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Abstract
An injection pulse-seeded terahertz-wave parametric generator (ips-TPG) has been demonstrated with gain enhancement in wide tuning range. Theoretical analysis denotes that the compensation of initial Stokes energy is favorable to the THz gain enhancement in wide frequency range, which is attributed to the improvement on interaction of stimulated polariton scattering (SPS) and difference frequency generation (DFG) processes. In the experiment, the THz frequency tuning range from 1.04 THz to 5.15 THz was achieved based on near-stoichiometric LiNbO3 (SLN) crystal. Compared with the traditional terahertz parametric oscillator (TPO) under the same experimental conditions, a significant enhancement of THz output energy was occurred in high frequency range. As the THz frequency increased from 1.9 THz to 3.6 THz, the enhancement ratios from 1.6 times to 34.7 times were obtained. Besides, the 3dB bandwidth of ips-TPG was measured to be 2.1 THz, which was about 2.6 times that of SLN-TPO. This THz parametric source with a relative flat gain in wide frequency range is suitable to a variety of practical applications.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The terahertz wave (THz wave) is located in the electromagnetic spectrum between the microwave and infrared regions, where abundant physicochemical information of matters deserves to be explored. With the rapid development of THz generation and detection technologies, many fields are achieving the leap from basic explorations to practical applications, such as biomedical imaging, security inspection and THz communications [1–3]. Currently, the operating frequency band of continuously tunable commercial THz sources are mainly located in the range of 0.1THz to 3THz. However, high-power, tunable THz sources with operating frequency above 3THz are required in some specific areas, including semiconductor inspection, intramolecular vibrations measurement and so on [4,5].
Terahertz wave parametric technology based on stimulated polariton scattering (SPS) has attracted a wide spread attention due to its advantages of high energy, wide tuning and room temperature operation. In the past three decades, many techniques have been proved to be beneficial to the performance of THz output efficiency and linewidth, like different coupling methods and cryogenic cooling crystal to reduce THz wave absorption effectively, subnanosecond pulses pumping to suppress stimulated Brillouin scattering (SBS), continuous-wave seed laser injection to narrow THz linewidth and enhancement of DFG process to increase THz output energy [6–15]. Meanwhile, a variety of SPS-active nonlinear crystals were employed in terahertz wave parametric techniques to obtain wide THz frequency tuning ranges, such as LiNbO3 (LN), KTiOPO4 (KTP), KTiOAsO4 (KTA) and RbTiOPO4 (RTP) crystals [16–23]. Among them, LN crystal is the most widely used gain medium because of high THz output energies and continuous frequency tuning range without gap. The recent works based on the near-stoichiometric LN crystal successfully increased the upper limit of frequency tuning range from 3 THz to 5 THz in the TPO and TPG systems [19,24]. However, their THz frequency range with high output energy was located between 1.4 THz to 2.0 THz. With increasing the THz frequency, the THz output energy decreased rapidly, which is attributed to the reduction of the three-wave interaction volume and the increment of THz absorption coefficient in LN crystal. In general, current THz parametric techniques based on LN crystal can provide a widely tunable frequency range but have a lower THz output energy at high THz frequency, especially above 2.5 THz.
In this study, we proposed an injection pulse-seeded terahertz-wave parametric generator (ips-TPG) with gain enhancement in wide tuning frequency range. Under the pump energy of 160 mJ and the tunable pulse-seed energy of 20 mJ, the maximum THz output signal was obtained to be 5.46 μJ at 1.79 THz, and the THz tuning frequency range of 1.04 THz to 5.15 THz was achieved. Compared with SLN-TPO, the maximum enhancement ratio of THz energy was 34.7 times at 3.6 THz. Meanwhile, the 3dB bandwidth of THz output was 2.1 THz, which was about 2.6 times larger than that of SLN TPO under same pump condition. In addition, the measured acceptance angle of THz generation was 0.42° at 1.79 THz. The THz output fluctuation was 5.62% over an hour. These characters make ips-TPG more suitable for practical application.
