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Terahertz-wave parametric oscillators (TPOs) have advantages of room temperature operation, wide tunable range, narrow line-width, good coherence. They have also disadvantage of small pulse energy. In this paper, several factors preventing TPOs from generating high-energy THz pulses and the corresponding solutions are analyzed. A scheme to generate high-energy THz pulses by using the combination of a TPO and a Stokes-pulse-injected terahertz-wave parametric generator (spi-TPG) is proposed and demonstrated. A TPO is used as a source to generate a seed pulse for the surface-emitted spi-TPG. The time delay between the pump and Stokes pulses is adjusted to guarantee they have good temporal overlap. The pump pulses have a large pulse energy and a large beam size. The Stokes beam is enlarged to make its size be larger than the pump beam size to have a large effective interaction volume. The experimental results show that the generated THz pulse energy from the spi-TPG is 1.8 times as large as that obtained from the TPO for the same pumping pulse energy density of 0.90 J/cm2 and the same pumping beam size of 3.0 mm. When the pumping beam sizes are 5.0 and 7.0 mm, the enhancement times are 3.7 and 7.5, respectively. The spi-TPG here is similar to a difference frequency generator; it can also be used as a Stokes pulse amplifier.
© 2015 Optical Society of America
1. Introduction
Terahertz-wave parametric oscillators are important terahertz-wave sources for having advantages of high peak power, widely tunable range, narrow line-width, high beam quality, good coherence, compactness, friendly use and room temperature operation [1–8].
In order to enhance the output pulse energies, many efforts have been made and numerous improvements have been achieved. K. Kawase et al. have tried many methods to couple the THz wave out from the rectangular parallelepiped MgO:LiNbO3 crystal used in TPOs, including grating coupler fabricated on the crystal surface [3], silicon prism coupler [4], and arrayed silicon prism coupler [5]. The arrayed silicon prism coupler has been proven to be an efficient coupler and applied in many terahertz parametric sources [8–11]. In 2006, T. Ikari et al. introduced a surface-emitted TPO configuration (SE-TPO) [6]. This design let the pump and the Stokes beams be totally reflected at the crystal surface and allowed the generated THz waves to be emitted perpendicularly to the surface without any output coupler. Later in 2010 they demonstrated an energy scalable TPO using the surface-emitted configuration. A maximum THz-wave output of 382 nJ/pulse was achieved at 1.46 THz using an 8.0 mm diameter pump beam with a pulse energy of 465 mJ [7]. D. H. Wu et al. reported a TPO with a recycled pump beam in 2009 [8]. The experiment result showed that, when the pump beam was recycled once in crossed-beam geometry, the terahertz beam output power increased almost four times in magnitude. Sun et al. [9] researched a TPO with a corner-cube resonator consisting of a corner-cube prism and a flat mirror in 2011. The TPO stability against cavity misalignment was significantly improved by at least 1 to 2 orders of magnitude compared with the conventional plane-parallel resonant configuration. W. T. Wang et al. [12] reported a surface-emitted TPO with multiple output beams by using a slab MgO:LiNbO3 crystal. The total output energy of the five THz-wave beams was 3.56 times as large as that obtained from the conventional surface-emitted TPO at the same experimental conditions.
However, the generated THz single pulse energies by TPOs so far are still very limited, in the range of hundreds of nanojoule. In this paper, the factors preventing TPOs from generating high-energy THz pulses and the corresponding solutions are analyzed. A scheme to generate high-energy THz pulses by using the combination of a TPO and a Stokes-pulse-injected terahertz-wave parametric generator (spi-TPG) is proposed and demonstrated.
