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Abstract
Using a nonlinear optical mixing known as a frequency up-conversion process, we demonstrate an optical cross-correlation technique for the detection and characterization of sub-nanosecond (sub-ns) terahertz (THz)-wave pulses. A monochromatic THz-wave pulse from an injection-seeded THz-wave parametric generator (is-TPG) was mixed with a near-infrared (NIR) pump pulse to generate a NIR idler pulse in a trapezoidal-prism-shaped MgO-doped lithium niobate crystal under the noncollinear phase-matching condition. By measuring pump-energy and crystal-length dependencies, we show that the frequency up-conversion of sub-ns THz-wave pulses with and without subsequent parametric amplification can be used for sensitive detection and intensity cross-correlation characterization, respectively. Using this cross-correlation technique, we reveal that the temporal profile of THz-wave pulses from the is-TPG driven by a 351-ps 1064-nm pump laser has slightly-frequency-dependent pulse width in the range of 150–190 ps at full width at half-maximum in the tunable range of 0.95–2.00 THz.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Recent progress in the efficient generation of terahertz (THz)-wave pulses via the nonlinear frequency down-conversion of near-infrared (NIR) laser pulses has been one of the key driving forces behind intensive THz-wave research in a wide range of fields in fundamental sciences and industrial applications [1–5]. In particular, injection-seeded THz-wave parametric generators (is-TPGs) based on stimulated Raman scattering by phonon-polaritons in a MgO-doped lithium niobate (MgO:LN) crystal have been established as a versatile tabletop source of continuously frequency-tunable THz-wave pulses [6,7]. As a result of the use of sub-nanosecond (sub-ns) NIR pump laser, the state-of-the-art is-TPG system generates monochromatic sub-ns THz-wave pulses with a peak power of several tens of kilowatts (kW) and covers a wide frequency range from 0.4 to 5 THz [8–12]. These is-TPG properties are suitable for non-destructive spectroscopic sensing and imaging applications [13–20]. Furthermore, with the sub-ns is-TPG as a source, we recently demonstrated high-speed THz-wave detection using electronic devices, such as a resonant tunneling diode [21] and different types of grating-gate plasmonic THz-wave transistors [22–24]. Such electronic devices exhibit readout waveforms with a temporal response of a few hundred picoseconds (ps) that are related to both the temporal profile of the input THz-wave pulse and the intrinsic temporal responses of the device.
Although high-speed electronics technologies for the THz-wave region have been developing in recent years, it is still difficult to characterize the temporal profile of high-peak-power THz-wave pulses generated by the sub-ns is-TPG because of the complex nonlinearities appearing in electronic devices. Therefore, an optical technique for the accurate characterization of the THz-wave pulse width is important not only as a characteristic parameter of the sub-ns is-TPG, but also for understanding fast-response device physics.
Conventionally, the time-domain waveform of an oscillating electric field of THz-wave pulses is characterized by utilizing a femtosecond (fs)-laser-based time-gated detection technique of a photoconductive antenna or based on the electro-optical effect [25–28]. However, such electric-field resolved time-domain techniques are not applicable to the current sub-ns is-TPG system because the pump source of a passively Q-switched microchip Nd:YAG laser has an inherently large pulse timing jitter of the order of nanoseconds (ns) to microseconds (µs) [29–31]. Consequently, no fs laser pulses can be synchronized with sufficient temporal resolution for the electric-field resolved time-domain detection of sub-ns THz-wave pulses from the is-TPG. Another possible approach to pulse characterization is the utilization of nonlinear optical interaction, such as second-harmonic-generation (SHG) autocorrelation with a nonlinear optical crystal. However, commonly used nonlinear optical crystals possess strong absorption in the THz-wave region, and thus, the SHG efficiency is extremely low for THz-wave pulses [32].
