The used laser system is a 1k-Hz amplified Ti:sapphire laser with pulse energy of 700 Jμ and pulse duration of 280 femtosecond. The experimental setup for multi- stage optical rectification is shown in Fig. 3-1. The first beam splitter reflects 10% of input power as gating beam, and the second beam splitter reflects 60% for first terahertz generation and transmitted 40% for second terahertz generation. The typical average pump power on the GaSe crystals is about 130mW and 150mW for the first and second stage respectively. The pump beam diameter for both stages is adjusted to be about 3 mm. Both GaSe crystals are configured for non-phase matched optical rectification. The terahertz radiation field generated from the first optical rectification stage of 2-mm thick GaSe crystal is guided into the second stage of 3-mm thick GaSe.
Again we block the residual optical pump laser with Teflon plates terahertz wave are passed through wire-grid polarizer to make sure the polarization. The terahertz pulse
from the two OR stages are aligned collinearly with two gold-coated parabolic mirrors and guided into ZnTe crystal. The time delay between the two terahertz pulses are carefully controlled with a translation stage. The optical chopper is used in this experimental arrangement to simultaneously modulate the optical pump beams for the first and second OR stage. Also the electro-optical sampling technique with a 1-mm thick ZnTe crystal is used. Terahertz radiation generated from either the first or second stage, or both could be recorded without moving any optical element.
By adjusting the terahertz pulses from the two GaSe optical rectification stages to temporally overlap. The optical path length of the pump pulse to the first GaSe stage is then varied to adjust the arrival time of the terahertz pulse at the second GaSe stage.
BS chopper BS
Fig.3-1 Schematic of coherent generation of terahertz radiation by multi-stage optical rectification in GaSe crystals. BS: Beam splitter; ND-Filter: Neutral Density filter; ITO: indium-tin-oxide glass plate; λ/4: quarter wave plate.
Figure 3-2 shows the time domain field amplitude of the terahertz output from the second OR stage as a function of the arrival time of the seeding terahertz field. In this case, the terahertz field generated in the second stage is added to the incoming THz seeding field. We can also map out the seeding terahertz pulse profile by scanning the first stage delay line while blocking the pump pulse to the second GeSe crystal. The resulting first terahertz pulse profile was shown as the square-symbols in Fig. 3-2. High degree of mutual coherence between the terahertz fields from the two GaSe OR stages was clearly revealed.
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THz field (V/cm)
Time delay (ps) first THz shape
(first THz time-domain waveform + 1198 V/cm)
Fig. 3-2 Terahertz field amplitude after the second stage is plotted as a function of arrival time of the seeding THz pulse. Dot-symbols present the terahertz output from the second OR stage. Square-symbols represent the first terahertz time-domain waveform from the first stage, which is scaled for the easy comparison with output from the second stage.
Figure 3-3 shows the terahertz time-domain waveforms and the spectra at three different time delays between the two OR stages. In these figures, the signal from the first stage is presented as black dashed curve and the pulse from the second stage is displayed with the red dashed-dot line. The superposed THz pulses from both stages are shown as the blue curve with open squares. By adjusting the time delay, the terahertz fields from the two OR stages can be superposed constructively or
destructively. To generate maximum terahertz field, the time delay of the two terahertz pulses should be adjusted for the best temporal overlap within 0.1 ps in our study, to yield constructive superposition over the entire spectral components involved.
In Fig. 3-3(a), the main peak of terahertz field from the second OR stage leads that from the first stage. However, the trailing part of the THz pulse from the second stage still overlaps and interferes with the THz field from the first stage. The coherent superposition nature is more clearly revealed in the frequency domain shown in the inset of the Fig. 3-3(a). Parts of the terahertz spectral components from the two stages are constructively added to produce higher spectral power while some spectral regions superpose destructively to yield lower spectral power. Thus the coherent superposition with multiple terahertz radiation sources offers a potential for the synthesis of terahertz field. In Fig. 3-3(c), the terahertz pulse from the second stage lags behind that from the first stage in such a way that the main positive peak from the second stage overlaps with the negative amplitude of the THz pulse from the first stage. The destructive superposition yields a spectrum shown in the inset of Fig.
3-3(c). The destructive superposition is caused by out-of-phase mixing of the terahertz field from the first stage with the optical pump pulse in the second OR stage. The spectral phase content of the terahertz field can then be imprinted onto the pump pulse.
In other words, when pump pulse in the second OR stage and terahertz field from the first stage are getting close and partly overlapped in the time domain, the seeding terahertz field will dominate the three-wave mixing process and lead to the output terahertz field profile variations. In the case of Fig. 3-3(c), the phase difference almost equals to π in the overlapped region between terahertz field from the first stage and the pump pulse in the second OR stage. Thus the terahertz field generated by the
pump pulse in the second OR stage is then superposed with the first THz field to yield a much weaker terahertz radiation output.
The highest terahertz field amplitude can be obtained by synchronizing the first and second OR stages to attain constructive superposition of terahertz fields in the second OR stage. This can be done by seeding terahertz field with the correct phase at a proper arrival time relative to the optical pump pulse of the second stage. The output terahertz field possesses the property of the seeding terahertz field but with higher amplitude. The inset of Fig. 3-3(b) presents the spectra of the terahertz radiation fields to reveal the amplification nature of terahertz radiation pulse after the coherent superposition of the two stages.
The terahertz signal measured by the electro-optical sampling technique could be affected by the dispersion of the terahertz signal; the velocity-matching condition between the terahertz and optical pulses, and non-perfect alignment. The theoretical simulation of the two OR stages with Eqs. (1)-(3) is performed in order to remove the artifacts in the practical experiment. To allow for a straightforward comparison of the THz spectral profile with the measured data, we assume a non-transform limited optical pump pulse with a spectral width < 1 THz. The absorption by the optical phonon mode of GaSe at 0.58 THz was also included in our simulation. The calculation results corresponding to the three different experimental conditions are presented in Figs. 3-3(d), 3(e), and 3(f). The simulation results agree well with the experimental data shown in Figs. 3-3(a), (b) and (c), respectively. This confirms that the theoretical model used to depict the coherent multi-stage optical rectification processes in GaSe crystals is satisfactorily accurate.
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Fig.3-3 Terahertz time-domain waveforms and spectra for three different time delay between the pump pulses of the first and second stages. (a), (b), (c) represent the experimental data at time delay 4.6ps, 0ps, 1ps, respectively. And (d), (e),
(f) depict the theoretical simulation results under same time delay condition corresponding to (a), (b), (c). In (a) and (d), the terahertz pulse from the second stage leads the signal from the first stage; in (b) and (e), the terahertz pulses from the first and second stages are overlapped in the time delay; in (c) and (f), the terahertz pulses from the second stage falls behind that from the first stage. Inset: corresponding spectra of the terahertz radiation.