2. Theoretical analysis
Owing to the fact that both second and third-order nonlinear processes are entangled, the THz wave generation based on the terahertz parametric process can be described by the coupled-wave equations under the small signal approximation and slowly varying amplitude approximation [25]:
where , and are the pump, Stokes and THz electromagnetic fields, respectively. and are the wave vector and dielectric constant of the Stokes (i = S) and THz (i = T) waves. and are the second- and third-order nonlinear coefficients, which denote the difference frequency generation (DFG) and stimulated polariton scattering (SPS) contributions to the THz generation process, respectively. is the angle between pump and THz beams. And the absorption coefficient is expressed as [26]:where the eigenfrequency , oscillator strength and damping constant are the inherent property of lowest order A1-symmetry mode in LiNbO3 crystal [27].The generated THz intensities can be numerically calculated by Eqs. (1)-(3) with initial conditions of pump energy (EP) of 150 mJ and Stokes energy of 20 mJ or 0 mJ. The numerical solutions were simulated by the Runge-Kutta algorithm. Figure 1 shows the calculated THz intensities of two kinds of initial conditions, which were normalized by maximum value of each curve separately for intuitive comparison. Compared with the maximum THz intensity in each curve, the THz generation capability under the initial Stokes energy of 20 mJ is stronger than that under the initial Stokes energy of 0 mJ in high THz frequency range. The calculated results show that the increase of initial Stokes energy was beneficial to a stronger THz generation in high THz frequency range. In addition, the qualitative explanation of the THz generation performance improvement in the high THz frequency range is as follows. In our experiment, the phase-matching conditions of SPS and DFG processes are simultaneously satisfied. Under the non-collinear phase matching condition, there are SPS and DFG processes during THz generation. The increase of THz frequency is accompanied by the decrease of three-wave interaction volume, which leads to the classical TPOs or TPGs systems are unable to achieve high Stokes gain. The low Stokes gain not only affects the efficiency of SPS process, but also has a negative impact on DFG process due to the low Stokes energy, which directly results in a reduction of THz energy. Thus, compensation for the low Stokes gain is the key to improve the THz generation capability in high THz frequency.
Fig. 1 The numerical solution of generated THz intensity with initial conditions of Stokes energy of 20 mJ and 0 mJ.
3. Experimental setup
The experimental setup of the injection pulse-seeded terahertz parametric generator (ips-TPG) is shown in Fig. 2. A Nd:YAG laser with repetition rate of 10 Hz and pulse-width of 10 ns was used as the pump source. The 1064 nm laser beam was divided into two equal parts by the mirror M1 coated with the transmission of 50% in the infrared range at the incident angle of 45°. The two separated 1064 nm laser beams were shaped and collimated by the telescope lens T1 and T2 respectively, which reduced the spot sizes of two laser beams to 5 mm. Mirrors M2 and M3 were coated with high reflection (HR) in the infrared range at the incident angle of 45°. One laser beam, converted into S-polarization by the half-wave plate (HWP1) and Brewster polarizer (BP1), was used as the pump beam of the ips-TPG and named Ep. The polarization of the other laser beam was adjusted by HWP2 for satisfying the phase-matching condition of the second harmonic generation (SHG) in a potassium titanium oxide phosphate (KTP1) crystal (7 × 7 × 10 mm3, θ = 90°, φ = 23.5°). The fundamental (1064.4 nm) and second harmonic (532.2 nm) waves were separated by M4 coated with high reflection (HR) at 532 nm and high transmission (HT) at 1064 nm. The 532 nm laser beam, as the pump beam of the single-resonant optical parametric oscillator (SR-OPO) system and named E0, was converted into P-polarization by HWP3 and BP2. The SR-OPO consisted of two flat mirrors M5 and M6 coated with HT at 532 nm and HR in the infrared range, a potassium titanium oxide phosphate (KTP2) crystal (10 × 8 × 20 mm3, θ = 90°, φ = 24.5°) and a Glan prism (GP). The output idler wave tuned from 1068.08 nm to 1084.76 nm was used as the pulse-seed laser. The mirror M7 coated with HR in the infrared range, was mounted on a rotating stage, which could vary the phase-matching angle between the pump and pulse-seed waves in a 1 mol.% magnesium oxide doped near-stoichiometric lithium niobate (MgO:SLN) crystal. And the MgO:SLN crystal was cut as an isosceles trapezoid configuration and the crystal surface was optically polished without the coating. Moreover, the energy of the infrared and THz waves were measured by energy meter (Newport, 1919-R) and calibrated Golay cell detector (TYDEX, GC-1P), respectively. The calibration of the Golay cell detector is specified by the manufacturer (Tydex, Inc.) to be 86.95 kV/W at the repetition rate of 10 Hz. A 1mm thickness black polyethylene sheet was used as the THz filter, which was covered on the detector in order to block the injection of scattered infrared wave. The wavelength in the infrared range was measured by optical spectrum analyzer (Agilent, 86142B).