In this study, we present an optical cross-correlation technique based on a nonlinear optical mixing (here referred to as frequency up-conversion) [33–35] for the detection and characterization of THz-wave pulses from the sub-ns is-TPG. The substantial difference between the method proposed here and the conventional electric-field resolved time-domain technique is the temporal resolution determined by the sub-ns pump pulse duration. We measured pump-energy and crystal-length dependencies of THz-wave up-conversion characteristics in a trapezoidal-prism-shaped MgO:LN crystal under the noncollinear phase-matching condition. Accordingly, we first show that the THz-wave up-conversion detectability is significantly enhanced by a high-gain subsequent parametric amplification process in the MgO:LN crystal. Thereafter, we show that the up-conversion process without subsequent parametric amplification enables the accurate characterization of the THz-wave pulse width generated by the sub-ns is-TPG via intensity cross-correlation between the pump and THz-wave pulses. Using this cross-correlation technique, we reveal for the first time that the THz-wave pulse width of the sub-ns is-TPG is slightly frequency dependent while tuning the THz-wave frequency.
2. Experimental setup
A schematic of the experimental setup is presented in Fig. 1. The NIR pump laser source was a laboratory-built sub-ns Nd:YAG master-oscillator power-amplifier (MOPA) system operated in a single longitudinal mode of 1064 nm, pulse energy of 16 mJ, and repetition rate of 200 Hz. The collimated output beam from the Nd:YAG MOPA was split by a beam splitter (BS) into two arms: one for THz-wave generation by the is-TPG process with a fixed pulse energy of 14 mJ and the other for THz-wave up-conversion process with variable pulse energy controlled by a polarizing beam splitter and two half-wave plates. A motorized optical delay line was introduced in the pump beam path to control the temporal overlap between the pump and THz-wave pulses in the up-conversion process [36].
Fig. 1. Schematic experimental setup. A laboratory-built sub-ns Nd:YAG MOPA was used to pump the two MgO:LN crystals: one was a rectangular used for THz-wave generation by the is-TPG and the other was a trapezoidal prism used for THz-wave detection by the up-conversion process. The NIR idler from the up-conversion process was detected by a NIR detector with wavelength filers and an aperture. The up-conversion-based cross-correlation traces between the pump and THz-wave pulses were recorded by scanning the optical delay line introduced in the pump beam path. The FWHM pulse widths of the NIR pump and NIR seeded idler from the is-TPG were measured by the conventional SHG autocorrelator or high-speed NIR photodetector (PD).
The experimental configuration of the is-TPG is similar to that previously reported [8,9,18]. For injection seeding to the NIR idler in the is-TPG process, a fiber-coupled external-cavity diode laser (ECDL: λ-Master series; Spectra Quest Lab., Inc.) with a wavelength-tunable range of 1067–1076 nm was used. The continuous-wave (CW) output from the ECDL was amplified up to 2 W using a Yb-doped fiber amplifier (CYFA-PB series; Keopsys SA). An achromatic injection seeding configuration consisting of a grating and lens pair (not shown in Fig. 1) was implemented on the seed beam path to satisfy the noncollinear phase-matching condition in the is-TPG process [37]. The gain medium of the is-TPG process was a rectangular-shaped 50-mm-long congruent MgO:LN crystal. A single prism coupler made of high-resistivity silicon (Si) was attached on the side surface of the MgO:LN crystal to extract the single-pulse-front THz-wave output from the crystal into free space [38–40].
The THz-wave pulses from the is-TPG were collimated by a cylindrical Tsurupica lens with a focal length of 50 mm. Thin-film attenuators were placed after the cylindrical lens to lower the THz-wave energy. Subsequently, the THz-wave pulses were focused by a Tsurupica lens with a focal length of 30 mm onto another MgO:LN crystal with a trapezoidal-prism shape for the up-conversion process. The advantage of the trapezoidal crystal compared to the rectangular crystal for the up-conversion process is that the THz-wave absorption loss inside the crystal can be minimized because the propagation length of the THz-wave pulse is close to zero for the interaction with the pump pulse [41]. In this study, we used a trapezoidal MgO:LN crystal with two different effective interaction lengths (L = 5 and 35 mm) to compare the up-conversion characteristics. According to the energy conservation law and the noncollinear phase-matching condition in the trapezoidal MgO:LN crystal, the NIR idler pulses were generated at difference frequency and subsequently parametric-amplified during propagation along the effective interaction length. The idler pulses from the up-conversion were filtered from the residual pump pulses spectrally by a pair of wavelength filters and spatially by an aperture. Thereafter, the idler pulses were measured using a NIR energy meter or a slow-response NIR photodetector (PD) with an electrical bandwidth of ∼500 kHz and a noise equivalent power of ∼3 pW/Hz1/2. Note that the amplitude modulation was applied to the THz-wave pulses by an optical chopper (not shown in Fig. 1) only for lock-in detection with the slow-response NIR PD.
