We report on phase matched THz emission from GaAs using the anomalous dispersion introduced by optical phonon absorption at the reststrahlenband in GaAs. For this system tunability of the emitted THz frequencies by changing the near infrared excitation wavelength is predicted. We investigate this phenomenon for an oversized double metallized GaAs waveguide. A shift in the THz spectra is observed when the near-infrared wavelength is varied. Enhanced emission is found when phase matching is achieved at 1.4 µm.
© 2010 OSA
An established way to generate broadband terahertz radiation is optical rectification of ultrashort laser pulses in nonlinear crystals. The stimulating near infrared (NIR) pulse induces a nonlinear polarization which follows the group velocity of the optical pulse and emits terahertz radiation. This was first demonstrated with picosecond pulses and later extended to femtosecond pulses [1,2]. In order to improve the efficiency of the generation process the phase velocity of the generated THz pulse has to match the group velocity of the NIR pulses along the length of the crystal. Otherwise THz pulses generated at different positions in the crystal would interfere destructively.
The phase-matching condition can be met in different ways. For instance in anisotropic birefringent crystals like GaSe, KDP or LiNbO3 it can be achieved by mixing an extraordinary beam with frequency ω1 with an ordinary beam with frequency ω2 by tilting the optical axis with respect to the polarization of the extraordinary beam. Adjusting this phase-matching angle allows one to tune the phase-matched THz frequencies and therefore the emitted spectrum . Another possibility to obtain phase-matching is a periodic variation of the χ(2) nonlinear coefficient in quasi-phase-matched (QPM) crystals. Optical rectification in a QPM crystal was first demonstrated in periodically-poled lithium niobate  and in GaAs . The idea of QPM rectification is that each inverted domain of a QPM crystal contributes a half cycle of the THz pulse and thus the THz wave packet has as many oscillation cycles as the number of QPM periods over the length of the crystal. Adjusting the orientation-reversal period allows one to tune the bandwidth and wavelength of the emitted THz radiation. The challenge is the patterning of the nonlinear susceptibilities in the crystals. For instance in diffusion bonded GaAs alternately rotated plates with <110> orientation are stacked together and a monolithic body with periodic change in the nonlinear coefficient is created. Techniques for the fabrication of QPM GaAs are described in . A third possibility to obtain phase-matching in optically isotropic materials, where no birefringence is possible, is to use the anomalous dispersion introduced by optical phonon absorption at the reststrahlenband in GaAs [7,8]. Here a phase-matching point exists, where one of the wavelengths lies in the THz range and the second, shorter wavelength is in the NIR around 1.4 μm. The reststrahlenband lies between those frequencies, giving rise to a non-monotonic refractive index n(ω). The reststrahlen region in semiconductors lies between the transverse and longitudinal optical phonon (33.1 meV and 36.1 meV in GaAs at room temperature, respectively ), where the dielectric constant becomes negative and electromagnetic propagation is forbidden. Nagai et al. have reported on generation and detection of a terahertz wave using a 0.5-mm-thick GaAs <110> oriented wafer with 1.56 μm pulses from a fiber laser . Marandi et al. proposed a tunable continuous-wave THz-source by an integration of a dielectric slab and a metallic slit waveguide in GaAs . THz emission from GaP and GaAs waveguide structures has been studied using fixed excitation wavelengths at 1 and 2 µm, respectively [12,13]. Furthermore results on the thickness dependence of the inverse process, namely electro-optic sampling with a GaAs crystal probed at a fixed wavelength of 1.55 µm, have been recently reported .
In this paper we present investigations on the excitation wavelength dependences of terahertz emission around the phase-matching point in a GaAs slab. To this end we calculate the coherence length between the stimulating NIR beam and the generated THz beam in such a GaAs slab. Experimentally we analyze the dependence of THz spectrum on excitation wavelength.
