Experimental approach to transverse wave-number selection in cavity nonlinear optics

Spontaneous transverse pattern formation is experimentally studied in a BaTiO₃ photorefractive oscillator under degenerate four-wave mixing conditions. A near self-imaging resonator of high Fresnel number and quasi-one-dimensional in the transverse plane is used. A fine control technique of the cavity detuning, Ω, is described. It allows a precise study of the relation of Ω with the transverse wave number k_⊥ of the roll patterns selected by the system. The law k_⊥²=−Ω∕a is verified, which evidences that wave-number selection is mainly dictated by the cavity geometry. The experimentally obtained value of the diffraction parameter a matches the theoretical prediction within the error intervals. The bifurcation diagram obtained by varying Ω shows homogeneous states and domain walls for positive Ω, roll patterns for negative Ω, and nonperiodic patterns for intermediate, negative detuning values. The latter are interpreted also in the frame of the cavity selection mechanism by taking into account the finesse of the cavity.