Bifurcations of the dark soliton and polarization domain walls in Kerr media

We present the result of our numerical investigations in the analysis of the bifurcations of the dark soliton and polarization domain walls. In order to analyze the bifurcations, it is convenient to reason in the spatial domain: the spatial dark soliton in the field U induces, through cross-phase modulation, a waveguide for the field V; U and V are the envelopes of both circular polarization components. Any guide mode of arbitrarily small amplitude in the field V propagates along the dark soliton in U. As a result, a stationary bound state of both polarizations is formed. From this, reasoning we anticipate that when the power in the guided mode V is increased into the nonlinear regime, the bound state can still exist at the expense of a reshaping of the profile of the dark soliton in U. The resulting bound states would therefore constitute a family of vector solitary waves, which branches for the dark nonlinear Schrodinger soliton. The branching point can be easily calculated analytically by means of a referenced method.