THz-wave generation via stimulated polariton scattering in KTiOAsO 4 crystal

A terahertz parametric oscillator based on KTiOAsO4 crystal is demonstrated for the first time. With the near-forward scattering configuration X(ZZ)X + Δφ, the polarizations of the pump, the Stokes and the generated THz waves are parallel to the z-axis of the crystal KTA. When the incident angle θext of the pump wave is changed from 1.875° to 6.500°, the THz wave is intermittently tuned from 3.59 to 3.96 THz, from 4.21 to 4.50 THz, from 4.90 to 5.16 THz, from 5.62 to 5.66 THz and from 5.92 to 6.43 THz. The obtained maximum THz wave energy is 627 nJ at 4.30 THz with a pump energy of 100 mJ. It is believed that the terahertz wave generation is caused by the stimulated scattering of the polaritons associated with the most intensive transverse A1 mode of 233.8 cm. Four much weaker transverse A1 modes of 132.9 cm, 156.3 cm,175.1 cm, and 188.4 cm cause four frequency gaps, from 3.97 THz to 4.20 THz, from 4.51 to 4.89 THz, from 5.17 to 5.61 THz and from 5.67 to 5.91 THz, respectively. ©2014 Optical Society of America OCIS codes: (190.4410) Nonlinear optics, parametric processes; (190.5890) Scattering,

At room temperature, KTA crystal is orthorhombic and belongs to noncentrosymmetric space group Pna2 1 and point group C 2v (mm2).The irreducible representation of the vibrational optical phonon modes for C 2v (mm2) point group gives 47A 1 + 48A 2 + 47B 1 + 47B 2 collection of modes [12].The symmetry species A 1 , B 1 , and B 2 are infrared active with dipole moments oriented along the z, x, and y directions, respectively [13].All four representations are Raman active.The transverse optical A 1 modes are located at 111. 5, 132.9, 156.3, 175.1, 188.4, 209.4 and 233.8 cm −1 and the 233.8 cm −1 mode has a very intense strength [13].It is because of the existence of the intense transverse optical A 1 mode which is both infrared-and Raman-active that KTA crystal has the potential to generate THz wave based on stimulated polariton scattering [14,15].
Polaritons are elementary excitations generated by the combination of photons and transverse optical phonons.They exhibit both phonon and photon behaviors.The stimulated polariton scattering aroused by infrared laser pulses is an efficient method to generate THz wave [14,15].Terahertz parametric oscillators (TPOs) based on stimulated polariton scattering have been intensively studied.They have many advantages, including operation at room temperature, compactness, widely tunable range and narrow linewidth [15].However, in the past nearly 20 years, only crystal LiNbO 3 or MgO:LiNbO 3 [15][16][17][18][19][20] was used as the nonlinear material in TPOs.The generated THz-wave frequency range is from 0.6 to 3.2 THz.The study of other nonlinear crystals for TPOs is crucial to expanding the THz-wave frequency range and application.In this work, a TPO using crystal KTA is demonstrated for the first time.The THz wave was intermittently tuned from 3.59 THz to 6.43 THz with four frequency gaps, from 3.97 THz to 4.20 THz, from 4.51 to 4.89 THz, from 5.17 to 5.61 THz and from 5.67 to 5.91 THz, respectively.The obtained maximum THz wave pulse energy was 627 nJ at 4.30 THz with a pump energy of 100 mJ.Firstly, an x-cut (θ = 90°, φ = 0°) KTA crystal of 5 × 5 × 30 mm 3 was used to realize the stimulated polariton scattering and to obtain the dependences of the Stokes wavelength, terahertz wavelength and terahertz wave refractive index on the phase-matching angle.The experimental setup is shown in Fig. 1.The resonant cavity for the Stokes wave was composed of the plane mirrors M1 and M2, and its length was 150 mm.They were respectively coated for high reflectivity (R > 99.8%) and partial transmission (T = 5.2%) at the wavelength range from 1060 nm to 1100 nm.Both the resonant cavity and the crystal KTA were fixed on a rotational stage, which was controlled to adjust the phase-matching angle θ in between the pump and oscillating Stokes waves inside the crystal.In this work, the pump source was a Qswitched Nd:YAG laser.Its wavelength, pulse width, beam diameter and repetition frequency were 1064.16nm, 8.2 ns, 2.4 mm and 10 Hz, respectively.According to the near-forward scattering configuration X(ZZ)X + Δφ in the stimulated polariton scattering [13], the Stokes wave propagated along the x-axis of the crystal KTA, the pump wave propagated with the angle θ in to the x-axis, the polarization of the pump wave was kept parallel to the z-axis by two half wave plates and a Brewster plate.The spectrum information of the oscillating Stokes wave was recorded by a spectrum analyzer (YOKOGAWA AQ6370C, 600-1700 nm, 0.05 nm). Figure 2 shows the angle-tuning characteristics of the Stokes wave in the stimulated polariton scattering of the crystal KTA.With θ ext (the angle between the pump and oscillating Stokes waves outside the crystal, θ ext = n p θ in , n p is the refractive index of the pump light) from 1.875° to 6.500°, the Stokes wave was tuned from 1077.88 to 1089.02 nm.But four wavelength gaps appeared.They will be discussed later.