3. Results and discussion
3.1 NIR pulse characterization
Prior to the THz-wave up-conversion experiment, we first characterized the pulse widths of NIR pump pulses and NIR seeded idler pulses from the is-TPG operated at 1.50 THz using the conventional SHG intensity autocorrelation technique [42]. As a nonlinear optical crystal of the SHG autocorrelator, we used an as-grown organic N-benzyl-2-methyl-4-nitroaniline (BNA) crystal with a thickness of 0.43 mm because the BNA crystal has a large second-order nonlinear coefficient and can be used for SHG of NIR pulses [43]. The NIR pulses to be measured were split by a beam splitter into two arms and subsequently focused into the BNA crystal. The resulting SHG signal intensity was measured as a function of optical delay time between the pulses. The signal was averaged 16 times at each delay time. Figures 2(a) and 2(b) shows the measured SHG autocorrelation traces of the pump pulse and the idler pulse from the is-TPG, respectively. The Gaussian-fitted autocorrelation widths at full width at half-maximum (FWHM) were measured to be 496 ps for the pump and 254 ps for the idler. The corresponding FWHM pulse widths (Δt) of the Gaussian-shaped intensity profile were 351 ps for the pump and 180 ps for the idler.
Fig. 2. NIR pulse characterization of pump and seeded idler from the is-TPG. [(a) and (b)] Measured SHG intensity autocorrelation traces and its Gaussian fitted curves and [(c) and (d)] measured high-speed PD waveforms of pump and seeded idler from the is-TPG operated at 1.50 THz, respectively. Note that all results are normalized.
For comparison with these SHG autocorrelation measurements, we also measured the intensity temporal profiles of these pulses using a fiber-coupled, 20-GHz-bandwidth high-speed NIR PD (DCS-30S; Discovery Semiconductors, Inc.) with a 40-GHz bandwidth oscilloscope. The results with an average of 16 traces are shown in Figs. 2(c) and 2(d). The FWHM pulse widths were measured to be 353 ps for the pump and 190 ps for the idler that were consistent with the SHG autocorrelation results shown in Figs. 2(a) and 2(b).
3.2 Characterization of is-TPG
We measured the output energy and frequency linewidth of the THz-wave pulses from the is-TPG employed in this study. Figure 3(a) shows the THz-wave pulse energy as a function of frequency measured using a calibrated pyroelectric detector (THZ20; Sensor- und Lasertechnik GmbH). The detector was posteriorly placed relative to the cylindrical lens. The continuously frequency-tunable THz-wave pulses were generated in the range of 0.9–2.7 THz with the maximum pulse energy of 0.47 µJ around 1.83 THz. The sharp dips observed in this THz-wave output spectrum are due to the absorption lines of water vapor in ambient air. Among these water vapor absorption lines, the one at 1.41 THz was used to estimate the frequency linewidth of THz-wave pulses from the is-TPG, as shown in Fig. 3(b). This measurement provides a more accurate result of the linewidth characterization for sub-ns THz-wave pulses than a scanning Fabry-Pérot etalon that were previously used [9,44]. This is because the mirror spacing of the scanning etalon is comparable with the physical length of sub-ns pulse width and the resulting interference visibility of the scanning etalon decreases. The measured absorption spectrum showed an FWHM linewidth of 7.5 GHz that was slightly broader than the pressure-broadened Lorentz absorption linewidth of 5.7 GHz in ambient air [45]. As shown by the fitting residuals in Fig. 3(b), the observed line shape was well fitted by a Voight function. By performing Voigt curve fitting with the Lorentz FWHM linewidth of 5.7 GHz, the Gaussian FWHM linewidth of the THz-wave pulses from the is-TPG was estimated to be 3.5 GHz. These measurements confirm that is-TPG produces monochromatic THz-wave pulses with wide frequency tunability.
