We report suppression of forward stimulated polariton scattering (SPS) in χ(2) structured media. Periodic poling in KTiOPO4 (KTP) leads to the destructive interference of phonon-polariton waves, which is responsible for the dependence of the SPS threshold on the poling period. This was confirmed by comparing the SPS thresholds in periodically-poled KTP (PPKTP) crystals with different poling periods. Further confirming the physical picture, we studied the changes in the Stokes power distribution as a function of the rotation angle of the PPKTP crystal.
© 2013 Optical Society of America
The coupling of electromagnetic modes with mechanical degrees of freedom has recently proved to be a very fruitful field of inquiry, resulting in the demonstration of cooling acoustic resonator modes and the engineering of stimulated Brillouin scattering in optical fibers [1, 2]. Coupling between the electromagnetic waves and the infrared-active optical phonon modes gives rise to phonon-polaritons propagating in the THz spectral range with a very distinct and strong dispersion pinned by the transversal-optical (TO) phonon resonances. Control of the energy exchange between the vibrational degrees of freedom and the electromagnetic field is crucial for the selective generation, steering and guiding of the polariton waves .
Ferroelectric crystals such as LiNbO3, KTiOPO4 (KTP), LiTaO3, and KNbO3 are characterized by strong infrared-active TO phonon resonances in the THz frequency range, which readily couple to the electromagnetic wave propagating in the crystal to produce phonon-polariton waves [4, 5]. The TO phonon resonances can contribute substantially to the magnitude of 2nd order susceptibilities, which is beneficial for the THz generation exploiting difference frequency generation (DFG) and optical rectification (OR) [6, 7]. While the 3rd order stimulated Raman scattering (SRS) is ascribed to the phonon branches that are both infrared- and Raman-active , the 2nd order parametric process associated with the same phonon branches can have a dominating contribution to SRS by polaritons [8–10]. In this case, the process is also called stimulated polariton scattering (SPS). Now, the ferroelectric nonlinear crystals can be periodically structured to achieve the quasi-phase-matching condition, which seemingly opens a route for tunable THz generation.
In this work, we show that periodic structuring of ferroelectric domains in KTP crystals drastically suppresses forward SPS. The phenomenon was first reported in  by the co-authors, but we here change the overall physical picture to include other related new phenomena such as dependency of SPS threshold on different poling periods as well as its phase-matching condition insensitive to the poling period. Using a narrowband near-infrared pump laser to ensure that the polariton frequency is far beyond the bandwidth of the pump, we first ruled out the optical rectification from the possible physical mechanisms for the polariton generation. In this case, the SPS can happen by optical parametric generation (OPG) with the concomitant phase-matching condition, dictated by the lattice resonances in the THz range. In addition to the OPG process, the 3rd order Raman process will also take place. As we show, the curious property of such a parametric process mediated by the polar lattice vibrations is that the scattering frequency becomes insensitive to the periodic poling, i.e. the tuning of THz waves cannot be achieved by χ(2) structuring as in usual DFG or OR processes. On the other hand, the SPS threshold has a strong dependence on the poling period. Due to the fact that the domain inversion does not change odd-order nonlinear susceptibilities, this would be a rather unexpected result if the 3rd order Raman scattering was the dominant part in the scattering mechanism. Based on the measurement of the SPS threshold as a function of the poling period, we elucidate here the physical mechanism of the SPS suppression and show that Raman scattering, though not a dominant effect, plays a crucial role. Furthermore, by exploiting the dependence of the SPS efficiency on the domain inversion period, we demonstrate that the Stokes sidebands can be individually enhanced or suppressed by simple rotation of the domain grating, thereby breaking the inherent spatial symmetry of the SPS process.
