Photonic quasicrystals for nonlinear optical frequency conversion

We present a general method for the design of 2-dimensional nonlinear photonic quasicrystals that can be utilized for the simultaneous phase matching of arbitrary optical frequency-conversion processes. The proposed scheme--based on the generalized dual-grid method that is used for constructing tiling models of quasicrystals--gives complete design flexibility, removing any constraints imposed by previous approaches. As an example we demonstrate the design of a color fan--a nonlinear photonic quasicrystal whose input is a single wave at frequency omega and whose output consists of the second, third, and fourth harmonics of omega, each in a different spatial direction.