  We introduce a system of two component two-dimensional (2D) complex
Ginzburg-Landau equations (CGLEs) with spin-orbit-coupling (SOC) describing a
wide-aperture microcavity laser with saturable gain and absorption. We report
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, $|\Delta S|=2$, 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 $\left( -1,+1\right) $ and $\left( 0,2\right) $, respectively. In
previous works, 2D localized states of these types were 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 VAV states, 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 both VAV 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 the
VAV 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.
