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 of 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 gain spectrum.
© 2002 Optical Society of America
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(190.5940) Nonlinear optics : Self-action effects
(230.4320) Optical devices : Nonlinear optical devices
Joel F. Corney and Ole Bang, "Plane waves in periodic, quadratically nonlinear slab waveguides: stability and exact Fourier structure," J. Opt. Soc. Am. B 19, 812-821 (2002)