Quadratic Nonlinear Interactions in 1-Dimensional Photonic Crystals

Abstract

Photonic crystals in 1-dimension constitute a frame that may be used to modify the quadratic nonlinear interaction in much the same way as in the 3-dimensional lattices considered previously in this book. Moreover, the simplicity of a 1-dimensional structure offers several advantages such as for instance to facilitate a controlled introduction of defects, or the study of the nonlinear interaction at resonance. In fact, it was shown that light localization within a defect of a 1 — dimensional multilayer periodic structure could lead to a strong enhancement or inhibition of the second order nonlinear interaction.1 Other 1-dimensional structures have been used to obtain a doubly resonant phase matched second harmonic generation (SHG).2 In such structures one may easily resolve the effective index of refraction dispersion and rigorously show that the phase matching mechanism is provided by the periodicity build into the material.3 More recently, such structures have also been used to induce all-optical changes in the transmission or reflection, when the nonlinear interaction is considered in a cascading configuration.