Realization of nonlinear Cherenkov frequency down-conversion by phase velocity modulation

Nonlinear Cherenkov radiations (NCR) have attracted increasing research interest in the past years. Similar to the traditional Cherenkov radiation effect in particle physics, NCR requires that the nonlinear polarization wave propagates faster than the harmonic waves. Cherenkov frequency up-conversions can be automatically realized in normal dispersion materials and extensive work on Cherenkov second-harmonic generation, sum-frequency generation and high-order harmonic generation have been reported in both bulk and waveguide systems. However, Cherenkov frequency down-conversion process is still a challenge for the restriction of phase velocity threshold. Recently, we have proposed two schemes to realize the degenerated Cherenkov difference-frequency generation (CDFG) by modulating the phase velocity of the nonlinear polarization wave using both quasi-phase-matching (QPM) and birefringence-phasematching (BPM) respectively. For the first scheme, we used the QPM method. The reciprocal vectors provided by the domain engineered structure can modulate the phase velocity of the nonlinear polarization wave, and particularly, the backward vectors can accelerate the nonlinear polarization wave. If the backward reciprocal vector is large enough, Cherenkov DFG can be realized. In experiment, a proton exchanged LiTaO3 planar waveguide with a poling period of 4.5 µm was used and the wavelengths of pump and signal were 532 and 1064nm respectively. At a radiation angle close to the theoretical one, the infrared CDFG spot can be observed with a CCD. For the second scheme, the birefringence property of KTP was utilized. For birefringent crystal, light with different polarization has different refractive index. By proper choice of the polarization states of the interacting waves, the refractive index of the signal wave can be larger than that of the pump wave, thus the phase velocity of the nonlinear polarization wave of the DFG process will exceed that of the harmonic wave. In experiment, we set the polarization of 532-nm pump and the 1064-nm signal waves along x and z axis of KTP respectively. CDFG was realized and some cascaded Cherenkov processes were observed as well. The method based on BPM can reduce the requirements for fabricating short-period domain structures and can be extended to mode-matching in waveguides for realizing nonlinear Cherenkov radiations.