<title>Periodic and quasi-periodic nonlinear photonic crystals</title>

Abstract

Nonlinear photonic crystals are materials in which the second order susceptibility is modulated, while the linear susceptibility remains constant. In this paper, quasi-phase matching possibilities in several different nonlinear photonic crystals are analyzed and compared. A periodic one-dimensional structure is usually employed for phase matching a single process, but we show that two processes can also be simultaneously phase matched by non-collinear interaction. Two-dimensional periodic modulation provides additional extension of the phase matching possibilities. The dependence of the process conversion efficiency on the specific choice of lattice, nonlinear motif and quasi-phase-matched order is analyzed. Further extensions are provided by quasi-periodic schemes. A very powerful method for designing quasi-periodic nonlinear structures, with either one-dimensional or two-dimensional modulation, is the socalled dual-grid method. This method practically enables to phase matched any set of nonlinear interactions, in any chosen direction of propagation. Finally, frequency conversion using a converter with pure rotation symmetry is analyzed and demonstrated.