Vortex modes supported by spin-orbit coupling in a laser with saturable absorption

Weintroduce a system of two component two-dimensional (2D) complex Ginzburg-Landau equations with spin-orbit-coupling (SOC) describing a wide-aperture microcavity laser with saturable gain and absorption.Wereport families of two-component self-trapped dissipative laser solitons in this system. The SOC terms are represented by the second-order differential operators, which sets the difference, |ΔS| = 2, between the vorticities of the two components.We have found stable solitons of two types: vortex-antivortex (VAV) and semi-vortex (SV) bound states, featuring vorticities (-1, +1) and (0, 2), respectively. In previousworks, 2Dlocalized states of these typeswere found only in models including a trapping potential, while we are dealing with the self-trapping effect in the latteraly unconfined (free-space) model. The SV states are stable in a narrow interval of values of the gain coefficients. The stability interval is broader for VAVstates, and it may be expanded by making SOC stronger (although the system without SOC features a stability interval too).We have found three branches of stationary solutions of bothVAV and SV types, two unstable and one stable. The latter one is an attractor, as the unstable states spontaneously transform into the stable one, while retaining vorticities of their components. Unlike previously known 2D localized states, maintained by the combination of the trapping potential and SOC, in the present system theVAV and SV complexes are stable in the absence of diffusion. In contrast with the bright solitons in conservative models, chemical potentials of the dissipative solitons reported here are positive.