2. An experimental evidence of SPS suppression
SPS suppression was first studied in a 1 mm thick, 12 mm long periodically-poled KTP (PPKTP) sample with seven different domain-gratings that are separated by 100 µm wide single-domain areas [Fig. 1(a)]. The domain-inverted structures that had poling periods ranging from 31.1 µm to 36.5 µm were 350 µm wide, and extended throughout the whole crystal length. As a pump source, we used a Ti:Sapphire regenerative amplifier operating at 818 nm with a FWHM spectral width of 0.7 nm, delivering pulses with a duration of 61 ps and an energy of 14 µJ. The pump beam propagated along the crystal x-axis; both the pump and the generated Stokes beams were polarized parallel to the polar z-axis. From the symmetric scattering pattern in the xy crystal plane, it is clear that the phonon-polariton field was polarized along the crystal z-axis, which is expected as the coefficient is the largest in KTP. All the experiments in this paper were performed at room temperature.
In the single-domain regions, the Stokes beams propagated noncollinearly with respect to the pump at an internal angle of 1.8° with a frequency shift of 5.9 THz [8, 11], while the central beam contained only the pump wave [Fig. 1(b)]. The noncollinear scattering corresponds to the phase-matching angle at the given polariton frequency, which in turn is determined by the maximum single pass gain for the polariton wave. Such gain peaks are located below the corresponding infrared-active TO phonon resonance where absorption losses are moderate . Figure 1(c) shows the efficiency of forward SPS measured with a beam size of 100 µm in diameter, while the entire sample was translated along the y-axis with a step size of 20 µm. In each periodically-poled region, one could clearly observe that the Stokes power was suppressed down to the noise level of the detector, whereas the conversion efficiency exceeded 40% when the whole process took place in the single-domain area.
For understanding of the SPS suppression in PPKTP, it is important to realize that the sequence of short and long titanyl bonds in KTP, which is responsible for the spontaneous polarization and for the observed phonon-polariton mode , is periodically inverted during periodic poling. This results in periodic sign reversal of the vibrational polarizability and leads to phase-shift of the polariton field generated in adjacent ferroelectric domains. In our experiment, this phase inversion results in the destructive interference of polariton waves where the polaritons generated in one domain propagate and destructively interfere with the ones generated in the next domain. This, in turn, decreases the amplitude of the polariton field in PPKTP compared to the one in single-domain KTP crystals. Moreover, this effect becomes more pronounced for shorter periods, since the build-up distance for the polariton fields is limited by the size of one domain. This brings about the decrease of the efficiency or equivalently an increase of the SPS threshold for shorter periods in PPKTP.
3. SPS threshold as a function of poling period
Indeed, the increase of the SPS threshold for shorter poling periods in PPKTP is confirmed experimentally by comparing the PPKTP crystals that have periodicities ranging from 9 µm to 500 µm with the SPS threshold in a single-domain KTP crystal. All crystals had the same length of 11.6 mm with the domain gratings extended through the entire crystal length. The same experimental setup was employed as before, with the pump pulse duration fixed at 50 ps for all the samples to ensure that SPS occurs in the steady-state regime, i.e. the pump pulse duration was substantially longer than the relaxation time of phonon-polaritons, which was experimentally determined to be about 2 ps. In the single-domain KTP sample, the threshold for SPS was reached at the pump pulse energy of 10 µJ, corresponding to a peak intensity of 0.6 GW/cm2, to generate 0.88 µJ of Stokes. This Stokes energy was used as a criterion to conveniently define thresholds in all the PPKTP crystals. Figure 2 shows the ratio of the forward SPS threshold in PPKTP crystals to that in the single-domain area as a function of the poling period. The measurements of the SPS threshold in the PPKTP crystals revealed that the threshold rapidly increases as the domain periodicity becomes shorter, which is in good agreement with our numerical simulations discussed below. For the crystals with poling periods shorter than 36 µm, the forward SPS was entirely suppressed, which means that the threshold of forward SPS was higher than that of the optical damage of the crystal.
Our calculation result in Fig. 2 confirms the experimental observation. We integrated the Stokes field generated by the nonlinear polarization at the Stokes frequency that contains three terms [9, 13–15]:9] for the frequency-dependent part of the dielectric function. The first two terms in Eq. (1a) take into account the 2nd order optical parametric generation, which is the dominant process in the proximity of the lattice resonances, while the third term represents the 3rd order stimulated Raman process. Since the electronic contribution is nearly frequency-independent in the infrared spectral range, we take the value = 15.4 pm/V  measured with frequency doubling of = 1064 nm. From the phase-matching condition [8, 11] pinned by the TO phonon resonances, the refractive index at 5.9 THz in KTP is calculated to be n = 4.1. Using the electro-optical (EO) coefficient of KTP = 35 pm/V  together with the numerical values for n and , the lattice coupling coefficient is estimated [18, 19] to be = 183 pm/V.