Phase-matching conditions of the stimulated polariton scattering in KTA crystal
In the stimulated polariton scattering, the pump, the Stokes and the THz waves must obey the energy conservation law and momentum conservation law (non-collinear phase matching condition).By using the relation in Fig. 2 and the refractive index of the lights from 1.06 to 1.09 μm [21], the dependence of the THz-wave frequency on θ ext and the dependence of n T on the wavelength of the THz wave can be obtained.For θ ext from 1.875° to 6.500°, the THzwave frequency is from 3.59 to 6.43 THz, and the THz-wave refractive index is from 3.189 to 5.262.The angle β between the THz and Stokes waves (the x-axis of the crystal) in the crystal is calculated to be from 53.70° to 70.46° for θ ext from 1.875° to 6.500°.If the THz wave is emitted through the zx surface, its incident angle at the surface zx is from 19.54° to 36.30°.But the critical angle resulting in the total reflection of the THz wave at the surface zx is less than 18.27°.So, extracting the THz wave from the crystal is a key problem like TPOs based on LiNbO 3 , where the arrayed Si-prism coupler [15,[17][18][19][20] and the surface-emitted configuration [16] are usually used.The surface-emitted configuration of the KTA-TPO is employed below.The shape of the crystal KTA used in the surface-emitted TPO is an isosceles trapezoid in its xy plane and is shown in Fig. 3(a).The angle between the base of the isosceles trapezoid and the x-axis is 30°.The thickness of the crystal along the z-axis is 5.0 mm.The longer base is 30.0 mm and the length of the trapezoid leg along the y-axis is 15.0 mm.The end surfaces of the crystal which the Stokes beam is perpendicularly incident to, are antireflection coated at the wavelength range from 1060 nm to 1100 nm.The pump and the oscillating Stokes waves are totally reflected when they are incident on the crystal base surface.The generated THzwave can be emitted nearly normal to the crystal base surface without need for any coupler.Figure 3(b) shows the experimental setup of the surface-emitted TPO based on KTA.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 THz-wave pulse was detected by a Golay Cell (GC-1D, TYDEX) connected to a digital oscilloscope (Tektronix DPO 4104B, 1 GHz, 8 GS/s).Its sensitivity is 0.37 μJ/V for the THz pulses whose widths are much shorter than the response time of the Golay Cell.A THz low pass filter (LFP 14.3-47, TYDEX) was fixed on the Golay Cell to block the scattered pump and Stokes lights.

