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 χ2 type nonlinearity as well as two-mode systems coupled via cubic χ3 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.

© 2015 Optical Society of America

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Corrections

5 November 2015: A correction was made to the funding section.


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