Transverse instability of hybrid solitons in the strong light-matter coupling regime

We investigate the transverse instability of two-component solitons forming in a planar waveguide operating in the regime of strong light-matter coupling. The instability emerges as a result of the coupling between transverse diffraction of the photonic component and nonlinearity of the material excitations. Solutions of three different forms are addressed which include bright, gray-dark, and gray-gray solitons. In the limit of long-wavelength transverse perturbations, the instability is described with an asymptotic expansion whose predictions agree with the results of numerical simulations. The dynamic development of instability of initially perturbed bright solitons leads to the formation of high-intensity spots in the photonic component. For gray-dark and dark-dark solitons, the transverse instability leads to the spontaneous nucleation of vortex-antivortex pairs which emerge in both fields as transient patterns.