments. Figure 1: The electromagnetic spectrum. Not to scale. The Terahertz Band Frequency [Hz] Wavelength [m] Energy [ev] Table 1: The Terahertz Band. 1.2 Terahertz generation using femtosecond lasers Femtosecond lasers, which are ultra short pulsed lasers, can be used in a number of different table-top schemes to generate terahertz radiation. One example of this is the generation of terahertz pulses by current surges in laser induced plasma. For this method, a femtosecond laser is transmitted through a crystal, where a portion is converted to the second harmonic of the laser wavelength. The pump laser, and its second harmonic is focused in air which creates a plasma. If there is a phase difference between the fundamental wavelength and the second harmonic, this produces a net electron current in the plasma. The electron density in the plasma will vary in time, which in combination with the electron current creates a current surge. This results in a terahertz pulse being emitted [3]. This method has been used to create broadband terahertz radiation at high peak fields, but with a conversion efficiency from pump laser energy to terahertz energy for the most part limited to A conversion efficiency up to approximately 10 3 have however been achieved. [4]. Optical rectification in nonlinear crystals is another methods which has been succesfull in generating terahertz pulses with relatively high efficiency. This method relies on a femtosecond laser to induce a time varying polarization density in the crystal, which results in terahertz frequencies being generated. The inorganic crystal LiNbO 3 is one example of crystals that can be used in this way. Conversion efficiency of 10 3 have been reached. However, the use of LiNbO 3 requires tilting of the pump laser pulse front in order to produce terahertz radiation. This complicates the method slightly, and it also makes it more difficult to focus the generated terahertz, because the shape of the intensity profile is distorted [5]. Terahertz pulses have been generated previously in the Ultrafast X-ray Science group using optical rectification in LiNbO 3, with a conversion efficiency of and maximum energy of 0.4 µj [6]. The process of optical rectification can also be employed using organic crystals. There are a number of different kinds of crystals that are capable of producing terahertz radiation, such as OH1, DAST and DSTMS. These have all been reported to generate terahertz at conversion efficiencies on the order of 10 2 [11],[7]. They also have the advantage that no pulse front tilting is needed. One disadvantage of the organic crystals is that they require a pump laser wavelength of µm. This means that an 3

8 1.3 Aim of project 1 INTRODUCTION optical parametric amplifier (OPA) must be used with the laser, which lowers the pump energy available. LiNbO 3, on the other hand, works with 800 nm, which is readily available from the Ti:Sapphire laser at FemtoMAX. The big difference in conversion efficiency between the inorganic and organic crystals should however make up for this. For this project, the organic crystal DSTMS is used to generate terahertz radiation. It has been reported that this particular kind of crystal can produce an especially high generation efficiency, up to 3-4 %, and has an absorption spectrum slightly better suited for terahertz generation than the very similar DAST crystal.[11], [12] 1.3 Aim of project The aims of this master s thesis project were: Generate terahertz radiation using the organic crystal DSTMS through optical rectification. Characterize the generated terahertz radiation. Optimize terahertz conversion efficiency. 4

9 2 THEORY 2 Theory 2.1 Nonlinear optics Light propagating through a medium 1 can be described by the wave equation: 2 E n2 2 E c 2 t 2 = P µ 2 t 2 (1) where E is the electric field, c is the speed of light in vacuum and n and µ are the refractive index and the permeability of the medium respectively. P is the polarization density of the medium, and it is a measure of the dipole moment induced in the medium by the electric field. E and P are here taken to be scalars. For high intensities the response of the material becomes nonlinear, and the relation between the polarization density and the electric fields can be expanded into a Taylor series, and arranged according to equation (2): P = ɛ 0 χe + 2dE 2 + 4χ (3) E (2) where χ is the linear electric susceptibility and d and χ (3) are the second and third order nonlinear coefficients. These are all material specific parameters. For linear materials, only χ is non zero, but for the case where higher order coefficients are also non zero, nonlinear effects can be observed when a strong electric field is applied to the medium. For this thesis, the focus will be on second order nonlinear interactions, and so the propagation material will be assumed to have a nonlinear polarization density described by equation 3. P NL = 2dE 2 (3) In order to investigate the nonlinearity of light, assume an electromagnetic field consisting of two frequency components, as given by equation 4. 1 Isotropic and homogeneous medium 5

