We present a detailed exploration of the behavior of gallium phosphide (GaP) crystals used for optical rectification (OR) of high average power (> 100 W), MHz repetition rate ultrafast lasers. We measure thermal load, Terahertz (THz) refractive index and THz yield over a wide temperature range (77 K to 500 K) in this unusual excitation regime. Our thermal load measurements indicate that nonlinear absorption remains the main contribution to crystal heating and thus the main limitation to scaling the conversion efficiency and show that cryogenic cooling can partly relax these limitations. Furthermore, we present first temperature-dependent refractive index measurements of GaP for frequencies up to 4 THz, showing only minor deviation from room temperature values and no significant degradation of coherence length. Last but not least, we present first experiments of OR in GaP at cryogenic temperatures and observe an increase in THz yield (30%) at cryogenic temperatures when using short pulse duration excitation, due to reduced THz absorption at broad THz bandwidth. Our results indicate that OR in cryogenically cooled GaP is a promising approach for achieving broadband, high-average power THz radiation using short-pulse (< 50 fs) excitation at even higher average power (>> 100 W) - performance that is readily available from state-of-the-art ultrafast Yb-doped solid-state lasers.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Ultrafast laser-driven THz sources for time-domain spectroscopy (TDS) have become ubiquitous in various fields of science and technology, and important efforts continue to be dedicated to improving their performance. This has resulted in many advances, mostly in terms of pulse energy, peak field and/or bandwidth . However, the average power of THz sources for TDS remains low (commercial sources operate with tens to hundreds of microwatts), particularly for broadband sources extending to frequencies significantly above 1 THz. Many applications in spectroscopy, imaging or remote sensing [2–4], would immensely benefit from an increase in average power, i.e. a high THz pulse energy at high repetition rate, allowing for faster measurements and/or higher signal-to-noise ratio.
These limitations in average power directly mirror the limited average power of most commonly used ultrafast driving lasers such as Ti:sapphire technology, which typically cannot deliver significantly higher power than a few watts and telecom-wavelength fiber lasers which are cost-efficient but deliver only up to few hundreds of milliwatts of power. However, in the last decades, many breakthroughs have been realized in ultrafast laser technology based on Yb-doped gain materials emitting at around 1 µm wavelength in different geometries, resulting in average powers exceeding the kW-level, and thus opening the door to laser-driven THz sources excited with much higher average powers [5–7]. Among the large family of high-average power ultrafast laser systems, we focus our attention on MHz repetition rate laser sources, in particular, mode-locked thin-disk oscillators providing this performance from one-box, amplifier-free setups, offering a promising path for high-average power THz sources at high repetition rate for applications where signal-to-noise ratio and measurement times are of critical importance .
In this goal, gallium phosphide (GaP) is a promising χ(2) nonlinear material for obtaining broadband and powerful THz beams. It is commonly used for optical rectification (OR) of ultrafast laser systems in the near infrared to generate THz radiation, and has received renewed attention in the last few years because of its favorable collinear velocity matching condition in the 1 µm region, where the above-mentioned high-average power, advanced laser systems are now available [9–15]. Furthermore, one of the most exploited advantages of GaP is that, contrarily to many of its other nonlinear material counterparts such as lithium niobate (LiNbO3) or zinc telluride (ZnTe), it enables to generate more broadband THz signals (typically extending up to 7 THz) using ultrashort driving pulses [9,16,17], with its first phonon absorption peak at 11 THz . Progress in pulse compression of high-average power lasers [19–21] therefore additionally supports the increased interest in this material. In our most recent results, we demonstrated that GaP is suitable for OR at record-high driving average power > 100 W [10,11], and further showed that state-of-the-art conversion efficiencies are feasible at these high driving average powers, reaching a THz average power up to 1.35 mW and bandwidths extending up to 6 THz , illustrating this material’s potential.
