General complex envelope solutions of coupled-mode optics with quadratic or cubic nonlinearity

摘要

The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two- and three-mode systems of differential equations coupled via quadratic chi(2) type nonlinearity as well as two-mode systems coupled via cubic chi(3) type nonlinearity. For the first time, a compact form of the solutions is given involving simple ratios of Weierstrass sigma functions (or equivalently Jacobi theta functions). A Fourier series is also given. All possible launch states are considered. The models describe sum- and difference-frequency generation, polarization dynamics, parity-time dynamics, and optical processing applications. (C) 2015 Optical Society of America