10 2.2 Terahertz generation 2 THEORY E(t) = Re{E(ω 1 )exp(jω 1 t) + E(ω 2 )exp(jω 2 t)} (4) Substituting equation 4 into 3, the polarization density induced by the propagating electric field can be calculated. The result is given by 5. P NL = 2dE 2 = 2d (1 2 E(ω 1) E(ω 2) 2 + (OR) E(ω 1) 2 exp(j2ω 1 t) + c.c. + (SHG) E(ω 2) 2 exp(j2ω 2 t) + c.c. + (SHG) (5) E(ω 1)E(ω 2 ) exp(j(ω 2 + ω 2 )t) + c.c. + (SFG) + 1 ) 2 E(ω 1)E (ω 2 ) exp(j(ω 2 ω 2 )t) + c.c. (DFG) The calculations show that additional frequencies will be added to the initial electric field. The contributions have been labeled to clarify what kind of nonlinear processes is at work. Optical rectification (OR) introduces a steady state polarization. Second harmonic generation (SHG) and sum frequency generation (SFG) result in up converted frequencies, and difference frequency generation (DFG) gives a down converted frequency component. The contribution to the polarization density by optical rectification is not time dependent, and will thus not contribute with a new frequency component to the electric field, whereas the other processes will. Difference frequency generation is responsible for terahertz generation, and will be the focus for the rest of this thesis. The amplitude of this component is given by equation 6. P NL (ω 1 ω 2 ) = 2dE(ω 1 )E (ω 2 ) (6) Up until this point, E and P have been described as scalars for simplicity. However, a more general description is given by a vector treatment. In this case, equation 6 becomes E 1 (ω 1 )E1(ω 2 ) P 1 (ω 3 ) d 11 d 12 d 13 d 14 d 15 d 16 E 2 (ω 1 )E2(ω 2 ) P 2 (ω 3 ) = 2 d 21 d 22 d 23 d 24 d 25 d 26 E 3 (ω 1 )E3(ω 2 ) P 3 (ω 3 ) d 31 d 32 d 33 d 34 d 35 d 36 E 2 (ω 1 )E3(ω 2 ) + E 3 (ω 1 )E2(ω 2 ) (7) E 1 (ω 1 )E3(ω 2 ) + E 3 (ω 1 )E1(ω 2 ) E 1 (ω 1 )E2(ω 2 ) + E 2 (ω 1 )E1(ω 2 ) where ω 3 is the difference frequency, ω 3 = ω 1 ω 2. The second order nonlinear coefficient is a tensor rather than a scalar, because the material is in general anisotropic and will have a different response in different directions. It can be seen that the strength of the difference frequency generation process will depend on the polarization of the electromagnetic field and the orientation of the propagation material, in addition to the d-tensor. [9] 2.2 Terahertz generation The process of difference frequency generation described above is used to generate terahertz radiation. But instead of just two frequencies in the initial electric field, a short laser pulse is used, which is comprised of many different frequencies. When the laser pulse enters a second order nonlinear medium, all the different frequency components can combine and create radiation at the difference frequencies. A femtosecond laser pulse has a spectral width on the THz order of magnitude. This means that the generated radiation will consist of frequencies in the terahertz region. The principle is shown in figure 2. 6

11 2.3 Phase matching 2 THEORY Figure 2: A femtosecond laser pulse (left) consists of many different frequencies, (ω 1, ω 2,...). The spectral width is Hz. Generated difference frequencies will thus be created at Ω 1, Ω 2, Hz. The result of a femtosecond laser pulse propagating through the nonlinear medium will be a broadband few-cycle pulse consisting of several frequencies around Hz, see figure 3. The shape of the pulse will be similar to the envelope of the femtosecond laser. Because the terahertz frequencies are so much lower than the laser frequencies ( Hz), this process is referred to as optical rectification, although it does not just correspond to a steady state polarization, but does in fact produce an additional frequency in the electromagnetic field. Figure Phase matching In order for the difference frequency generation process to take place, a phase matching condition, given by equation 8, must be fulfilled. k(ω + Ω) k(ω) = k(ω) (8) where ω and ω + Ω are frequencies within the pump beam, and Ω is the desired terahertz frequency. The phase matching condition will assure that the terahertz radiation is generated in phase. A poor phase matching will result in destructive interference of the generated radiation, and lower the generation efficiency. Equation 8 can also be understood as the principle of conservation of momentum. The phase 7