At these excitation powers, crystal damage and other undesirable thermal effects are expected to become significantly stronger and may very well constitute the limiting factor for further average power scaling, and these aspects have never been investigated so far. This is particularly true for systems with high repetition rate in the multi-MHz regime as targeted in our work, since strong focusing is required to reach sufficient intensity for efficient nonlinear conversion. In this regime, cryogenic cooling of GaP can become increasingly beneficial to reduce thermal load and potentially increase conversion efficiency, which motivated us to perform this detailed study. Furthermore, a reduction in phonon absorption at cryogenic temperatures can increase the generated THz bandwidth, which becomes feasible with the above-mentioned advances in pulse compression of high-average power ultrafast laser systems. However, to the best of our knowledge, no thorough experimental exploration of temperature-dependent effects that could affect OR (origin of thermal load, thermal lensing, refractive index changes) has so far been reported with GaP. While THz generation at cryogenic temperatures is well documented in LiNbO3 (owing to its strong phonon resonance at ∼ 7.7 THz and resulting detrimental THz reabsorption effects) [22–24], to the best of our knowledge, no reports on OR in cryogenically cooled GaP have been reported. Furthermore, while previous studies give some valuable insights [25–31], a full temperature-dependent crystal characterization has so far not been reported.
Here, we explore cryogenic cooling of GaP as a potential path for power upscaling of broadband high-power THz sources based on high-average power femtosecond laser excitation. We base our measurements on excitation with our home-built 100 W-class thin-disk laser, operating at ∼ 13 MHz repetition rate. We explore thermal effects in the crystal and evaluate the deposited heat due to linear and nonlinear absorption, showing that at room temperature, nonlinear absorption remains the main contribution to thermal effects in the crystals. Furthermore, we show measurements of temperature-dependent refractive index of GaP at THz frequencies up to 4 THz in a temperature range from 77 K up to 500 K, which to the best of our knowledge have so far not been reported. Based on our measurements, we then discuss the resulting effects on phase matching and their impact on OR efficiency. Finally, we perform first cryogenically cooled OR experiments and compare the generated THz power for long (580 fs) and short (88 fs) excitation pulses in a wide crystal temperature range, showing an improvement of 30% in the case of short pulse excitation using cryogenic cooling of 2 mm thick GaP, as well as an enhanced THz bandwidth at cryogenic temperatures. As high-average power, short-pulse ultrafast laser systems become more widespread, we believe these measurements will represent a valuable resource for the community. Finally, we conclude our study by discussing next power scaling steps of broadband THz pulses using kW-class excitation powers.
2. Experimental setup
The experimental setup for investigation of OR in GaP at cryogenic temperatures is depicted in Fig. 1. Our driving laser source is a self-built Yb:LuAG thin-disk oscillator that is soliton mode-locked using a semiconductor saturable absorber mirror (SESAM). The laser system emits at a central wavelength of 1030 nm and provides pulses with a duration down to 534 fs at a repetition rate of ∼ 13 MHz, at an average output power of up to 123 W. The nearly Fourier-limited pulses can be temporally compressed with high efficiency to 88 fs at 112 W of average power using a Herriott-type multi pass cell (MPC) for spectral broadening, followed by dispersion compensating mirrors. Further details about the laser source and the pulse compression setup can be found in Refs. [10,11].
