Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals

Quadratic nonlinear photonic crystals are materials in which the second order susceptibility is spatially mod- ulated while the linear susceptibility remains constant. These structures are significantly different than the more common pho- tonic crystals, in which the linear susceptibility is modulated. Nonlinear processes in nonlinear photonic crystals are governed by the phase matching requirements, which are determined by the reciprocal lattice of these crystals. Therefore, the modulation of the nonlinear susceptibility enables to engineer the spatial and spectral response in various three-wave mixing processes. It enables to support the efficient generation of new optical fre- quencies at multiple directions. We analyze three wave mixing processes in nonlinear photonic crystals in which the modula- tion is either periodic, quasi-periodic, radially symmetric or even random. We discuss both one-dimensional and two-dimensional modulations. In addition to harmonic generations, we outline several new possibilities for all-optical control of the spatial and polarization properties of optical beams in specially designed nonlinear photonic crystals. Some examples of nonlinear photonic crystals. Top line: 2D Periodic crystals; center line: 1D quasi-periodic crystals, sym- metric and anti-symmetric all-optical deflectors; bottom line: radially symmetric structures.