Electromagnetically induced transparency for two intense waves in plasma

The coupled propagation of two electromagnetic waves in plasma is studied in order to find the conditions for induced transparency. This means unattenuated propagation of the waves through plasma which is overdense, and thus opaque, for one (or both) of them. This is made possible by a modulation of the refractive properties of the plasma, due to a relativistic increase in the electron mass, or to a variation in electron density caused by longitudinal plasma oscillations driven by the ponderomotive potential associated with the beat of the waves. Starting from a relativistic fluid description, we make an Ansatz containing two transverse monochromatic electromagnetic plane waves, and longitudinal plasma oscillations at the sum and difference of their frequencies. For weakly relativistic intensities we derive coupled dispersion relations, which take into account the polarization of the waves and the nonlinearities with respect to both their amplitudes. This serves to explore the conditions for induced transparency and the modes of propagation.