12 2.4 Crystal optics 2 THEORY matching condition can be expressed in more useful terms by using the definitions of group and phase velocity in equation 9: ( dk ) 1, ( k ) 1 v g (ω) = v(ω) = (9) dω ω where v g and v are the group and phase velocities. The group velocity is the velocity of the pump pulse, which is different from the phase velocity due to dispersion in the material. Evaluating both sides of equation 8 gives the phase matching condition expressed through refractive indices in equation 10: LHS : k(ω+ω) k(ω) ( ) 1 = Ω N(ω) Ω Ω Ω ω k c 0 RHS : k(ω) = Ω v(ω) = Ω n(ω) c 0 } = N(ω) n(ω) = 0 (10) where N(ω) and n(ω) are the group and refractive indices. The group refractive index is given by equation 11. dn N = n λ 0 (11) dλ where λ 0 is the central frequency of the laser pulse. How well the condition in equation 10 is met will affect the generation efficiency. [8] 2.4 Crystal optics All nonlinear processes are results of interaction with a material [8]. For difference frequency generation, crystals are used as mediums. Crystals are materials which have a periodic structure, where identical groups of atoms are positioned repetitively after each other. The crystal axes are used to define the three dimensional periodic structure [10]. The optical axis are lines around which there is symmetry of the optical response, and are not necessarily the same as the crystal axes. For a crystal to be used as an effective DFG medium, some conditions on the optical properties must be met. For materials that are centrosymmetric, the second order nonlinear coefficient is zero, so that no second order processes are possible. This is relatively common for crystals, and excludes many of them from being used for difference frequency generation. In addition, the crystal must have a refractive index for the generated frequency that matches the group index of the pump laser, in accordance with the phase matching condition in section DSTMS The organic crystal DSTMS 2 meets the requirements for terahertz generation. A schematic view of the DSTMS crystal structure is shown in figure 4. The crystal axis a is approximately parallel to the optical axis x 1. The x 1 -axis for the crystal is parallel to the E 1 - and P 1 -components in equation 7. 2 The full chemical name is 4-N,N-dimethylamino-4 -N -methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate 8

13 2.4 Crystal optics 2 THEORY (a) DSTMS belongs to the monoclinic space group which has the basic crystal structure shown here. a, b and c are the crystal axes. This figure is adapted from reference [14]. (b) A more detailed view of the crystal structure, including relationship to the optical axes of the crystal. [12] Figure 4 As was discussed in section 2.1, the second order nonlinear coefficient is a tensor, and the effective coefficient, d eff will depend on the polarization of the pump laser and the orientation of the crystal. A high d eff is key for efficient difference frequency generation. The benefit of DSTMS is that its second order nonlinear coefficient tensor allows strong second order effects. The d 11 -component of the tensor is very high, d 11 = 214pm/V 3, compared to other materials [12]. The d 11 -component is also approximately a factor 10 larger than any other component of the tensor. By examining equation 7 one can conclude that the best generation efficiency will then be reached when the polarization of the pump laser is parallel with the x 1 -axis. This will generate terahertz radiation that is also polarized in the x 1 -direction. For a propagation direction perpendicular to the x 1,x 2 -plane, and polarized parallel to the x 1 -axis, the refractive index for terahertz frequencies and the group index for pump laser frequencies have been calculated using parameters and equations given by references [13] and [12]. The results are shown in figures 5a and 5b. For a pump wavelength between 1400 nm and 1600 nm, DSTMS is clearly very well phase matched with a generated frequency at 1 THz and above 1.5 THz. However, absorption of the generated terahertz in the crystal must also be taken into account. The absorption coefficient is shown in figure 5c. Around 1 THz there is an absorption peak which will suppress generation at that frequency. The center frequency of the pump laser is chosen at 1500 nm, and terhertz frequencies above 1.5 THz are expected to be generated efficiently. 3 For a more detailed description of the numbering of the components, see reference [9] 9

14 2.5 Useful equations 2 THEORY (a) (b) (c) Figure 5: (a) The refractive index for terahertz frequencies in DSTMS. (b) Group index for pump laser wavelengths in DSTMS. (c) Absorption spectrum of terahertz frequencies in DSTMS. Calculated according to [13] and [12] As can bee seen in figure 5, one can not expect exact phase matching at all frequencies. However, a small phase mismatch can be tolerated, but the longer the propagation distance is through the crystal, the more sensitive the generation process is to the mismatch. A measure of how thick the crystal can be and still generate effectively is the coherence length, L c, defined in equation 12. L c = 2π k, k = ( N(ω) n(ω)ω ) c 0 (12) where k is the mismatch between the pump laser and the generated radiation. When designing an experimental setup for terahertz generation, the crystal thickness will be a compromise: a thicker crystal means the laser will generate terahertz during a longer time, a thinner crystal will decrease destructive interference. For terahertz generation in DSTMS, the maximum effective length (which also takes absorption into account) has been determined to be approximately 0.5 mm for a pump wavelength of 1500 nm. The effective length varies with respect to both pump wavelength and generated terahertz frequency. [12] 2.5 Useful equations During the course of this project, there are a few basic equations that have been used while building the setup and evaluating results. They are presented here to simplify reading the rest of this report. 10