Fig. 3. Characterization of THz-wave pulses from the is-TPG. (a) Measured THz-wave pulse energy from the is-TPG as a function of frequency. (b) Measured spectrum of water vapor absorption line at 1.41 THz in ambient air and its Voigt fitted curve (bottom) and the fitting residuals (top). The Gaussian frequency linewidth of THz-wave pulses was estimated to be 3.5 GHz at FWHM.
3.3 THz-wave up-conversion detection and cross-correlation
Next, we investigated the characteristics of THz-wave up-conversion detection in a single trapezoidal MgO:LN crystal by replacing two different effective interaction lengths of L = 5 mm and 35 mm. In this up-conversion measurement, the THz-wave frequency of is-TPG was fixed at 1.50 THz, resulting in an idler wavelength of 1070.2 nm. The pump and THz-wave pulse energies were controlled by the power controller and thin-film attenuators, respectively, as shown in Fig. 1. The position of the optical delay line in the pump beam path was fixed to obtain the maximum idler pulse energy. The beam diameter of the collimated pump pulses at the trapezoidal MgO:LN crystal was approximately 0.90 mm at FWHM, corresponding to a peak intensity of 0.86 GW/cm2 for 1.91-mJ energy of the 351-ps pump pulse.
Figure 4(a) shows the idler pulse energy as a function of the input THz-wave pulse energy for three different pump pulse energies of 0.02, 0.20, and 1.91 mJ. For both the interaction lengths of the MgO:LN crystal, the idler pulse energy increased with an increase in the pump pulse energy. When the pump pulse energy was fixed, the idler pulse energy was linearly proportional to the input THz-wave pulse energy with a slope coefficient of 1, as shown by the solid and dashed lines in Fig. 4(a), except for the saturation region observed with L = 35 mm for a THz-wave pulse energy above 1 nJ. Such saturation behavior was observed only in the efficient up-conversion process because of the pump depletion and cascaded processes in the MgO:LN crystal [46–48]. At the maximum pump pulse energy of 1.91 mJ, the minimum detectable THz-wave pulse energy and dynamic range for L = 35 mm were approximately 1 fJ and 86 dB, respectively, that were enhanced by three orders of magnitude compared with the result for L = 5 mm. This detectability enhancement was achieved by subsequent parametric amplification of the idler pulses that occurred in the MgO:LN crystal. The detection noise level of the idler pulse energy was around 30 pJ in this study.
Fig. 4. Pump-energy and crystal-length dependencies of up-conversion detection and cross-correlation. (a) Measured idler energy as a function of the input THz-wave energy for three different pump energies and two different effective interaction lengths. The is-TPG frequency was fixed at 1.50 THz. The blue solid and red dashed lines show the linear relation with a slope of 1. (b) Measured parametric amplification factor of idler energy as a function of the pump energy at 1.50 THz. The dashed curve shows the calculated exponential function of the product of parametric gain coefficient for the idler (gi) and crystal length difference of ΔL = 30 mm with a fitting parameter of γ = 0.22. (c) Normalized cross-correlation traces and (d) measured cross-correlation FWHM widths of 1.50-THz pulses for different pump pulse energies and two different effective interaction lengths.
Figure 4(b) shows the measured amplification factor of the idler as a function of the pump pulse energy at a fixed THz-wave frequency of 1.50 THz. In this study, the amplification factor was defined as the ratio of the idler pulse energy for L = 35 mm to that for L = 5 mm. For comparison with this experimental result, we calculated the amplification factor by considering an exponential function of the product of the theoretically calculated parametric gain coefficient for the idler (gi) [41,49,50] and the crystal length difference, ΔL = 30 mm. The calculation results are shown by the dashed curve in Fig. 4(b). The best-fitted curve was obtained by including a fitting parameter of γ = 0.22 expressed as exp(γ·gi·ΔL). The amplification factor increased exponentially with an increase in the pump pulse energy because the high pump intensity resulted in a high parametric gain for the idler in the parametric amplification process [41,49,50]. This result indicates that the high-gain subsequent parametric amplification process is crucial for sensitive THz-wave up-conversion detection. Therefore, increasing the interaction length and/or pump intensity further could enhance the minimum detectability down to a pulse energy of aJ (10−18 J) or less [48,51].
