Electromagnetic wave propagation below cutoff

Summary form only given, as follows. A small amplitude electromagnetic wave can propagate in a plasma below cutoff in the presence of a high frequency large amplitude wave. This is referred to electromagnetically induced transparency (EIT). We extend the analysis of EIT to include relativistic and collisional effects as well as density gradients. We show that the small amplitude wave is unstable in certain parameter regimes. Well above cutoff the instability goes over to the usual backward Raman instability. In addition, the propagation of a large amplitude wave in an inhomogeneous plasma and its penetration beyond the critical surface is analyzed.