Quasipatterns in second-harmonic generation

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Abstract
A cascade of two-dimensional quasipatterns is predicted in intracavity optical frequency doubling due to a polarization instability at the fundamental frequency. Amplitude equations derived from a microscopic model of the frequency conversion process show that quasiperiodic structures of arbitrary orientational order can be spontaneously selected due to bulk nonlinear effects when detuned operation for both fundamental and second-harmonic fields occurs. Multistability and coexistence of patterns and quasipatterns is also discussed.