2. Factors preventing a TPO from generating high-energy THz pulses
The principle of the terahertz-wave parametric sources is the stimulated polariton scattering [1, 3, 13–15]. During this process, the energy conservation ωp = ωS + ωT and the momentum conservation kp = kS + kT must be satisfied, where ωp, ωS, and ωT are the angular frequencies of the pump, Stokes and terahertz waves, respectively. kp, kS, and kT are the wave vectors of the three waves, respectively. Because of the large refractive index of the LiNbO3 or MgO:LiNbO3 crystal in the terahertz spectral range, only noncollinear phase-matching can be obtained, shown in Fig. 1(a). For terahertz-wave frequency from 1 to 3 THz, the angle θ between the pumping and the Stokes beams inside the crystal is from 0.43° to 1.39°. The angle between the terahertz and pumping beams is in the vicinity of 65°. For the typical parametric process shown in Fig. 1(b), the increment of the THz-wave intensity in the y1 direction can be written as [12]
where coefficients α and g are given by where ωT, kT, εT and nT are the angular frequency, wave vector magnitude, dielectric constant and refractive index of the THz wave, ε0 and µ0 are the vacuum permittivity and permeability, respectively, ε∞ is the high-frequency dielectric constant, d33 and dQ are the nonlinear coefficients related to the pure parametric process (second-order) and Raman (third-order) scattering process, respectively. ni (i = P, S) are the refractive indexes of the pump and the Stokes lights, Ii (i = P, S, T) are the intensities of the pump, the Stokes and the THz-wave lights, c is the light speed in vacuum. In the overlapping area of the pump and the Stokes beams, the THz wave is amplified along the y1 direction in the crystal according to Eq. (1). A higher value of IP(x1, y1, z)·IS(x1, y1, z) and a larger overlapping area are very important to a higher terahertz wave generation.What factors prevent a TPO from generating high-energy THz pulses? First, a higher IP(x1, y1, z) will generate a higher IS(x1, y1, z) and an even higher IP(x1, y1, z)IS(x1, y1, z). However, the incident pump pulse intensity is restricted by the relatively low damage threshold of the MgO:LiNbO3 crystal. Second, when a Stokes pulse is built up, the pumping pulse is significantly depleted. That means, there is a time interval between the peaks of the pump and Stokes pulses [16]. While the THz-wave generation is related to the product of the pump intensity and the Stokes light intensity, this incomplete temporal overlap between the pump and Stokes pulses impairs the parametric process. Third, due to the limitation of the resonant cavity for the Stokes wave and the small phase matching angle between the pumping and the Stokes beams, the pumping beam size cannot be very large. In addition, the Stokes beam size in the cavity is less than the pump beam size [17]. The relatively small pumping beam size and the incomplete spatial overlap between the pumping and Stokes beams constrict the effective interaction volume of the three mixing waves.
To solve these problems, one solution is to use very short pulses (subnanosecond) as the pumping source in an injection-seeded terahertz parametric generator (is-TPG). The pumping pulses can reach very high peak power density before the damage of the crystal. By using Q- switched pulses as short as 420 ps as the pumping source and a continuous wave laser as the seeding, H. Minamide et al. obtained terahertz pulses with 5 µJ energy and ~100 ps width by using is-TPG [10, 11].
Here we give another method to solve these problems. High-energy terahertz pulses in duration of nanoseconds are generated by using the combination of a TPO and a surface-emitted spi-TPG and by increasing the pumping pulse energy and beam size. The duty of the TPO here is to generate Stokes pulses. They are used as the seed of the surface-emitted spi-TPG. The time delay between the pump and Stokes pulses is adjusted to guarantee they have good temporal overlap. The pump pulses have large pulse energies and a large beam size. The Stokes beam is enlarged to make its size be larger than the pump beam size to give a large effective interaction volume.
3. Experimental setup
The schematic diagram of the experimental setup for the combination of a TPO and a spi-TPG is shown in Fig. 2. There were two 5.0 mol % MgO doped LiNbO3 crystals. The rectangular one with dimensions of 50 (x) mm × 10 (y) mm × 5 (z) mm was used for the TPO. The pentagonal one was used for the spi-TPG. The shape of the pentagonal crystal is shown in Fig. 3. The pentagonal MgO:LiNbO3 crystal was cut from an isosceles triangular crystal shown as A′B′C. The lengths of sides A′B′ and B′C were 85 mm. The values of angles A′ and C were 65°.The Stokes beam went into the crystal perpendicularly to side AE. It traveled along the x-axis, then was totally reflected at side BC and went out perpendicularly to side CD. According to the phase matching condition, the angle between the generated THz beam and the Stokes beam was about 65°, so the generated THz could be emitted perpendicularly to side BC. For the sake of not too heavy sample, we cut the areas of triangles ABA′ and EDB′ off the crystal. The crystal’s thickness along the z-axis was 10.0 mm. All the input and output facets of the two crystals for the pumping and the Stokes beams were antireflection coated at the wavelength range from 1060 to 1100 nm.