THz radiation is generated via OR in several <110>-cut anti-reflection (AR) coated GaP crystals (position (1) in Fig. 1) with a spot size of ∼ 1 mm (NIR beam diameter at 1/e2 intensity level). In our previous publication we achieved optimum conversion efficiency using a ∼ 1 mm spot size . The same spot size is consequently chosen in this work. A future study could also include a spot size sweep, to evaluate whether the optimal intensity is modified by cryogenic cooling. The generated THz radiation is collimated and refocused by four aluminum off-axis parabolic mirrors with 180 mm diameter and 160 mm focal length. The residual NIR beam is transmitted through a 10 mm hole in the first parabolic mirror and is blocked by a beam dump. Using a beam splitter, a small portion of this beam is diverted onto a CMOS camera for a characterization of the beam profile after THz generation. For THz transmission measurements the sample (without AR coating) is placed in the common focal point of the second and third parabolic mirrors (position (2) in Fig. 1. The THz electric field is characterized via electro-optic sampling (EOS), using <110>-cut GaP crystals for detection. Here, a small fraction of the total laser output (∼ 1%) serves as the probe beam. The delay is realized with a retroreflector mounted on a mechanical shaker (15 Hz) and an additional mechanical delay line. The EOS scheme follows the standard configuration including a quarter-wave plate, followed by a Wollaston prism and a balanced photodetector. The THz waveform is then sampled via an oscilloscope and averaged over 50 traces. To measure the THz power, the detection crystal is replaced by a calibrated commercial pyroelectric power meter (Ophir RM9-THz). Special care is taken to block residual scattered NIR radiation on the detector. For this purpose, a sheet of black paper is placed in front of the power meter. The transmission of the black paper is characterized via EOS and is compared with the transmission value while placing a second sheet of black paper in front of the THz power meter. The results are in a good agreement and are accounted for in the reported values of the THz power. The THz measurements take place in a purged box with a dry nitrogen atmosphere (relative humidity of less than 10%) to prevent absorption in water vapor. For control of the GaP crystal temperature, a continuous flow cryostat is used, which can provide temperatures from 77 K to 500 K using liquid nitrogen cooling. For THz generation experiments the cryostat entrance window is UV fused silica, while the exit window is z-cut-crystal quartz. For THz transmission experiments both entrance and exit windows are z-cut-crystal quartz. All windows are plane-parallel, have a thickness of 3 mm and are AR-coated for a wavelength of 1030 nm. In the future, these studies can be extended to lower temperatures, by using liquid helium cooling. We note that the excitation powers may vary slightly between experiments in this work, due to differing laser alignments on different experimentation dates, leading to slightly different available output powers. Nevertheless, the actual available power level is always considered in all our experiments.
3. Thermal effects
3.1. Observation of strong thermal effects, effects on the pump and the THz beam
Thermal lensing caused by strong thermal gradients and the resulting refractive index variations can be used as an indicator for the thermal state of the crystal. These strong thermal effects can be visualized by observing the far-field beam profile after propagation through a 2 mm thick GaP crystal by observing the intensity pattern with a CMOS camera that was placed between the first parabolic mirror and the beam dump (see Fig. 1). Figure 2(a) and Fig. 2(b) show the intensity pattern of the NIR beam (88 fs duration) with respective average powers of 45 W and 112 W incident on the GaP crystal at 290 K. The observed fringe patterns resemble Bessel-beams generated by a linear elliptical axicon [32,33], typically observed in the presence of strong thermal lensing caused by a Gaussian beam. In order to confirm the assumption that the thermal lens is the main cause of the observed beam distortion, we rule out a self-focusing induced lens caused by the optical Kerr-effect by numerically propagating our excitation pulse through the crystal, using a home-programmed 3D nonlinear propagation code, applying the nonlinear refractive index coefficient of GaP for NIR . Our model is based on the numerical solution of the nonlinear Schrödinger equation using the split-step Fourier method. The model takes into account linear (dispersion) and nonlinear (intensity dependent refractive index) effects of pulse propagation in spatial (x,y) and temporal (t) domains, allowing to evaluate eventual spatial-temporal couplings that can lead to beam degradation at high peak intensities . Our simulation indicates that at room temperature the self-focusing effect for the excitation power of 112 W (corresponding to a peak intensity of 19.8 GW/cm2 at 1 mm beam diameter) leads to a negligible reduction in the beam size (0.2%) after 2 mm propagation. Kerr-lensing can thus be excluded as possible source for the observed beam profile evolution, thus confirming that strong thermal lensing is present. In Fig. 2(c), the intensity pattern of the NIR at 77 K and an excitation power of 112 W is illustrated. The observed beam pattern is very similar to that at 290 K with a lower excitation power of 45 W thus showing a strong reduction of the thermal lensing effect by cryogenically cooling GaP at high excitation powers. Note, that though the cryostat windows lead to a small change of absolute intensity and fringe size, the qualitative evolution of the intensity profiles with temperature is unaffected.