15 2.5 Useful equations 2 THEORY The Gaussian beam The pump laser and the terahertz radiation have been approximated by Gaussian beams. The beam divergence, Θ 0, of a Gaussian are given in equation 13. Θ 0 = λ πw 0 (13) where W 0 is the beam waist. This relation, which connects the beam divergence with the wavelength (and therefor frequency), is used to estimate the generated terahertz frequency. This is however only accurate if the terahertz are being generated at the beam waist and in the focus of the laser. Therefor, equation 13 can only be used as an indication of the generated frequency.[8] Telescope A telescope that (de)magnifies a beam can be built using two lenses, according to figure 6. The magnification, M, is given by equation 14 M = f 1 f 2 (14) Figure 6: Setup of demagnifying telescope. Malus Law The intensity of light transmitted through a polarizer is modulated according to Malus Law, equation 15 I = I 0 cos 2 (θ) (15) where θ is the angle between the initial polarization of the light and the axis of the polarizer. Brewster angle For p-polarized light impinging on a boundary between two media, there is a specific incidence angle for which the reflection coefficient will be zero. This angle is called the Brewster angle, and is given by equation 16.[8] Θ B = tan 1( n ) 2 (16) n 1 where n 1 is the refractive index before the boundary, and n 2 is the refractive index after the boundary. This phenomenon can be used when filtering out an unwanted wavelength from a beam containing several wavelength components. The process of generating terahertz radiation through optical rectification in an organic crystal is a collinear process, which means that the generated terahertz will propagate parallel to the pump laser. Since not all of the pump laser is converted into terahertz, the radiation propagating out of the crystal will consist of both terahertz and 1500 nm. The 1500 nm must be filtered out in order to only measure the terahertz. A filter that absorbs only the pump laser can be placed after the crystal to achieve this. 11

16 2.5 Useful equations 2 THEORY However, the filter might reflect some of the terahertz radiation, and thus making it difficult to measure accurately. Placing the filter so that the angle between the pump laser and the normal vector of the filter is equal to the Brewster angle, Θ B, will ensure that none of the terahertz radiation is reflected. The pump laser will however still be filtered out, because the Brewster angle does not affect absorption. [8] Imaging with a lens A camera with an objective is used to image the terahertz source, i.e. the terahertz profile at the crystal. In order to focus the source on the camera chip, the camera is placed according to the imaging equation f = 1 z z 2 (17) The beam source diameter is calculated from the captured image according to equation 18. y 2 = z 2 z 1 y 1 (18) Figure 7: Imaging with a lens. The objective of the camera (the lens) images the object, y 1, on the camera chip, y 2. 12

17 3 METHOD 3 Method 3.1 Equipment Laser system The light source used is a pulsed Ti:Sapphire laser. This laser has a wavelength of 800 nm which is converted into a 1500 nm pump beam using an optical parametric amplifier, OPA. Inside the OPA, a portion of the 800 nm is shifted to a second wavelength that is possible to tune. The two wavelengths are mixed to create a third wavelength, the desired output wavelength which in this case is 1500 nm. The output energy from the OPA is approximately 15 % of the output from the laser. However, the higher conversion efficiency for DSTMS compared to crystals using 800 nm as pump wavelengths should make up for this loss. The pulse length is according to specifications 40 fs and the repetition rate was set to 100 Hz as to not damage the DSTMS crystal. The average power supplied to the experimental setup varied during the course of the measurements, from 50 mw to 90 mw, corresponding to a laser energy of 0.5 to 0.9 mj. However, there were significant daily fluctuations of the laser power, and it could reach as low as 30 mw DSTMS crystal The DSTMS crystal diameter is 6 mm and the thickness 0.54 mm. This thickness is approximately the maximum effective length for generation of terahertz radiation [12]. The crystal is cut so that the ab-plane is the same as the crystal surface. For maximum generation, it is positioned so that the a axis (approximately parallel to the x1 axis) is parallel to the polarization of the pump laser, and the c axis is parallel to the pump beam direction. During manufacturing, the crystal was damaged with two large cracks as a result. The undamaged area in the center of the crystal was just over 2 mm in one direction. For this reason, the laser was initially focused to a smaller spot size, so not to illuminate the cracks and potentially damage the crystal 13