When the pump pulse energy was 0.02 mJ, the up-conversion characteristics for the two different interaction lengths were identical as shown in Fig. 4(a). This is because the parametric gain is negligibly small, and the resulting parametric amplification factor is approximately 1, as shown in Fig. 4(b).
To characterize the THz-wave FWHM pulse width of is-TPG by the up-conversion process, we measured the idler output as a function of the delay time between the pump and THz-wave pulses by scanning the optical delay line introduced in the pump beam path, as shown in Fig. 1. This allowed us to record the intensity cross-correlation trace between the reference 351-ps pump pulses and the THz-wave pulses to be measured.
Figure 4(c) shows the normalized cross-correlation traces for three different pump pulse energies of 0.02, 0.20, and 1.91 mJ measured at the fixed THz-wave frequency of 1.50 THz. To compare the results between the two different interaction lengths of L = 5 mm and 35 mm, the cross-correlation FWHM width of the experimentally measured traces as a function of the pump pulse energy is shown in Fig. 4(d). The cross-correlation FWHM width for both interaction lengths decreased with an increase in pump pulse energy, resulting in different values between the two interaction lengths: the results for L = 35 mm showed the shorter cross-correlation widths that that for L = 5 mm. This tendency was attributed to the subsequent parametric amplification process, as shown in Fig. 4(b). Furthermore, the cross-correlation FWHM width with L = 35 mm reached the minimum value around a pump energy of 1 mJ and subsequently increased for the pump pulse energies above 1 mJ because of the saturation effect, as observed in Fig. 4(a).
In contrast to the high-gain region of the subsequent parametric amplification process, nearly identical cross-correlation traces for L = 5 and 35 mm were obtained for a pump energy of 0.02 mJ, as shown by the bottom trace in Fig. 4(c). This indicates that up-conversion without subsequent parametric amplification can be used to characterize the THz-wave FWHM pulse width by the intensity cross-correlation measurement between the pump and THz-wave pulses. In this non-amplification region with a pump energy of less than 0.05 mJ that corresponds to a peak intensity of 23 MW/cm2, the cross-correlation FWHM width was measured to be 397 ps. From this cross-correlation width and the pump pulse width of 351 ps characterized by SHG autocorrelation, as shown in Fig. 2(a), the THz-wave pulse width at 1.50 THz was derived to be 185 ps at FWHM by assuming a Gaussian pulse shape. This result is in excellent agreement with the SHG autocorrelation result of the seeded idler pulses from the is-TPG, as shown in Fig. 2(b). This demonstrates that the up-conversion-based cross-correlation in the non-amplification region provides a reliable characterization result of the THz-wave pulse width. The corresponding time-linewidth product of the sub-ns THz-wave pulse is equal to 0.65 that is approximately 1.5 times larger than a Fourier-transform limited Gaussian-shaped pulse with a 3.5-GHz linewidth, as shown in Fig. 3(b). This is probably because the intensity profile of THz-wave pulses from the is-TPG is not an ideal Gaussian pulse shape.
We note here that, although the pulse width of the idler generated in the up-conversion process could be measured using a high-speed PD, it was difficult to retrieve the THz-wave pulse width from the direct characterization of the idler pulse width. This is because the generated idler waveform was affected by 1) the temporal overlap between sub-ns pulses of NIR pump and THz wave and 2) the subsequent parametric amplification process that is strongly dependent on the pump pulse energy as shown in this study.