A THz camera was inserted into the focal point of the final parabolic mirror (replacing the detection crystal in Fig. 1) in order to investigate whether the THz beam profile is adversely affected by the observed thermal lens. We note, that for all temperatures and excitation powers no noticeable change of THz beam profile could be observed, showing that this thermal lens does not directly affect the generated THz beam.
3.2. Origin of thermal load
So far, most experiments of OR in GaP were performed under low average power, high peak power excitation. In this regime, it is well-known that the main limitation in reaching high conversion efficiencies is due to multi-photon absorption effects [28,36]. The main goal of this section is to identify up to which extent this assumption can also be made in the case of high average power excitation. In fact, in the case of high average powers and high repetition rates (i.e. small laser excitation spots), a significant amount of heat can be generated due to NIR absorption. Both linear and nonlinear absorption of NIR radiation have detrimental effects on OR: on the one hand, the absorbed radiation is not available for the nonlinear conversion process. Secondly and most importantly, NIR absorption results in the generation of heat and free charge carriers. A large temperature rise in the crystal could result in thermal damage (of the crystal itself or its coating at the surface). Furthermore, the charge carriers generated by multi-photon absorption (MPA) can absorb THz radiation [27,28] and therefore further reduce the attainable THz output power. In the following, we quantify heat power generation due to linear and nonlinear NIR absorption in GaP, excited with ∼ 100 W average power at typical intensities for OR (17.7 GW/cm2 for 1 mm beam diameter). From this we gain a better understanding of the role that NIR absorption plays in our unusual excitation regime.
The experimental setup used for measuring the thermal load on the crystals is the same one as used in the OR experiments presented above (Fig. 1). In order to measure the total heat power deposited in the crystal, we use the following procedure: the sample is kept under a constant flow of liquid nitrogen, while a temperature-controller keeps the crystal at a constant target temperature via an additional heating element. When the sample is illuminated, the heating due to NIR absorption in the GaP crystal leads to a reduction of the heater power supplied by the temperature-controller. The difference of measured heater power for the illuminated and non-illuminated sample then corresponds to the heat generation by NIR absorption for a given target temperature. Here, the base temperature was decreased below 77 K by applying vacuum to the nitrogen line. Several data points were taken at each excitation power. In order to distinguish between linear and nonlinear absorption, we modify our laser to provide continuous-wave (CW) radiation instead of ultrashort pulses by replacing the SESAM with a highly reflective (HR) mirror. Measurements under these conditions give only the contribution of linear absorption to the heat power. When performing the same measurements with the mode-locked laser, we measure the accumulated effect of linear and nonlinear absorption. For this, the NIR pulses with 88 fs duration were utilized. For the latter experiment the maximum achievable power was 95 W, resulting in a peak intensity of 16.8 GW/cm2 on the GaP crystal.
Figure 3 shows the mean heat generation due to the NIR laser beam at 290 K and 77 K for different excitation powers. As expected, for CW operation the measured data for each temperature clearly show a linear increase in the generated heat as a function of excitation power. The errorbars in x- and y-direction represent the standard deviation of the data points. As we can see, at 290 K an excitation power of 100 W results in the generation of 1.6 W of heat in the GaP crystal. This value is reduced by 7.6% when the crystal is cooled to 77 K. For 88 fs pulses a clear nonlinear dependence of the generated heat on the excitation power can be observed, as indicated by third-order polynomials fitted to the data. The observed nonlinear behavior can be attributed to an expected combination of two- and three-photon absorption [27,28] in GaP. First, we observe that the heat generated by nonlinear absorption is significantly higher than in the case of linear NIR absorption for both temperatures. At 290 K a driving average power of 100 W results in the generation of 6.6 W heat in the crystal, which is larger by a factor of 4 compared to the heat generated by linear NIR absorption at the same excitation power. Second, we observe a significantly stronger temperature dependence for the heat generated by nonlinear absorption than in the case of linear absorption. By cryogenically cooling the GaP crystal to 77 K the generated heat is reduced by 26%. This behavior can be attributed to the origin of the nonlinear absorption. Multi-photon absorption drives the electronic transition between valence and conduction band. Cooling the crystal leads to an increase of the electronic band gap, causing a decrease of transition probability for the given NIR spectrum. At higher excitation average powers, we can expect this difference to become larger, and the benefit of cryogenic cooling to become more apparent. It is important to keep in mind that a higher average power at same repetition rate and pulse duration results in a higher peak power, where normally one would have to enlarge the spot size to keep the intensity constant, to avoid catastrophic damage caused by nonlinear absorption effects. Our measurements indicate that cryogenic cooling would allow to apply higher intensities with reduced detrimental heating due to nonlinear absorption, which should result in a higher conversion efficiency.