4. Results and discussion
In our experiment, the pulse-seed was generated by the SR-OPO mentioned above. The SR-OPO operated near the degeneracy point with type-II phase matching. While the P-polarization signal wave transmitted the GP and oscillated in the cavity, the S-polarization idler wave reflected out of the cavity by the GP, was used as the pulse-seed wave for ips-TPG system. The completely overlap of pump and pulse seed beams in the time domain was achieved by controlling the optical path of the pump beam. The time domain profiles of two beams were measured by fast response InGaAs detector (Thorlabs DET08C) after M7 and shown in the inset of Fig. 3. The tuning characteristics of the idler wave from the SR-OPO were shown in Fig. 3. When the tuning angle of the KTP2 (φ-angle tuning) varied from 0° to 10.5°, the idler wavelength tuning from 1068.08 nm to 1084.76 nm was measured. When the pump energy (E0) was 110 mJ, the idler energy was about 23 mJ, which was relatively stable throughout the entire tuning wavelength. Furthermore, with the pump energy (E0) increased, the maximum idler energy was up to 37.5 mJ. Besides, in order to correctly calculate the THz frequency, the generated Stokes wavelength was monitored by the optical spectrum analyzer. The measured Stokes wavelength was also shown in Fig. 3. It is clear that the wavelength of pulse seed and Stokes are almost identical, and no other wavelengths are found at the same time. Based on the energy conservation law, the corresponding THz frequency is calculated by the difference of wavelengths of pump and pulse seed waves.
Fig. 3 The measured Stokes wavelength and the output characteristics of the idler wave from the SR-OPO. Inset: the time-domain profiles of the pump and pulse seed waves.
Figure 4 shows the measured THz tunable output characteristics of ips-TPG under the pump energy (EP) of 150 mJ and pulse-seed energy of 20 mJ. With the pulse-seed wavelength changes from 1068.34 nm to 1084.20 nm, the corresponded THz output frequency was tuned from 1.04 THz to 5.15 THz. The maximum and minimum THz output energies were obtained to be 4.98 μJ at 1.79 THz and 115.01 nJ at 5.15 THz, corresponding to the detected voltages of 4333 mV and 100 mV, respectively. Considering the broad-linewidth operation and low THz energy in TPG system without seed laser injection [28], the THz tunable output characteristics of traditional SLN terahertz parametric oscillator (SLN-TPO) that we proposed previously [19] were measured to make a convincing comparison. Under the same pumping conditions, the tunable range of 1.25 THz to 3.72 THz was achieved, and the maximum THz output energy was 3120 mV at 1.74 THz in SLN-TPO. Moreover, the THz output enhancement ratios between ips-TPG and SLN TPO were calculated. We can clearly see that a dramatic improvement on THz output energy was occurred in the high THz frequency range. While the THz frequency increased from 1.9 THz to 3.6 THz, the enhancement ratios grew up significantly from 1.6 times to 34.7 times. Meanwhile, the enhancement ratio at 1.24 THz was 17.5 times. In general, although the THz output peaks of ips-TPG and SLN TPO were located at about 1.8 THz with similar output energies, the performance of ips-TPG far exceeds SLN TPO in terms of the tunable range and THz output energies at high frequencies (>2.5 THz), whose trend is consistent with calculated results in section 2. The dramatic enhancement of THz output can be attributed to the increase of initial Stokes energy, which originated from the tunable pulse-seed laser injection. The injection of pulse seed not only provides a frequency selection mechanism to concentrate the Stokes gain with in a relative narrow Stokes frequency band and participates the feedback amplification of SPS process to enhance the THz generation, but also increase the interaction between the pump and Stokes wave in DFG process.