It should be pointed out that the phase-matching condition for the Stokes beam was observed to be independent of the poling period in our experiments, in which the Stokes beam in PPKTP crystals showed no appreciable shift either in frequency or geometry regardless of the poling period. This absence of the quasi-phase-matching can be understood as follows. The parametric amplification of the Stokes wave in SPS is seeded by the Stokes field produced by the 3rd order spontaneous and stimulated Raman scattering, which corresponds to the third term in Eq. (1a). The phase of this field is not affected by the periodical poling, in contrast to the periodic sign reversal in . Then the nonlinear polarization at the polariton frequency in Eq. (1b) will be forced to change its phase by π with the same periodicity as the 2nd order nonlinear coupling coefficients, and . This has the same effect as adding a phase mismatch into the nonlinear polarization at the polariton frequency. At the same time, according to Eq. (1a), the grating-vectors in the parametric process (the first two terms) are canceled out in the 1st order approximation. The result is that the phase-matching condition for the Stokes beam in PPKTP remains the same, unaffected by the periodic domain structure, while the SPS is suppressed due to the destructive interference of the polariton waves and periodic deamplification in the parametric process.
4. Asymmetric Stokes power distribution in a rotated PPKTP crystal
This physical picture is further confirmed by studying the asymmetric changes in the Stokes power distribution as a function of the crystal rotation. For this purpose, the PPKTP crystals in the same configuration as described before were rotated around the crystal z-axis, while the output powers of the two Stokes beams were recorded for each angle. Figure 3 shows the relative powers generated in two Stokes beams as a function of the rotation angle of the PPKTP crystal with the periodicity of (a) 500 µm and (b) 150 µm, together with our numerical calculations using Eq. (1a). It is worth noting that the asymmetry in the Stokes power distribution becomes more pronounced with a shorter poling period, which can be understood as follows. When a periodically-poled crystal is rotated around the z-axis, the SPS scattering geometry, as shown in Fig. 1(b) does not change, because the phase matching conditions remain the same. We verified this experimentally for all the periodicities where forward SPS threshold could be reached. However, the symmetric parametric amplification picture does change, i.e. the symmetry is broken in the rotated crystal because the polariton field builds up asymmetrically after experiencing different propagation length in each domain. This results in an asymmetric output power distribution in the Stokes beams.
For instance, as shown in Fig. 4(a), the polariton field propagating to the left experiences the longer effective domain period and thus higher amplification than the polariton propagating to the right. This corresponds to a lower SPS threshold, or equivalently higher efficiency for the Stokes beam propagating to the right. As a result, the relative powers generated in the two Stokes beams vary as a function of the rotation angle of the crystal [Fig. 4(b)] whereas the scattering geometry remains the same.
We have demonstrated forward SPS suppression in PPKTP, which is a result of the periodic inversion of the vibrational polarizability of the lattice that leads to a reduction of the amplitude of the polariton field through the destructive interference and the parametric deamplification. In this case, the polariton frequency is determined by the phase matching condition dictated by the dispersion of the polariton waves pinned by the TO phonon resonances and does not change with periodic structuring. Further confirming our physical picture, we also showed that this physical mechanism is fully compatible with the asymmetric changes in the Stokes power distribution with the fixed scattering geometry in a rotated PPKTP crystal. This asymmetry in the Stokes output power results from the polariton waves propagating through different effective periods in the rotated PPKTP crystals. The experiments and the analysis in this work have been done using periodically-poled KTP crystals. However, the physical mechanism is rather general and should be applicable to other widely-used ferroelectrics such as LiNbO3 and LiTaO3.
We would like to acknowledge the Swedish Research Council (VR), Linné Center ADOPT, and Göran Gustafsson Foundation, and Swedish Foundation for Strategic Research for financial support of this work.
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