The measured heat generation was used to estimate the temperature in the focal point of the NIR driving laser. For this purpose, the generation crystal was approximately modeled as a cylinder. A gaussian laser spot in the center was assumed as a heat source, while the cylinder mantle surface serves as heat sink at constant cryostat temperature. Heat source and sink then provide boundary conditions for the numerical solution of the heat diffusion and transport equations. Using the heat values generated from 88 fs pulses at 100 W at a cryostat temperature of 290 K we estimated a temperature of 306 K in the center of the beam, while at a cryostat temperature of 77 K a central temperature of only 80 K was estimated. This behavior can be understood in the context of the temperature-dependent thermal properties of GaP. The thermal conductivity of GaP increases from 110 W/(m K) to 500 W/(m K) when cooling from 290 K to 77 K . At the same time the specific heat of GaP drops from 430 J/(kg K) to 150 J/(kg K) , which leads to a massive increase in thermal diffusivity. Cryogenic cooling therefore not only allows for a much more efficient heat removal in the steady-state but also leads to significantly shorter reaction times to changes in applied thermal load. Though these are only approximate values, this confirms that efficient cryogenic cooling leads to a more homogeneous temperature profile inside the generation crystal, thereby reduced thermal lensing and contributes to an improved NIR beam quality.
4. Temperature-dependent THz refractive index of GaP
Knowledge of the temperature-dependent THz phase-matching behavior is crucial for understanding and optimizing optical rectification at high excitation powers and cryogenic temperatures. For this purpose, we used our TDS setup to measure the THz refractive index of GaP at THz frequencies in a temperature range from 77 K to 500 K. Using these measurements, we calculate the temperature-dependent coherence length, to evaluate possible phase matching degradation. For these measurements, we used the THz-TDS setup described above (Fig. 1). A water-cooled 500 µm thick GaP crystal was used as the generation crystal at room temperature, allowing in our experimental setup for a THz generation bandwidth extending up to 5 THz using 88 fs driving pulses. The THz radiation was focused onto a <110>-cut plane-parallel GaP crystal (without AR coating) with polished surfaces and a thickness of 113.2 ± 0.1 µm that was placed in the cryostat between the second and the third parabolic mirrors (position (2) in Fig. 1). A 500 µm thick GaP was used as the detection crystal. The time-domain THz electric field transmitted through the GaP crystal in the cryostat, denoted as sample signal ES(t), was then recorded via THz-TDS, while the THz electric field transmitted through the empty cryostat ER(t) was used as reference signal. The frequency-domain THz electric field of the sample ES(ω) and the reference ER(ω) were then obtained by Fourier transformation.
4.1. Measurement of the refractive index
To measure the refractive index, we employ the etalon effect caused by multiple reflections in a sample with the thickness that is comparable to the THz wavelengths, which is a simple and robust technique to evaluate the refractive index. The Fabry-Pérot fringes can be observed in the transmission power spectrum, which is obtained by dividing the THz power spectrum of the sample by the reference (|ES(ω)|2/|ER(ω)|2). Figure 4 shows the transmission power spectrum of the GaP crystal at a temperature of 300 K as well as the THz power spectra of the sample |ES(ω)|2 and the reference |ER(ω)|2 from which it was obtained. Note, that the transmission power spectrum is only shown for frequencies up to 4 THz. For frequencies between 4 THz and 5 THz the signal-to-noise ratio did not allow any additional Fabry-Pérot fringes to be identified. The spectra in Fig. 4(a) show a pronounced dip at 3.8 THz, that is not due to water absorption or cryostat window but due to velocity mismatch in the generation crystal. It can further be seen, that for some frequencies the transmittance appears to be greater than one. This is the result of small alignment differences between measurements of sample and reference, but does not affect the determination of the refractive index, which relies only on the fringes’ peak positions.
