  Spin-orbit interactions which couple spin of a particle with its momentum
degrees of freedom lie at the center of spintronic applications. Of special
interest in semiconductor physics are Rashba and Dresselhaus spin-orbit
coupling (SOC). When equal in strength, the Rashba and Dresselhaus fields
result in SU(2) spin rotation symmetry and emergence of the persistent spin
helix (PSH) only investigated for charge carriers in semiconductor quantum
wells. Recently, a synthetic Rashba-Dresselhaus Hamiltonian was shown to
describe cavity photons confined in a microcavity filled with optically
anisotropic liquid crystal. In this work, we present a purely optical
realisation of two types of spin patterns corresponding to PSH and the
Stern-Gerlach experiment in such a cavity. We show how the symmetry of the
Hamiltonian results in spatial oscillations of the spin orientation of photons
travelling in the plane of the cavity.