18 3.1 Equipment 3 METHOD further. The crystal as it looked before the experiments began is shown in figure 8. Unfortunately, the crystal was still damaged further during measurements. Figure 9 shows what the crystal looked like at the end of the project. Figure 8: DSTMS crystal at the start of measurements Figure 9: The crystal was burnt while focusing the laser to hard. The burn mark can be seen in the center. The initial cracks also spread significantly Detection Two different detection methods were used. A pyroelectric detector from Microtech Instruments specifically intended for terahertz detection was used with an oscilloscope in order to capture the THz waveform and determine the power of the generated terahertz. A chopper was used along with the detector to modulate the frequency at 10 Hz. It should be noted that the operating spectral range of the detector is THz, whereas the generation method used for this project can be expected to produce a significant amount of radiation up to 5 THz[11]. The second detection method was a THz camera that was used to capture the beam profile. 14

19 3.2 Building the setup 3 METHOD 3.2 Building the setup Figure 10 shows the first experimental setup. Mirrors M1 and M2 are 2 inch silver coated mirrors used to direct the beam into the setup and align the beam through the telescope. A telescope was used to demagnify the beam, increasing the fluence. L1 is a plano-convex lens with a focal length of f = 300 mm, and L2 is a plano-concave lens with focal length f = -50. The lenses were positioned with curved surfaces facing out of the telescope to minimize spherical aberrations. The L2 lens was positioned on a translation stage in order to adjust the size of the laser spot on the crystal. Mirrors M3 and M4 are 1 inch silver mirrors used to direct the beam onto the DSTMS crystal. The crystal was placed in a rotational mount and positioned so that the x1 axis was parallel to the laser polarization, in accordance with section 2.4. A pump laser energy up to 500µJ was delivered to the experimental setup, of which approximately 60 % reached the crystal. Due to the collinear nature of the experiment, it was necessary to filter out the 1500 nm pump beam, in order to only measure the THz radiation. This posed a bit of a challenge. Finding a readily available material that transmitted THz but blocked 1500 nm was not trivial. Although Si should transmit 1500 nm, it was discovered that almost all the power of the pump beam was absorbed when using a Si-wafer. This is discussed in section 3.5. In this initial experimental setup, the pump laser was s-polarized so that the Brewster angle could not be used when filtering, and there was some loss of terahertz radiation due to reflection of the wafer. Using two wafers, it was possible to determine the transmittance of the THz radiation. For the pyroelectric detector, one Si-wafer was used to filter the pump beam. The detector was placed directly behind the crystal in order to detect possibly very divergent THz radiation. For the camera, which is extremely sensitive, 2 wafers were used to avoid damage. Figure 10: Experimental setup 3.3 Measurements Initial generation and detection Terahertz radiation was first generated using the setup in figure 10 with an s-polarized 1500 nm pump beam, filtered through one Si-wafer and detected with the pyroelectric THz detector. A strong indication that it was in fact terahertz radiation, was observing the measured power drop to zero when removing the crystal while keeping the pump laser on. Another quick test was rotating the crystal around the propagation axis, and observing the power decrease when the x1 axis was rotated away from its initial position. The position of the negative lens was adjusted to focus the laser and find the position for maximum generation. The size of the laser spot on the crystal was a compromise. On one hand, in order to have good generation efficiency, a high laser fluence is preferable. On the other hand, it is important not to exceed the crystal s damage threshold. An accurate idea of the beam size is therefor important. Due to the pump laser being outside the visible spectrum, this was a bit difficult as there was no camera available able to capture the beam profile. The beam was imaged using an laser viewing card and there 15

