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arXiv · 1512.03092

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

Graham D Hesketh
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Abstract

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.

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Graham D Hesketh. 2015-12-09. General complex envelope solutions of coupled-mode optics with quadratic or cubic nonlinearity. https://doi.org/10.1364/josab.32.002391

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