3.4 Cross-correlation characterization of is-TPG
In the non-amplification region, we measured the frequency dependence of the THz-wave FWHM pulse width of the is-TPG by the up-conversion-based cross-correlation, as shown in Fig. 5(a). By tuning the injection seed wavelength in the is-TPG, the THz-wave frequency was tuned in the range of 0.95–2.00 THz. At each THz-wave frequency, the incident angle of the THz-wave pulses at the trapezoidal MgO:LN crystal was slightly adjusted to obtain the maximum idler intensity. Accordingly, we observed that the THz-wave FWHM pulse width was slightly dependent on the frequency with a maximum of 190 ps at 1.45 THz and decreased to approximately 150 ps by tuning the frequency to a lower or higher frequency side. This indicates that the is-TPG in the high-gain region around 1.5 THz produces a slightly longer THz-wave pulse than that in the low-gain region. This frequency dependence might be caused by the parametric gain profile in the is-TPG process [41,49,50].
Fig. 5. Cross-correlation characterization of THz-wave pulse width of is-TPG. (a) THz-wave pulse width at FWHM as a function of frequency measured by up-conversion-based cross-correlation in the non-amplification region. The FWHM pulse width of the intensity temporal waveforms measured by a commercial SBD detector is also shown for comparison. (b) Measured up-conversion-based cross-correlation trace with its Gaussian fitted curve and (c) measured intensity temporal waveform of a commercial SBD detector for 1.00-THz pulses.
Figure 5(b) shows the up-conversion-based cross-correlation trace measured for the 1.00-THz pulse from the is-TPG. From a Gaussian fitting of this trace, the THz-wave pulse width was derived as long as 161 ps at FWHM. For comparison, we used a commercially available fast-response THz-wave detector of a Schottky barrier diode (SBD: WR1.0ZBD; Virginia Diodes, Inc.) [52]. The measured intensity temporal waveform of the 1.00-THz pulse with a 40-GHz bandwidth oscilloscope is shown in Fig. 5(c), illustrating a waveform with a pulse width of 117 ps at FWHM. The FWHM pulse width measured within the working range of the SBD detector is shown in Fig. 5(a). A similar frequency dependence was observed, but with a shorter pulse width than that obtained by the up-conversion-based cross-correlation. This comparison reveals that the commercial zero-biased SBD detector shows a temporal waveform with an underestimated pulse width for the sub-ns is-TPG source that may be due to the intrinsic nonlinearity in the SBD. This result demonstrates that up-conversion-based cross-correlation in the non-amplification region is a promising technique for the characterization of sub-ns THz-wave pulses.
4. Conclusion
We demonstrated up-conversion-based detection and cross-correlation characterization of monochromatic sub-ns THz-wave pulses from an is-TPG source with a trapezoidal-prism-shaped MgO:LN crystal. We showed that the minimum detectability of the THz-wave up-conversion detection is significantly enhanced by a high-gain subsequent parametric amplification process in the MgO:LN crystal, which is consistent with the previous results [46,48]. We also showed that up-conversion without subsequent parametric amplification can be used to characterize the FWHM pulse width of the THz-wave temporal profile by an intensity cross-correlation measurement between the pump and THz-wave pulses. Accordingly, we revealed that the THz-wave FWHM pulse width of the is-TPG driven by a 351-ps 1064-nm pump laser is slightly-frequency-dependent and varies from 150 to 190 ps in the tunable range of 0.95–2.00 THz, corresponding to approximately half of the input pump pulse width. This cross-correlation technique provides more reliable results compared with the current fast-response THz-wave detector. Furthermore, we note here that a frequency up-conversion process based on sum-frequency generation [53–57] is also useful for cross-correlation characterization. Our results demonstrate that the nonlinear optical mixing process is a powerful technique for detecting and characterizing THz-wave pulses.
Acknowledgments
The authors thank H. Ito, M. Kumano, and A. Satou for fruitful discussions, M. Kitanaka for his help in linewidth measurement of the is-TPG, and M. Saito for the BNA crystal growth. This work was supported in part by FY2021 RIKEN-Tohoku University Science and Technology Hub Collaborative Research Program, Japan-China Scientific Cooperation Program between JSPS and NSFC Grant Number JPJSBP120207407, and Innovative Science and Technology Initiative for Security Grant Number JPJ004596, ATLA, Japan.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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