20 3.4 Final setup and measurements 3 METHOD was some uncertainty as to how well the card depicted the beam profile. Furthermore, the card had to be moved around, making it difficult to estimate the spot size. In addition, irregularities in the laser beam caused some discrepancy in how the spot diameter was estimated, see section 3.5. These concerns lead to caution when focusing. In order to ascertain the dimensions of the laser spot, knife-edge measurements can be performed in horizontal and vertical directions. This, however, takes a bit of time and setting up, and is not practical to do while trying to optimize generation. Knife-edge measurements were made at one point to determine laser beam size and fluence, but for the most part this was estimated using the laser viewing card. Despite precautions, the crystal was burnt at one point when the laser was focused to hard. The following measurements were performed in order to characterize the generated radiation: Polarization measurements Polarization measurements were performed in order to help verify that it was in fact terahertz frequencies that were generated. First, the effect of the pump laser polarization was investigated. The polarization was rotated using a half wave plate. The change in THz radiation was detected with the pyroelectric detector as well as the camera. The electric field component parallel to the x1-axis of the crystal is the component mainly expected to contribute to the terahertz generation, due to the large d 11 -component in equation 7. The intensity of the pump energy in this polarization thus exhibits a quadratic decrease as the polarization angle is rotated. Since the terahertz radiation scales quadratically with the pump, the generated terahertz energy was expected to have a cos 4 dependency on the polarization angle of the pump laser. The polarization of the generated radiation was also investigated using a terahertz polarizer. This was placed after the crystal and before the detector, and the transmitted power was measured as a function of the polarizer angle. Pump power dependence The pump power dependence of the generated terahertz radiation was measured. The pump power was tuned between 0 and 300 µj using a set of polarizers. Wavelength scan The final measurement using the terahertz detector was investigating the dependence on the pump laser wavelength. The pump beam was tuned over the range nm, optimized at 20 nm intervals. The actual wavelength of the pump laser was measured with a spectrometer. At wavelengths close to 1600 nm the power of the pump laser significantly decreased, which most likely affected the reliability of the results negatively. Measurements using the THz camera The terahertz camera was used to image the terahertz beam profile. It was used with and without objective. Using the objective, it was possible to image the terahertz source. Without the objective, the terahertz radiation was captured directly on the camera chip giving an accurate image of the beam profile. Images were captured at three different distances from the crystal, allowing the divergence to be determined, which in turn gives an idea of what frequencies are being generated. Thermal powermeter There were attempts at detecting the terahertz radiation using a thermal sensor. Unfortunately these were not successful as the fluctuations were on the same scale as the terahertz power. 3.4 Final setup and measurements After terahertz radiation had been successfully generated and characterized, the experimental setup was improved to optimize generation and facilitate detection, see figure 11. The pump laser polarization was switched to p-polarization using the λ/2 - plate so that the Brewster angle could be used when filtering 16

21 3.5 Additional notes 3 METHOD out the pump laser. Some changes were also made to the laser system, allowing more pump energy, up to almost 900µJ, to be delivered to the experimental setup. In an effort to increase the generation efficiency, a 1:8 telescope was installed to allow for a higher fluence. However, contrary to initial assumption, a higher generation efficiency was reached when defocusing the pump laser to a larger spot on the crystal. The telescope was therefor switched to a 1:5 lens system, resulting in a laser spot diameter of 4-5 mm. A gold parabolic mirror was used to focus the THz radiation on the detector. The parabolic mirror allowed the terahertz radiation to be detected further away from the crystal, and it also made it possible to detect radiation from a source larger than the active area of the detector. Three Si-wafers were placed at the Brewster angle to filter out the 1500 nm, see section 2.5. The Brewster angle was found by rotating the wafers until maximum power was detected. However, even with the parabolic mirror, detecting the generated THz radiation was a challenge. Due to terahertz radiation being outside the visible spectrum, it was difficult to affirm that all radiation was being detected. A very small adjustment of the detector could manifest in a great change in detected power. Figure 11: The final experimental setup. Aside from the fluence, the generation efficiency can also be influenced by the pump pulse length. This was adjusted using a compression grating in the OPA, and could be seen to significantly increase the terahertz power. During the course of measurements, the crystal continued to crack. Initially, care had been taken to not illuminate the cracks, but this became less feasible over time, especially when a larger spot size was determined preferable. 3.5 Additional notes Tha bandgap of Si is 1.12 ev which is significantly higher than the energy of the pump laser: a wavelength of 1500 nm corresponds to approximately 0.8 ev. Absorption of the pump laser was however clearly observed, and this is most likely due to two-photon absorption. The two-photon absorption coefficient has been calculated in reference [15] for similar circumstances, and seem to correspond fairly well to what was observed during these measurements. Along with the 1500 nm radiation, some green light was also inadvertently supplied from the OPA. This was most likely due to frequency up-conversion of 1500 nm and 800 nm light (from the Ti:Sapphirelaser), which can occur in all interfaces in the setup. This light was highly focused after the telescope, and there was some concern as to how it might affect the crystal. A green filter was placed by the first lens, however, green light was still visible after the telescope and it was not possible to completely get rid of this. This light was also visible on the laser viewing card, distorting the beam profile. It made it more difficult to align the telescope, as well as focusing the beam correctly on the crystal. 17