The position of the transmission maxima is directly related to the real part of the refractive index according to:
Figure 5(a) shows the obtained values of the refractive index at discrete frequencies for each temperature. An increase in the refractive index values in dependence of frequency and temperature is clearly visible. Using the temperature-dependent refractive index in the NIR region  the Sellmeier equation was fitted to our experimental data for each temperature:
From the obtained Sellmeier equation the values of the refractive index at each frequency for the entire temperature range were calculated. Figure 5(b) shows the resulting curves for the frequencies ranging from 0.5 THz to 4 THz with a 0.5 THz step-size in between. A monotonic, moderate increase in the refractive index with temperature can be observed for each frequency.
4.2. Effect on phase matching conditions
In order to relate the above measurements to a potential change in velocity matching, we calculate the coherence length (effective interaction length in OR) as a function of temperature and frequency. The coherence length (lc) is expressed as:30] and THz refractive index values from our measurements (see Fig. 5 and Table 1), we calculated the coherence length as a function of THz frequency for each temperature. The results are illustrated in Fig. 6(a). As we can see, the coherence length decreases with increasing frequency, and the temperature only changes this function minimally. Figure 6(b) shows the temperature-dependent coherence lengths normalized to the value at 300 K. Comparing the coherence length at lower temperatures to their respective room temperature value, a slight reduction can be observed across the entire frequency range. The reduction in coherence length is the highest at 0.5 THz (5.6%) and becomes almost negligible at higher frequency of 4 THz (< 2%). On the other hand, for all frequencies an increase of the coherence length can be observed upon heating GaP from 300 K to 500 K, which would however result in detrimental heating effects.
This indicates that cooling GaP to cryogenic temperatures is a promising route for upscaling the excitation power to the kW level since no significant degradation of phase matching conditions is expected. In this way an improved heat extraction and decreased NIR absorption can be achieved without significantly affecting collinear velocity matching conditions. For higher frequencies, the coherence length becomes shorter as expected, and temperature dependence becomes negligible, which is beneficial when applying even shorter pulses at high-average power that require thin crystals for phase matching. At the same time, thinner crystals experience a higher average thermal load per unit volume due to linear and nonlinear NIR absorption, when assuming an exponential drop in NIR intensity versus penetration depth. Because of this, thin crystals potentially benefit even more from cryogenic heat extraction when applying short pulses. One interesting point observed in our data is that at high temperatures velocity matching is not adversely affected: this is of critical importance when excitation powers of > 100 W are applied where the center of the crystal becomes significantly hotter than its surrounding, confirming the good results obtained at room temperature, which did not appear to be severely limited by thermal effects .
5. THz generation at cryogenic temperatures
In order to confirm the potential of cryogenic cooling for THz generation, we performed preliminary measurements of OR as a function of temperature. We measured THz average power in a temperature range from 77 K to 290 K at an excitation average power of ∼ 100 W. In this experiment we avoid increasing the crystal temperature above room temperature to prevent damage of the crystal coating. We generate THz pulses in two configurations: (1) directly driven by the oscillator with 580 fs pulses (average power of 101.4 W), (2) driven by shorter 88 fs pulses with an average power of 95 W, obtained after pulse compression as indicated in our experimental setup. We used a 2 mm thick GaP crystal as the generation crystal in the cryostat (position (1) in Fig. 1), which was chosen as a compromise in generation efficiency for these two excitation conditions, in order to be able to make comparative measurements. It is however worth noticing that at room temperature, the best efficiency with short pulses was obtained using a 1 mm thick crystal , however at the expense of achievable spectral bandwidth. We note that in the Refs. [10,11] the generation GaP was placed in a water-cooled mount and not in a cryostat.