To further evaluate the performance of ips-TPG quantitatively, the THz energy attenuation factor was defined as follows:
where is the maximum THz output energy, and is the THz output energy at each frequency point. It is worth mentioning that the smaller the value of , the stronger the THz generation capability at this frequency point.Figure 5 shows the THz energy attenuation factors of ips-TPG and SLN TPO. For the ips-TPG, the THz energy attenuation factors of 4.41 dB, 0.3 dB, 0.65 dB and 3.27 dB were realized at 1.24 THz, 2.16 THz, 2.61 THz and 3.58 THz, respectively. As comparison, the THz energy attenuation factors of SLN-TPO were 15.39 dB, 3.01 dB, 6.37 dB and 16.88 dB at 1.24 THz, 2.24 THz, 2.53 and 3.53 THz, respectively. In addition, the 3dB bandwidth was introduced to characterize THz output performance over the whole tuning frequency range. Within the 3dB bandwidth, the THz output energy at each frequency point exceeded the half of the maximum THz output energy. As shown in Fig. 5, the 3dB bandwidths of ips-TPG and SLN TPO were 2.1 THz (1.3 THz to 3.5 THz) and 0.8 THz (1.4 THz to 2.2 THz), respectively. About 2.6 times improvement on 3dB bandwidth proves that the ips-TPG has a larger dynamic range and relatively flat output curve over a wide frequency range. From the experimental results above, the ips-TPG is more conducive to practical applications in the high THz frequency range.
Figure 6 shows the effect of the pump energy and pulse-seed energy on the THz output characteristics. Under a fixed pulse-seed energy of 20 mJ, the THz output energies of ips-TPG at 1.79 THz were measured at different pump energies, as shown in Fig. 6(a). Obviously, the THz output energy increased near-linearly with the increasing of pump energy, and the maximum THz output energy was obtained to be 5.46 μJ under the pump energy of 160 mJ. Meanwhile, when the pump energy was fixed at 100 mJ, the THz output energy was measured under the pulse-seed energies varied from 0.42 mJ to 37.5 mJ, as shown in Fig. 6(b). It is clear that the THz output curve can be divided into two parts. Firstly, the THz output energy increased near-linearly with the pulse-seed energy increasing from 0.42 mJ to 8.17 mJ. After that, with the continuous increasing of pulse-seed energy, the THz output increased slowly and saturated gradually. Meanwhile, the larger pump energy, the larger pulse seed energy required for the saturation. For a certain pump energy, the less pulse seed energy required for saturation as THz frequency increasing. The results indicate that the inherent THz generation capability is mainly limited by the pump energy. However, the pulse-seed laser injection could compensate the low Stokes gain to a certain extent, which is beneficial to the inherent THz generation. In our experiment, the phase-matching conditions of stimulated polariton scattering (SPS) and difference frequency generation (DFG) are simultaneously satisfied. As shown in Fig. 6(b), considering that the energy ratio between pump and pulse-seed was about 8:1 as the saturation occurred, it is much higher than that when saturation occurs a pure DFG process. Therefore, we infer that there are SPS and DFG processes during THz generation. Under a fixed pump energy, the SPS and DFG processes exist simultaneously. When the pulse-seed energy is small, the THz generation is mainly dominated by SPS process. With the pulse seed energy increasing, the THz generation is dominated by DFG process gradually. Because the underutilization of pump energy in crystal, there is still a portion of pump energy consumed by SPS process. As the pump energy is more fully utilized, the THz output energy is higher. Until the seed energy reaches a certain value, the saturation of THz energy is induced by the saturation of DFG process, which is attributed to that the conversion efficiency of DFG process could be the maximum when the energies of two interacted waves are close [29]. In addition, Fig. 6(b) shown the threshold energies of ips-TPG under different pulse-seed energies. When the detected THz signal voltage was slight higher than the noise voltage of Golay cell (about 10mV), the pump energy was defined as threshold energy. The significant threshold reduction caused by the pulse-seed laser injection was observed. When the pulse-seed energy of 37.3 mJ, the minimum threshold energy was 11.9 mJ. Compared with the TPG system without seed laser injection, the threshold energy of the ips-TPG was reduced by 9.66 times.
