  Rashba spin-orbit interaction leads to a number of electromagnetic
cross-correlation effects by inducing a mixing of electric and magnetic degrees
of freedom. In this study, we investigate the optical properties of a magnetic
Rashba conductor by deriving an effective Hamiltonian based on an
imaginary-time path-integral formalism. We show that the effective Hamiltonian
can be described in terms of toroidal and quadrupole moments, as has been
argued in the case of insulator multiferroics. The toroidal moment turns out to
coincide with the spin gauge field induced by the Rashba field. It causes
Doppler shift by inducing intrinsic spin current, resulting in anisotropic
light propagation (directional dichroism) irrespective of the polarization. The
quadrupole moment on the other hand results in a magneto-optical phenomenon
such as a Faraday effect for circularly-polarized waves.