22 4 RESULTS 4 Results The transmission of the Si wafer for THz radiation was determined to be 59%. The terahertz radiation was first observed on the oscilloscope using the terahertz detector, as presented in figure 12. The wave shape of the signal is due to the chopper working at 10 Hz, allowing the peak to peak voltage to be measured. The power could be extracted using the responsivity curve for the detector, included in the appendix, section 6.2. The finer saw tooth pattern is due to the repetition rate, 100 Hz, of the pump laser. A knife-edge measurement on the pump laser was performed. The results are presented in table 2. Pump laser Terahertz radiation Energy on crystal 262 µj Energy 1.53 µj x FWHM 1.3 mm Conversion efficiency 0.58 % y FWHM 1.2 mm Fluence 20.5 mj/cm 2 Table 2: Data from the initial detection of terahertz generation. The maximum generated terahertz energy, achieved using the second experimental setup, was 3.75 µj, corresponding to a conversion efficiency of 0.71%. This maximum energy and conversion efficiency are almost a factor of 10 higher than had previously been achieved in the Ultrafast X-ray science group, using the inorganic crystal LiNbO 3 [6]. No knife-edge measurement was made of the pump laser at this point, although the beam diameter was estimated to 4 mm, corresponding to a fluence of approximately 4 mj/cm 2. 18

23 4 RESULTS Figure 12: THz waveform captured on oscilloscope. The results from varying the polarization of the pump laser are presented in the graph shown in figure 13. The measured data does not correspond to a cos 4 -function, which is the result that was initially expected. This is further discussed in section 5. Figure 13: Terahertz power as a function of pump laser polarization. 0 corresponds to vertically polarized light. The crystal was positioned with the x 1 -axis in the vertical direction. The red curve is the theoretically expected cos 4 -function. Figure 14 includes a series of pictures taken by the camera, illustrating what was seen while adjusting the pump laser polarization. The terahertz radiation can be seen to disappear when the laser polarization is made horizontal. 19

24 4 RESULTS Figure 14: Images of THz spot using camera with lens. The polarisation of the pump laser was rotated using the λ/2-plate between pictures. From upper left to lower right corner the polarization is scanned from vertical to horizontal and back to vertical. The halo is due to automatic scaling of the camera. As the terahertz intensity decreases, this halo grows stronger. It does not correspond to actual radiation. 20

25 4 RESULTS The polarization of the terahertz radiation is investigated in figure 15. There is a maximum of the transmission through the polarizer at an angle close to 90, which is parallell to the crystal s x1-axis, and the power follows a cos 2 -function. This indicates that the terahertz radiation is linearly polarized light along the x1-axis, according to Malus law, equation 15. This is also what is expected from the discussion in section 2.4. Figure 15: Terahertz energy transmitted through a polarizer. The polarizer transmits vertically polarized light at 90. The pump laser energy dependence of the terahertz energy is depicted in the graph shown in figure 16, and a log-log graph is incuded for easier analysis. The first few data points fit well with a second order function, which is to be expected for terahertz generation. However, there is a deviation from this for higher pump energies, likely due to saturation. No knife-edge measurement was performed in conjunction with this measurement, so it is not known exactly at what fluence the saturation begins. (a) (b) Figure 16: (a)terahertz energy dependence on pump energy. (b) plotted in a log-log scale. 21

26 4 RESULTS The results from the wavelength scan are shown in figure 17. Note that the terahertz energy has been modulated by the square of the pump energy for comparison between the different pump wavelengths, due to the second order nature of the generation process. However, observing the results in figure 16, this might not give the most accurate result. The significant increase in efficiency at higher pump wavelengths is somewhat misleading. The increase was due only to a decrease in pump energy, no increase in terahertz energy was detected. The data from the measurement is included in the appendix, section 6.1. Figure 17: Wavelength scan of the pump laser. The data points in blue mark points where the pump power was below 80% of the average pump power. 22

27 4 RESULTS The terahertz source, imaged using the camera lens, is shown in figure 18. A horizontal cross section of the spot was taken and a Gaussian function was fitted to the intensity distribution. The FWHM was then determined to be 1.7 mm, taking the magnifying effect of the lens in to account, according to section 2.5. Figure 18: To the left, the terahertz source is imaged using the camera lens. To the right is a cross section of the spot and a Gaussian fit. The camera was also used to determine the divergence of the terahertz beam. The images of the beam profiles at three different positions are shown in figure 19. A horizontal cross section were used, as the lagging of the camera distorted the spots in the vertical direction, and FWHM calculated. The divergence was calculated by fitting a straight line to the measured FWHM, and determined to be θ 0 = This corresponds to a frequency of 4 THz, according to section 2.5. As the terahertz is not generated in the focus of the pump laser, this calculation only gives an indication of the center frequency and mainly serves as a confirmation that radiation in the correct frequency region is being generated. 23

28 4 RESULTS (a) (b) (c) Figure 19: The THz beam profile captured on the camera chip at distances a) 6.2 cm, b) 9.1 cm and c) 12.5 cm. A scale with beam divergence in degrees is included in figure (a) for clarity. The lines in the images are due to lagging in the camera software. The camera was also used with the second experimental setup, figure 11. This image is at, or very near, the focus of the parabolic mirror. Due to the power being significantly higher with the second setup, the camera was kept further away from the crystal, and carefully moved closer until a good image was captured, so as not to damage it. 24