Fig. 6 (a) The THz output energy of ips-TPG under different pump energy. (b) The THz output energy and threshold energy under different pulse-seed energy.
Figure 7 shows the acceptance angle of THz generation in the ips-TPG. The acceptance angle is defined that the output energy decreased to 40.5% of the maximum under a certain frequency, which is caused by the angle mismatch [30]. The 0° was defined as the angle between pump and pulse seed beams with the maximum THz output energy. When the pump and pulse-seed wavelengths were fixed at 1064.4 nm and 1070.8 nm respectively, the THz energies were measured under the angle between pump and pulse-seed beams varying from −0.6°to 1.0°. At the same time, the generated Stokes wavelength was monitored by the optical spectrum analyzer. It is clear that the acceptance angle of the ips-TPG was estimated to be about 0.42°. Within the acceptance angle, a drift of the Stokes central wavelength was less than 0.3 nm, the corresponding the THz central frequency drift was less than 87 GHz. Considering the linewidth of pulse seed wave was about 0.33 nm, the drift of THz central frequency could be further decreased by narrowing the linewidth of pulse seed. In addition, the measured acceptance angles at different frequencies were shown in the inset of Fig. 7. As the THz frequency increasing, the acceptance angle gradually decreased. Because the traditional TPO systems is angle-sensitive and easily detuned, such a large acceptance angle makes the performance of ips-TPG insensitive to the angle, which is more suitable for practical applications.
Fig. 7 The acceptance angle of THz generation in the ips-TPG. Inset: the acceptance angle at different THz frequency.
Furthermore, the THz output energies of ips-TPG under the pump energy of 100 mJ and pulse-seed energy of 20 mJ were measured at 1.79 THz, as shown in Fig. 8. It is obvious that a stable operation of ips-TPG was achieved over an hour. As shown in the inset of Fig. 8, the THz output fluctuation was measured under different pulse-seed energies. With the increase of pulse-seed energy, the THz output fluctuation slowly decreased and tended to be a constant. The minimum THz output fluctuation was obtained to be 5.62% under the pulse-seed energy of 35 mJ. Considering large fluctuations of pump and pulse-seed energies of 1.82% and 2.66% respectively, it is inferred that the THz output stability could be further improved by enhancing the stability of pump and pulse-seed lasers.
Fig. 8 The THz output stability of ips-TPG over an hour. Inset: the THz output fluctuations under different pulse-seed energies.
5. Conclusion
In conclusion, an ips-TPG with gain enhancement in wide tuning frequency range was demonstrated in this paper. The maximum THz output energy of ips-TPG was 5.46 μJ at 1.79 THz, and the THz frequency range was continuously tuned from 1.04 THz to 5.15 THz. Through the compensation of initial Stokes energy by pulse-seed laser injection, a significant enhancement of THz output energy was achieved in high THz frequency range (> 2.5 THz). With the THz frequency increasing from 1.9 THz to 3.6 THz, the THz output enhancement ratios between ips-TPG and SLN-TPO were from 1.6 times to 34.7 times. Besides, the 3dB bandwidth of ips-TPG was 2.1 THz, which was about 2.6 times that of SLN-TPO. The THz energy enhancement mechanism for ips-TPG can be attributed to the increase of interaction in SPS and DFG processes. Furthermore, the large acceptance angle and relatively stable THz output energy of ips-TPG can promote its practical prospect.
Funding
The National Basic Research Program of China (973) (2015CB755403); National Natural Science Foundation of China (NSFC) (61775160, 61771332, 61705162, U1837202); China Postdoctoral Science Foundation (2016M602954); Postdoctoral Science Foundation of Chongqing (Xm2016021).
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