2. Principle and experimental setup
The slab used in this experiment is made from a 625 µm thick <100> oriented, semi-insulating GaAs wafer. It is cleaved starting from the flat of the wafer with a length of 6 mm and a width of 2 mm. Since the surface of the flat in such a wafer has <110> orientation, the second-order susceptibility tensor has a nonzero component, and therefore the facets can be employed as coupling surfaces for the NIR excitation beam (Fig. 1 ). A waveguide for TE modes is generated by evaporating chromium-gold layers on the upper and lower facets of the slab before cleavage. Furthermore, this metallization enhances the overlap between the NIR beam and the generated THz beam.
For comparison, a 625 µm thick <110> oriented GaAs crystal (bulk) was utilized. An optical parametric amplifier (OPA 9840) from Coherent Inc. tunable between 1100 nm and 1600 nm is used for excitation. The OPA is driven by a cavity-dumped Ti:sapphire regenerative amplifier (RegA 9040, Coherent Inc.). The pulses have a repetition rate of 250 kHz and pulse duration of 100 fs. The power and spot size (full width at half maximum, FWHM) are 50 mW and 70 µm, respectively for the excitation beam. Sampling was conducted by applying a part of the 800 nm beam, which is driving the OPA, to a 200 µm thick ZnTe crystal. The terahertz signal and the sampling beam are combined by a tin doped indium oxide coated mirror and focused on the ZnTe crystal by a pair of off-axis parabolic mirrors. The transmitted sampling beam is separated in its vertical and horizontal components by a polarization sensitive beamsplitter cube. Balanced detection is performed using a λ/4-plate before the beamsplitter and two photodiodes. Due to the THz-induced birefringence in the ZnTe crystal the change of this balanced signal is proportional to the terahertz field . For lock-in detection the excitation beam is chopped with 1.3 kHz. A mechanical delay stage is utilized to adjust the time delay between the THz pulse and the sampling pulse.
3. Results and discussion
The creation of THz pulses in a difference frequency mixing process involves three different electric fields that have to fulfill the wave equation simultaneously. The conservation of momentum requires the wave vectors to fulfill the phase-matching condition
Δk = k (ω opt + ω THz) – k (ω opt) – k (ω THz) = 0. A measure for the walk-off caused by the different velocities of the optical pulse envelope and the phase of the THz wave is the coherence length lc ( = π/Δk) which can be expressed as16]. The refractive index in the THz range (n THz) is obtained by the measured phase difference in a THz time domain spectroscopy setup as described in Ref [17–20]. Figure 2 shows the result of such a measurement and a calculation based on a Lorentz oscillator model (red line). Using Eq. (1) and the refractive index in the NIR and THz range we can calculate the coherence lengths as a function of the NIR excitation [Fig. 3(a) ]. Because of the pole in Eq. (1) the coherence length becomes infinite for certain pairs of NIR wavelength and THz frequency. This is the region where the phase-matching is perfect. This region shifts to higher THz frequencies, if the NIR wavelength is tuned to shorter wavelengths, e.g. 3.0 THz matches 1250 nm while 4.2 THz matches 1100 nm [Fig. 3(b)].
In Fig. 3(a), the pole of lc shows strong broadening for lower THz frequencies. In particular, for a frequency of 2 THz the coherence length is 2 mm from 1260 nm to 1350 nm while for a frequency of 1 THz the corresponding wavelength regime ranges from 1260 nm to 1450 nm. For a frequency of 0.5 THz the phase-matching for crystals up to a thickness of 1 mm is even perfect over the whole laser tuning range of 1.1 to 1.6 μm [Fig. 3(a)]. For a slab length of 6 mm and a near infrared excitation at a wavelength of 1.35 µm with a spectral width of 100 nm phase matching can be achieved up to frequencies of 2 THz. It is therefore apparent that for crystal thicknesses of less than 2 mm no significant tuning of the THz output is possible by adjusting the NIR excitation wavelength. On the other hand the dispersional broadening of the NIR pulse, which is not included in our description of lc, places an upper limit for an optimum crystal thickness.