Figure 7(a) shows the dependence of measured THz power on the generation crystal temperature. For each experiment, the values of THz average power are normalized to the value at room temperature. For 580 fs pulses an average THz power of 71.8 µW was achieved at 290 K, whereas for 88 fs an average THz power of 614 µW was observed. These values are as measured and do not include the THz losses due to cryostat window (varying, up to 27%). The measured total losses in generated THz power are 21% for 580 fs excitation pulses and 27% for 88 fs driving pulses. These losses do not, however, change the observed temperature dependences shown in Fig. 7(a). We note that a direct comparison between obtained THz powers here and the Refs. [10,11] is not straightforward due to differing experimental parameters.
As it can be seen from Fig. 7(a), for the longer 580 fs pulses the THz average power decreases by 12% when the GaP is cooled to 77 K (unpurged condition), whereas for the 88 fs pulses the THz average power increases by 30% (purged condition) when cooling the crystal to 77 K. Note, that for the THz radiation generated by 580 fs pulses purged conditions do not result in a significant change in power, because the attenuation of these small frequencies is negligible. In this case the maximum power is found at frequencies below 1 THz, that are almost unaffected by water absorption .
First, we note that in all cases, the change in obtained power is not significantly affected by cooling the crystal: a slight reduction is observed for long pulse excitation, whereas a slightly larger increase is observed with short pulse excitation. The origin of the reduction in THz average power for 580 fs driving pulses is not fully elucidated yet as many competing effects are in place. In the case of the short pulses, however, the small THz average power enhancement at cryogenic temperatures could be partly due to the reduced THz linear absorption at higher frequencies, which are generated with the shorter driving pulses. In order to illustrate this effect, we present in Fig. 7(b) the measured THz spectrum for each experiment at 290 K and compare their overlap with the literature linear absorption coefficient of GaP at room temperature . As expected, linear absorption affects the broader THz spectrum (from 88 fs driving pulses) more significantly than the narrower THz spectrum (from 580 fs driving pulses). Additionally, it is important to keep in mind, that for broader THz bandwidths a larger fraction of the THz light is lost through the 10 mm hole in the first parabolic mirror which serves to separate the NIR excitation beam from the generated THz light. This effect affects more strongly the higher frequency components which are more concentrated on the axis, and these components are enhanced at cryogenic temperatures. Furthermore, as we showed in Fig. 6(a), the high-frequency components are not ideally phase matched in a 2 mm thick crystal, causing a narrower spectrum than potentially achievable with 88 fs pulse duration. However, as mentioned above, in order to compare the effect of cooling, it is fair to compare same thickness samples; a thicker sample was chosen to achieve significant power levels with long pulses and be able to confirm a trend.
A comparison of the respective THz spectra generated by 88 fs and 580 fs pulses at different temperatures serves to further illustrate the role of linear THz absorption at higher frequencies. Figure 7(c) shows the normalized THz power spectra obtained from long and short excitation pulses at 290 K and 77 K. While no significant change upon cooling is visible in the THz spectrum generated by 580 fs driving pulses, a slight enhancement of the spectral power at frequencies above 2.5 THz can be observed in the THz spectrum generated by 88 fs pulses. This behavior is consistent with our explanation of higher frequencies being more strongly affected by linear THz absorption, an effect that decreases at cryogenic temperatures. An even more pronounced effect can thus be expected from thinner generation crystals, that allow for higher THz bandwidths. To illustrate this, spectra of THz pulses generated with 88 fs pulses in a 1 mm thick GaP were recorded (Fig. 7(c)). First, we note, that the recorded spectrum spans a visibly broader frequency range at both temperatures when compared to the spectra for 2 mm thick GaP. As expected, a very pronounced enhancement of the spectral power at frequencies above 2 THz can be observed upon cooling. The spectra for the 2 mm and 1 mm thick crystals contain pronounced dips at 3.5 THz and 3.8 THz, respectively, that are the result of velocity mismatch. Measurements of THz average power generated with the 1 mm thick crystal showed an increase upon cooling, however the observed power enhancement was ∼ 40% lower than that observed in the 2 mm thick crystal before, possibly due to the precision of the measurement with lower absolute values. It should be noted, that the spectra shown in Fig. 7(c) are normalized to their respective maxima in order to highlight the temperature-dependent changes in bandwidth for different excitation pulse durations and crystal thicknesses. They do not, however, depict the temperature-dependent changes in total average THz power.