Surface-emitted TPO in KTA crystal
In the experiment, the polarization of the pump wave was kept parallel to the z-axis.When θ ext was 2.875° and the pump energy was 90 mJ, the polarization of the THz wave was measured by an HPDE THz-polarizer (TYDEX), as shown in Fig. 4. When the polarizer direction was parallel to the z-axis of the crystal KTA, the measured energy of the THz-wave pulse was the maximum.It decreased with the increase of the angle α between the polarizer direction and the z-axis of the KTA crystal.Limited by the sensitivity of the Golay Cell, it became undetectable with the angle α above 80°.When α was above 100°, the Golay Cell started to respond to the generated THz wave again.This indicated that the THz-wave polarization was parallel to the z-axis of the crystal KTA. Figure 5 shows the tuning characteristics of the THz and the Stokes waves from the KTA-TPO at a fixed pump energy of 100 mJ.With θ ext from 1.875° to 6.500°, the THz wave was tuned from 3.59 to 6.43 THz.But there were four THz-wave frequency gaps, from 132 to 140 cm −1 , from 150 to 163 cm −1 , from 172 to 187 cm −1 and from 189 to 197 cm −1 .The tuned THzwave frequency range was divided into five parts, Range I from 3.59 to 3.96 THz, Range II from 4.21 to 4.50 THz, Range III from 4.90 to 5.16 THz, Range IV from 5.62 to 5.66 THz and Range V from 5.92 to 6.43 THz.The four frequency gaps are located in the vicinities of the transverse optical A 1 modes of 132.9, 156.3, 175.1 and 188.4 cm −1 , respectively.The transverse optical phonon modes are strongly infrared absorbing.A simple dispersion relation for an undamped harmonic oscillator is given by [22,23] ( ) ( ) where ε r (∞) is the high-frequency dielectric constant, ω TO is the radian frequency of the transverse optical (TO) A 1 mode and ω LO is the radian frequency of the longitudinal optical (LO) mode.The radian frequency ω of a polariton is [22,23] ( ) where k is the wave vector of the polariton.For ω TO < ω < ω LO , Eq. ( 2) has no solution because of ε r (ω) <0.It suggests that no electromagnetic wave at the frequency range from ω TO to ω LO is able to generate or propagate in the crystal.The Stokes wave is not able to oscillate because it is generated with the generation of the polariton (THz wave) in the stimulated polariton scattering.So, the Stokes wave frequency gaps appear corresponding to the frequency gaps of the THz wave.For the frequency ranges outside ω TO < ω < ω LO , the THzwave energy and the output Stokes energy have the same changing tendency.Keeping the pump incident angle θ ext at 2.875°, the THz wave output at 4.30 THz as a function of the pump energy was measured, as shown in Fig. 6.As the pump energy reached 45 mJ (the pump intensity 121 MW/cm 2 ), the THz wave started to be detected by the Golay Cell and the Stokes wave could be measured.Their output energies increased with increasing pump energy.Under the pump energy of 100 mJ (the pump intensity 270 MW/cm 2 ), the output energies of the THz and the Stokes waves were 627 nJ and 5.6 mJ, respectively.

Conclusion
In conclusion, a surface-emitted TPO based on crystal KTA has been proposed and demonstrated according to the experimental study on the angle-tuning characteristics of the Stokes wave in the stimulated polariton scattering.With the near-forward scattering configuration X(ZZ)X + Δφ, the polarization of the THz wave was measured along the z-axis of the crystal KTA.When the incident angle θ ext of the pump wave was from 1.875° to 6.500°, the THz wave was tuned from 3.59 THz to 6.43 THz, except four frequency gaps, from 3.97 THz to 4.20 THz, from 4.51 to 4.89 THz, from 5.17 to 5.61 THz and from 5.67 to 5.91 THz.These frequency gaps are just located in the vicinities of some A 1 modes of the crystal KTA, where the electromagnetic waves can neither propagate nor generate in the crystal.The maximum output energy of 627 nJ was obtained at 4.30 THz with a pump energy of 100 mJ.

Fig. 1 .
Fig. 1.Experimental setup of the stimulated polariton scattering in a cuboid KTA crystal.

Fig. 2 .
Fig. 2. Angle-tuning characteristic of the Stokes wave in the stimulated polariton scattering of the KTA crystal.

Fig. 3 .
Fig. 3. (a) Shape of the crystal KTA used in the surface-emitted TPO; (b) Experimental setup of the surface-emitted TPO based on crystal KTA.

Fig. 4 .
Fig. 4. Measured polarization of the generated THz wave using an HDPE polarizer.

Fig. 5 .
Fig. 5. Measured energies of the THz and the Stokes waves at different frequencies.
The measured maximum THz-wave pulse energy was 627 nJ at 4.30 THz of Range II, and the Stokes-wave pulse energy of 5.6 mJ was obtained at the corresponding wavelength of 1080.66 nm.The other peak energies were 517 nJ at 3.82 THz of Range I, 522 nJ at 4.72 THz of Range III, 222 nJ at 5.64 THz of Range IV, and 402 nJ at 6.27 THz of Range V, respectively.