Solitons in quadratic nonlinear photonic crystals.
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families. Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably.
A Time-Splitting Spectral Method for Three-Wave Interactions in Media with Competing Quadratic and Cubic Nonlinearities
This paper introduces an extension of the time-splitting spectral (TSSP) method for solving a general model of three-wave optical interactions, which typically arises from nonlinear optics, when the transmission media has competing quadratic and cubic nonlinearities. The key idea is to formulate the terms related to quadratic and cubic nonlinearities into a Hermitian matrix in a proper way, which allows us to develop an explicit and unconditionally stable numerical method for the problem. Furthermore, the method is spectral accurate in transverse coordinates and second-order accurate in propagation direction, is time reversible and time transverse invariant, and conserves the total wave energy (or power or the norm of the solutions) in discretized level. Numerical examples are presented to demonstrate the efficiency and high resolution of the method. Finally the method is applied to study dynamics and interactions between three-wave solitons and continuous waves in media with competing quadratic and cubic nonlinearities in one dimension (1D) and 2D. AMS subject classfications: 65M70, 78M25, 42A10
Analysis of all-semiconductor intracavity optical parametric oscillators
We propose a novel scheme for efficient parametric generation of mid-IR light by use of an optical cavity, incorporating a semiconductor nonlinear medium and a semiconductor laser amplifier. We evaluate theoretically the threshold and the conversion efficiency of the proposed scheme and show its advantages over conventional optical parametric oscillators.