  Inverse Faraday effect (IFE) in superconductors is proposed, where a static
magnetization is generated under the influence of a circularly polarized
microwave field. Classical modeling of the IFE explicitly provides
superconducting gyration coefficient in terms of its complex conductivity. IFE
is then considered as a source of nonlinearity and gyrotropy even at a
low-power microwave regime giving rise to a spectrum of phenomena and
applications. Microwave-induced gyroelectric conductivity, Hall effect,
microwave birefringence, flux quantization and vortex state are predicted and
quantitatively analyzed. Peculiar microwave birefringence in gyrotropic
superconductors due to radical response of superelectrons has been highlighted.