The pump laser was a multi-longitudinal mode Q-switched Nd:YAG laser. The laser beam had a top-hat profile. The pulse width, the beam diameter and the repetition frequency were 8.4 ns, 7.0 mm and 10 Hz, respectively. The pump laser polarization was parallel to the z-axis of the crystal. The laser beam from the Nd:YAG laser was separated into two parts by a beam splitter. The first part, which was reflected by mirror M7, was used as the pump beam of the spi-TPG. Two half wave plates and a Brewster plate were employed as the attenuator to adjust the energy of the pump pulse and to ensure that the pump laser polarization was parallel to the z-axis of the crystal. An aperture was used to adjust the pump beam size, the pulses whose energy densities were identical, but beam sizes were different could be obtained. The second part served as the pump beam of the TPO. The Stokes wave oscillating cavity mirrors M2 and M3 were respectively coated with high reflectivity and partial transmission (T = 60%) at the wavelength range from 1050 nm to 1090 nm. The cavity length was about 210 mm. The TPO was mounted on a rotating stage. Telescope T1 with a ratio of 2.3:1 was used to reduce the pump beam size for the TPO. Two half wave plates and a Brewster plate in this portion had the same function as those in the other portion. The generated Stokes beam from the TPO was directed to the pentagonal MgO:LiNbO3 crystal with an angle of 1.50° with respect to the pump beam of the spi-TPG which propagated perpendicularly to the end-surface of the crystal. The time delayer on the way of the Stokes beam was used to adjust the temporal overlapping between the Stokes pulse and the pump pulse of the spi-TPG. Telescope T2 with a ratio of 1:3.5 was located between M5 and M6 to enlarge the Stokes beam size.
The energies of the pump and the Stokes laser pulses were measured by an energy sensor (J-50MB-YAG, Coherent Inc.) connected to an energy meter (EPM2000, Coherent Inc.). The energy of the THz-wave pulse was measured by a Golay Cell (GC-1D, TYDEX) connected to a digital oscilloscope (Tektronix DPO 4104B, 1 GHz, 8 GS/s). A THz low-pass filter (LFP 14.3-47, TYDEX) which was covered on the Golay Cell, was used to block the scattered pump and Stokes lights with a transmittance of about 80% at the THz-wave frequency.
In the process of measurement for the THz wave, the entrance window of the Golay Cell behind the THz low-pass filter was covered by a metal plate with a pin hole of 1 mm in radius. By moving the Golay Cell with respect to the THz wave source, the intensity distribution was measured. The pulse energy was obtained by integrating the energy density over the THz beam size. The distance between the THz-wave output surface of the MgO:LiNbO3 crystal and the entrance window of the Golay Cell was 1.0 cm. During the measurements, no optical damage was observed in the crystal.
The angles between the pump beam and the Stokes beam outside the crystals in the TPO and the spi-TPG were fixed at 1.50°, and the corresponding angles inside the crystal θ were 0.70°. The wavelength of the pump wave was 1064.16 nm and the central wavelength of the Stokes wave was 1070.76 nm. The corresponding THz wavelength was 173 µm. The injected Stokes pulse energy was 9.81 mJ with a pulse width of 5.2 ns.
4. Results and discussions
The output energies of the THz-wave and the amplified Stokes pulses for different pump beam energy densities and sizes are showed respectively in Fig. 4 and Fig. 5. As can be seen from these two figures, the bigger the pump energy density and the beam size, the higher the output THz-wave energy and the amplified Stokes pulse energy. When the pump beam diameter was 7.0 mm and the pump energy density was 0.90 J/cm2, the corresponding pump energy was 346 mJ, the maximum output THz-wave and Stokes pulse energies are 16.8 V and 118 mJ, respectively.
Fig. 5 The output energies of the amplified Stokes pulses for different pump beam energy densities and sizes.
Figure 6 shows the spi-TPG performance in comparison with that of the traditional surface-emitted TPO for the same pumping beam diameter of 3.0 mm. The surface-emitted TPO used the same pentagonal MgO:LiNbO3 crystal. It can be seen that the output THz-wave energy of the spi-TPG is much larger than that of the surface-emitted TPO. We attribute this performance improvement to the complete spatial and temporal overlaps between the pumping and Stokes beams. When the pumping pulse energy density was 0.90 J/cm2 (the corresponding pumping pulse energy was 63.6 mJ), the THz pulse energy from the spi-TPG is 1.8 times as large as that obtained from the TPO. When the pumping beam sizes were 5.0 and 7.0 mm, the enhancement times were 3.7 and 7.5, respectively.
