We predict a novel nonlinear electromagnetic phenomenon in layered
superconducting slabs irradiated from one side by an electromagnetic plane
wave. We show that the reflectance and transmittance of the slab can vary over
a wide range, from nearly zero to one, when changing the incident wave
amplitude. Thus changing the amplitude of the incident wave can induce either
the total transmission or reflection of the incident wave. In addition, the
dependence of the superconductor transmittance on the incident wave amplitude
has an unusual hysteretic behavior with jumps. This remarkable nonlinear effect
(self-induced transparency) can be observed even at small amplitudes, when the
wave frequency ω is close to the Josephson plasma frequency ωJ.Comment: 9 pages, 7 figure