Three-dimensional structures in diffractive and dispersive nonlinear ring cavities

Abstract

Using a weakly nonlinear theory, we analyse the stability and the relative stability of the three-dimensional patterns that spontaneously appear in a coherently driven passive optical ring cavity filled with a dispersive dielectric medium with instantaneous Kerr nonlinearity. We show that in the anomalous dispersion regime, the body-centred cubic lattice structure is stable over patterns of lower symmetry in the vicinity of the bifurcation point.