Localized chaos of elliptically polarized cavity solitons in broad-area VCSEL with saturable absorber

We introduce a spin-flip model for a broad-area Vertical-Cavity Surface-Emitting Laser (VCSEL) with a saturable absorber. We demonstrate simultaneous existence of orthogonally linearly polarized and elliptically polarized cavity solitons. We show that polarization degree of freedom leads to period doubling route to spatially localized chaos of the elliptically polarized cavity solitons.