Quadratic Interactions in Finite, One-Dimensional, Photonic Band Gap Structures with Deep Gratings: beyond the Undepleted Pump Regime

Abstract

We theoretically study quadratic interactions in finite, one-dimensional, photonic band gap structures with deep gratings, under strong pumping and global phase matching conditions. For second harmonic generation, we find that above a certain input intensity a dynamics reminiscent of a competitive, multi-wave mixing process takes hold: the pump field is mostly reflected, revealing a novel type of optical limiting behavior, while forward and backward generation is generally balanced. We also study the case of parametric down-conversion, where an intense second harmonic signal is injected in order to control a much weaker fundamental beam. Our results reveal the onset of a new process that has no counterpart in bulk materials: both transmission and reflection display an unexpected, unusual, resonance-like effect as functions of input second harmonic power.