29 4.1 Summary 4 RESULTS Figure 20: THz beam profile captured on chip near the focus of the parabolic mirror. 4.1 Summary Terahertz radiation was successfully generated. The maximum energy and generation efficiency reached were 3.75 µj and 0.71% respectively. This was achieved for a laser energy of 0.53 mj at the crystal, and a laser spot of approximately 4 mm. The divergence of the terahertz beam was measured to Θ 0 = 1 which corresponds to a frequency of 4 THz. The generation process was confirmed to be a second order process, dampened however by saturation above a certain fluence. 25

30 5 DISCUSSION AND CONCLUSIONS 5 Discussion and conclusions The first challenge of the project was to ascertain that it was in fact terahertz radiation that was measured. Because the generation efficiency of the terahertz is so low, detection of an unwanted wavelength, even if only very little, will significantly disturb the results. The crystal was removed on several occasions to confirm that the detected power disappeared, and that none of the pump laser was detected. The pump polarization dependency measurement did not give the expected result. This might however be due to an oversimplification in the theory. The simple cos 4 -relation only takes into account the d 11 -component of the nonlinear coefficient tensor, which makes sense as long as all radiation (pump laser and generated terahertz) is parallel to the x 1 -axis. When the polarization of the pump laser is rotated however, it might be necessary to consider additional off-axis d-components coupling the different polarization components. A more thorough theoretical evaluation is needed in order to understand the measured data. However, the measurement of the terahertz polarization gave the precise results expected. Throughout the project, detecting the terahertz was a difficulty. Due to the small active area of the detector, it is possible that not all generated radiation was detected, mainly during measurements with the first setup. It is difficult to say how much, if at all, this affected the measurements of pump polarization dependence and wavelength scan. The laser beam was for the most part focused to a FWHM of less than 2 mm, and the active area of the detector was placed approximately 1 cm from the crystal. The maximum measured terahertz energy and generation efficiency achieved were relatively high compared to similar terahertz generation methods. The efficiency was not quite as high as have been reported elsewhere, which can probably be attributed to differences in pump energy and fluence. The results from the pump power measurements show that the generation process can saturate at a certain fluence. Above this, there can be an increase in generated terahertz energy, but not necessarily in generation efficiency. The highest measured generation efficiency was obtained for a pump pump fluence well below the saturation point, and for a laser spot of 4 mm, which means that all of the crystal was not used. Had a high enough pump energy been available to illuminate all of the crystal at the threshold of saturation, it is very likely that a higher generation efficiency would have been reached. 26

31 5.1 Future work 5 DISCUSSION AND CONCLUSIONS There might also have been other contributing factors, such as crystal quality and thickness. Issues with detection might also have played in. The spectral range of the pyroelectric detector was on the lower end of the generated radiation, and it is not exactly known how well the higher frequencies were detected. The detector was also used with a black filter that will further lower the detected power. The wavelength scan produced some curious results. As have been mentioned before, the high efficiency for longer pump wavelengths is due to low pump power and a stable terahertz power. The simplest explanation then would be that there was an issue with detecting the pump power, and not that the power itself decreased. Possibly, changing the wavelength might have affected the alignment and steered the beam slightly outside the detector. 5.1 Future work The experimental setup can be improved in a number of ways. Firstly, approximately 35% of the pump power was lost between entering the setup and hitting the crystal. This could be greatly improved by using a design with less mirrors, and using lenses optimized for 1500 nm (only one of the lenses in the second setup was optimized for the pump wavelength, and none in the first). Secondly, using a xyztranslation stage for the detector would make it easier to find the optimum placement, adjusting it by hand was too unstable to be efficient. A camera able to capture laser beam profile would be very useful when characterizing the relationship between the pump laser and the generated terahertz radiation. Quicker and more accurate measurements could be made of the alignment and focus, and divergence measurements could be performed. Further investigations should also be made into the pump power dependence in order to maximize generation efficiency. Having knowledge of the spectral components of the generated radiation is also desirable, and this would require other detection methods than were available during this project. 27

32 6 APPENDIX 6 Appendix 6.1 Wavelength scan Pump wavelength [nm] Pump power [mw] Terahertz power [mv] sdev [mv] Microtech Pyroelectric Detector Table 3: Measured data from the wavelength scan. Operating spectral range Active area Typical responsivity Optimal modulation frequency THz 2mm x 3mm 1000 V/W 5-30 Hz Table 4: Properties of the pyroelectric detector. 28