Bakunov  has studied this broadening and found for 100 fs NIR pulses only a small influence for crystals below 1 cm length. In Fig. 4 experimental THz spectra from the GaAs slab are plotted for several exemplary excitation wavelengths. As predicted by the phase-matching model in Fig. 3, the shorter the excitation wavelength the higher the frequency components in the emitted spectra. On the low-frequency side the spectra are cut off around 300 GHz. This is attributed to the cutoff of the lowest order mode of the TE waveguide. From an analytical calculation the cutoff frequency is expected at 100 GHz . However, numerical simulations of the structure, taking into account the 70 µm near infrared spot size, yield a cutoff frequency of 300 GHz (not shown) .
On the high-frequency side we observe the expected shift to higher THz frequencies for shorter excitation wavelengths. However, no sharp peaks in the spectrum occur at high frequencies [e.g. at 3 THz for an excitation wavelength around 1250 nm as predicted in Fig. 3(b)], but rather a shift of the high-frequency edge is observed in the THz spectrum excited at different NIR wavelengths. One reason for this is the sharper pole of the coherence length for higher THz frequencies. The typical bandwidths of the OPA spectra are 100 nm. Convoluting these spectra with the coherence length leads to much better overlap for lower THz frequencies. Therefore frequency components between 0.5 to 1 THz always fulfill the phase-matching criteria with a spectrally broad laser pulse. For larger crystal lengths or narrower excitation spectra it should be possible to tune the higher THz frequencies by adjusting the excitation wavelength. The second reason for this drop on the high-frequency side is a geometrical one. This is because higher THz frequencies have the drawback of a stronger multimode characteristic of the waveguide. Due to random imperfections these modes get out of phase and thus the signal smears out after multiple reflections at the interfaces in the slab resulting in a sharply reduced outcoupling efficiency . Both limitations on the high as well as on the low frequency side result in a preference for frequencies between 0.5 to 2.5 THz. We note that the detection bandwidth of our system is around 3 THz, as indicated by the spectrum for the bulk GaAs. The limitation is due to the duration of the NIR pulse and the phase matching in the ZnTe sensor crystal.
So far the normalized spectra were discussed; in the following the field amplitude in the time domain will be addressed. In principle the THz field amplitude should be enhanced, if the phase-matching condition between the NIR excitation beam and the generated THz beam is fulfilled. In Fig. 5(a) the THz field is plotted in dependence of the excitation wavelength. The maximum THz field emission (peak to peak) occurs at an excitation wavelength of around 1.4 µm. This maximum highlights that a NIR laser pulse with a bandwidth of 100 nm and a central wavelength of 1400 nm matches most of the THz frequencies in Fig. 3. The dependence of the 20 dB bandwidth on the excitation wavelength is illustrated in Fig. 5(b). It is shown that the bandwidth remains constant up to 1400 nm and then decreases to less than half of the maximum value, when the excitation wavelength is increased by 150 nm. The reason for this narrowing in the emitted spectra is the already discussed shift of the high-frequency part of the spectra (cf. Fig. 4) due to the phase-matching condition. On the low frequency side the aforementioned frequency cutoff in the slab prevents a “red” shift of the spectra. This underpins that the phase-mismatch in the slab between THz signal and NIR beam grows for excitation wavelengths above 1400 nm.
In conclusion, we have studied optical rectification of fs NIR pulses in the range 1100-1600 nm in a GaAs slab waveguide. The best phase-matching point for broadband THz generation was found to occur at an excitation wavelength of 1400 nm. The spectral width of the THz radiation was observed to depend on the excitation wavelength. The previously predicted opportunity of tuning the emitted THz spectra was confirmed, but the tunability was not as strong as expected. This is because the sharper divergence in the coherence length for higher THz frequencies favors an overlap of a 100 nm broad NIR pulse for frequencies between 0.5 up to 1.5 THz. These frequencies are always phase-matched and dominate the emitted spectra. Additionally a thinner slab could enhance the outcoupling efficiency of the slab for higher THz frequencies.
The authors are grateful to A. Dreyhaupt and M. Wagner for participation in preliminary experiments and discussions. Research was conducted in the scope of GDRE: “Semiconductor sources and detectors of THz frequencies.”
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23. These simulations were realized by using the commercial finite element solver Comsol.