It is important to note that while cryogenic cooling leads to moderate improvements in average THz power, it provides a very promising method for upscaling the incident average power with short (< 50 fs) pulses, which were however not available at the time of these experiments. Due to the efficient heat removal and suppression of undesirable thermal effects significantly higher average excitation powers (∼ 1 kW) may be used for THz generation. This is especially interesting for thinner crystals (thicknesses < 1 mm), since they enable the generation of large THz bandwidths. Here, further pulse compression to durations below 50 fs allows for a maximum THz bandwidth within the constraints of velocity matching and at the same time increases conversion efficiency due to higher peak powers for a given constant average excitation power. An upscaling of average excitation power then is expected to increase the generated THz power across the entire available bandwidth. Combining thin cryogenically cooled GaP with kW-average power, sub-50 fs excitation, average THz powers as high as tens of mW with broad spectral coverage in the (1- 7 THz) region can be expected. At this point, it is noteworthy to highlight that the corresponding single-cycle pulses with broad spectral coverage are significantly shorter than those generated with higher conversion efficiency in LiNbO3. This means that at a lower average power, the peak field achieved might very well be comparable to state-of-the-art high average power THz sources , which starts to approach high enough values for nonlinear spectroscopy applications.
6. Conclusion and outlook
In conclusion, we present here an extensive investigation of cryogenically cooled GaP for optical rectification of high-average power (> 100 W) and high repetition rate (> MHz) ultrafast lasers. To the best of our knowledge, such a comprehensive temperature-dependent study had so far not been reported. In summary:
- - We explored temperature-dependent thermal effects caused by NIR absorption in the crystal, showing that nonlinear absorption is still the dominant contribution to heating, which can be partly reduced by cooling to cryogenic temperatures, along with the strong thermal lensing of the pump beam.
- - We explored velocity matching conditions at different temperatures, by performing THz-TDS measurements of GaP in a wide temperature range (77 K to 500 K) at frequencies extending up to 4 THz, which were so far not reported in the literature. From the measured refractive index, the temperature-dependent Sellmeier equation for GaP in the THz region was obtained showing no significant degradation in phase matching at cryogenic temperatures compared to room temperature.
- - We compare temperature-dependent average THz power and bandwidth (77 K to 290 K) for long (580 fs) and short (88 fs) driving pulses at ∼ 100 W in a 2 mm thick crystal. For 88 fs pulses and THz bandwidths extending to 4 THz our measurements showed a moderate increase of 30% in the average THz power by cooling the crystal to 77 K. Such a power enhancement can be attributed to a reduction in the THz-phonon absorption which is stronger for a larger THz bandwidth (resulting from shorter 88 fs pulses) due to the vicinity to the phonon resonance at 11 THz. An even more pronounced enhancement of the spectral power for frequencies above 2 THz was demonstrated in THz radiation generated by 88 fs pulses in 1 mm thick GaP.
Deutsche Forschungsgemeinschaft (EXC 2033 – 390677874 – RESOLV); Alexander von Humboldt-Stiftung (Sofja Kovalevskaja Award).
We thank the group of Prof. Martin Hoffmann from Ruhr University Bochum (Chair of microsystems technology) for the thickness measurement of our samples.
We acknowledge support by the DFG Open Access Publication Funds of the Ruhr-Universität Bochum.
The authors declare that there are no conflicts of interest related to this article.
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