Phase matching in nonlinear chi((2)) photonic crystals

We analyze harmonic generation in a two-dimensional (2D) chi((2)) photonic crystal and demonstrate the possibility of multiple phase matching and multicolor parametric frequency conversion. We suggest a new type of photonic structure to achieve simultaneous generation of several harmonics; we also present both general analytical results and design parameters for 2D periodically poled LiNbO(3) structures.