Fig. 6 Comparison of the THz-wave energies between the spi-TPG and the TPO for the same pump beam diameter of 3.0 mm.
Figure 7 shows the pumping and depleted pumping pulse waveforms. The pumping pulse was deeply depleted and a large amount of pumping energy was consumed and converted into energies of the Stokes and the THz pulses.
Fig. 7 Waveforms for the pump (a) and depleted pump (b) pulses. The pump energy is 302 mJ and the pump beam size is 7.0 mm.
It was found that the THz-wave beam distribution was symmetrical in the vertical direction and unsymmetrical in the horizontal direction. Figure 8 shows the THz-wave beam distributions for different pump beam sizes in the case of 0.71 J/cm2 pumping energy density. Area Ι in the Fig. 9 shows the overlapping area of pump and Stokes beams in the crystal. According to Eq. (1), THz wave is amplified along the y1 direction. In the area x1>0, the THz-wave gain length decreases with increasing x1, resulting in decreasing THz wave output along the x1 direction. In the area x1<0, the generated THz wave in the overlapping area of pump and Stokes beams has been absorbed strongly by the crystal in area ΙΙ. The THz-wave intensity at point O is the largest. It could be inferred that the THz wave beam distribution is unsymmetrical in the horizontal direction (x1 direction). In the z direction, due to symmetrical distribution of pump and Stokes beams in the overlapping area, the distribution of THz-wave intensity in vertical direction (z direction) is symmetrical. These are consistent with the distributions of THz wave illustrated in Fig. 8.
Fig. 8 Terahertz wave beam distributions in the vertical direction (a) and the horizontal direction (b) for different pump beam sizes in the case of 0.71 J/cm2 pump energy density.
The unit of the THz-wave energy we have adopted in this paper is the output voltage of the Golay Cell. Because the Golay Cell supplier has provided us with the voltage responsibility only used for continuous wave (CW) signals. Some efforts have been made to calibrate a similar Golay Cell and determine the responsibility for quasi-CW or pulsed signals [18]. We would not like to use it before further confirmation. However, from the experimental results, it is easy to see the output THz pulse energy enhancement by the combination of a TPO and a spi-TPG.
The terahertz parametric source in this paper is similar to a difference frequency generator (DFG). The difference is that DFG involves only second-order nonlinear process [19–21], while the scattering process in this parametric source involves both second- and third-order nonlinear processes. To some extent, the setup in this paper is something between a DFG and a spi-TPG.
The experimental setup here can also be used as a Stokes pulse amplifier. Because the purpose here is to generate terahertz wave, the incident Stokes pulse is enlarged to make its size be larger than the pump beam size. This makes the pumping pulse be fully used. If the purpose is to amplify the Stokes pulse, the beam size of the Stokes pulse should be smaller than the pump beam size.
4. Conclusions
In conclusion, a method to generate high-energy THz pulses by using the combination of a TPO and a spi-TPG has been proposed and demonstrated. The Stokes pulses generated from the TPO had a pulse energy of 9.81 mJ and a pulse width of 5.2 ns. They were used as the seed of the surface-emitted spi-TPG. The delay between the pump and Stokes pulses was adjusted to guarantee they had good temporal overlap. The Stokes beam was enlarged to make its size be larger than the pump beam size to guarantee they had good spatial overlap and to give a large effective interaction volume. The pump pulses can have a large pulse energy and a corresponding large beam size, keeping the energy density smaller than the damage threshold of the nonlinear crystal. When the pumping pulse energy density was 0.90 J/cm2 and the pumping beam size was 3.0 mm, the generated THz pulse energy from the spi-TPG was 1.8 times as large as that obtained from the TPO. When the pumping beam sizes were 5.0 and 7.0 mm, the enhancement times were 3.7 and 7.5, respectively. This gives a clue to get high energy nanosecond THz pulses. If the pumping pulses with larger energy and beam size are used, more THz pulse energies are expected. Considering the injected Stokes pulse energy is as large as 9.81 mJ, the setup in this paper is something between a DFG and a spi-TPG.
Acknowledgments
This research is supported by the National Natural Science Foundation of China (61475087, 11174185, 11204160), the Fundamental Research Funds of Shandong University (2014QY005) and China Postdoctoral Science Foundation Funded Project (2013T60665).
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