  A nonperturbative interaction of an electronic system with a laser field can
substantially modify its physical properties. In particular, in two-dimensional
(2D) materials with a lack of inversion symmetry, the achievement of a regime
of strong light-matter coupling allows direct optical tuning of the strength of
the Rashba spin-orbit interaction (SOI). Capitalizing on these results, we
build a theory of the dynamical conductivity of a 2D electron gas with both
Rashba and Dresselhaus SOIs coupled to an off-resonant high-frequency
electromagnetic wave. We argue that strong light-matter coupling modifies
qualitatively the dispersion of the electrons and can be used as a powerful
tool to probe and manipulate the coupling strengths and adjust the frequency
range where optical conductivity is essentially nonzero.
