Magneto-optical signature of broken mirror symmetry of two-dimensional conductors

An unusual aspect of macroscopic electrodynamics of two-dimensional mirror-odd conducting structures bound up with the band spin-orbit coupling $H_{so}=\alpha(\mathbf{p}\times\mathbf{c})\cdot \sigma$ of current carriers (where $\mathbf{c}$ is one of two nonequivalent normals to a given structure) is pointed out. Namely, it is shown that due to the spin-orbit coupling the presence of the in-plane magnetic field $\mathbf{H}_{0}$ gives rise to a dependence of the reflection/transmission amplitudes on the structure orientation $\mathbf{c}$, the wave-vector of the incident radiation $\mathbf{q}$, and $\mathbf{H}_{0}$ of the form $\mathbf{q}\cdot(\mathbf{c}\times\mathbf{H}_{0})$. This $\mathbf{q}$- and $\mathbf{H}_{0}$-odd dependence can be the foundation of the optical way to determine the value of the spin-orbit coupling $\alpha$.