2015/12/09 by Graham D Hesketh · 2 citations
Physics and Astronomy · #nlin.PS #nlin.SI #physics.optics
paper · pdf · doi:10.1364/josab.32.002391
published as J. Opt. Soc. Am. B 32, 2391-2399 (2015)
arxiv created 2015/12/09 · arxiv updated 2015/12/16
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.