Biconical emission of spatially mode-locked patterns with wave-number ratio root 2 in a ring cavity device

Bioconical emission with wave-number ratio root 2 is observed in the numerical simulations of the ring cavity with diffraction effects, on the defocusing side of the resonance. As the intensity of the plane-wave beam increases, a sequence of stationary patterns is observed, and understood via a nonlinear analysis. The first pattern with (4-4) peaks is a bisquare resulting from a strong coupling between two quasiresonant sets of modes with wave numbers K and root 2K. This pattern destabilizes at the onset of the drift bifurcation, into a new (4-4) pattern with a smaller wavelength, that splits into two twisted bisquares, with a 53 degrees rotation angle ensuring the wave-vector locking, or the spatia periodicity of this (8-8) structure.