We consider transverse effects in a planar resonator with a quadratically nonlinear medium where the incident field is at the fundamental frequency. The resonator is assumed to be resonant for both the fundamental and second harmonics. Different scenarios of destabilization of the plane-wave solutions are investigated in dependence on the driving field and the detunings from the resonances. Numerical simulations demonstrate the existence of dynamical and stationary patterns.
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Etrich et al. (1997) studied this question.
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