A polarization- and direction-independent phase-matching for third harmonic generation

We proposed a nearly perfect phase-matching for third harmonic generation (THG) in photonic crystals (PhCs), which is independent of the polarization and propagation direction of the fundamental wave. Taking an AlN-like Kerr medium as an example, equal effective refractive indices of the fundamental and the triple frequencies were achieved for both the TM and TE modes simultaneously by fabricating this dispersive medium into a two-dimensional square-lattice PhC. Furthermore, the THG conversion efficiency were numerically calculated by using the nonlinear finite-difference time-domain method to simulate Gaussian pulses with TM and TE polarizations propagating along the high-symmetry directions of the PhC (ΓX and ΓM), respectively. The simulation results show that all THG conversion efficiencies increase with the propagation length like a parabola regardless of the polarization and the propagation direction of the incident fundamental wave, indicating a nearly perfect phase matching. (paper)