Plane waves in periodic, quadratically nonlinear slab waveguides: stability and exact Fourier structure

Details Plane waves in periodic, quadratically nonlinear slab waveguides: stability and exact Fourier structure Plane waves in periodic, quadratically nonlinear slab waveguides: stability and exact Fourier structure

2001-05-17

arxiv.org/abs/nlin/0105041v2

Nonlinear Sciences

Pattern Formation and Solitons

10 Pages, 13 figures (some in two parts) new version has some typos removed and extra references and explanation added

Scientific paper

10.1364/JOSAB.19.000812

We consider the propagation of broad optical beams through slab waveguides with a purely quadratic nonlinearity and containing linear and nonlinear long-period quasi-phase-matching gratings. An exact Floquet analysis on the periodic, plane-wave solution shows that the periodicity can drastically alter the growth rate of the modulational instability but that it never completely removes the instability. The results are confirmed by direct numerical simulation, as well as through a simpler, approximate theory for the averaged fields that accurately predicts the low-frequency part of the spectrum.

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