Secondary Instabilities of optical Hexagons in Sodium Vapor

where C, X and Yare the deviations of the cooperativity parameter, external and intracavity field amplitudes from their values at the onset of bistability, all of them assumed to be small. f is the time, and p is a relaxation time that depends on the inverse of K, yL and yll, the decay rates of the field amplitude, medium polarization and population inversion, respectively. a = 2 /ZW,K is the diffraction parameter, w, being the cavity frequency, and c the speed of light. Vz is the transverse laplacian. A =(a, -2w,) l (yl +ZK) is the detuning parameter (the external field frequency w, is set to be equal to that of a two-photon laser with the same parameters), which is assumed to be small (weakly dispersive limit). Finally, CO= 2.7100 is the minimum value of the cooperativity parameter for hysteresis to exist in absorptive (A = 0) 20B [2], and g a 1.2766 and h E 0.4069 are numerical constants.