Threshold of induced transparency in the relativistic interaction of an electromagnetic wave with overdense plasmas

An exact analytical investigation of the stationary solutions describing the interaction between high-intensity laser radiation and an overdense plasma is presented. Both the relativistic and striction nonlinearities are taken into account, and their joint action gives rise to a solitary solution. This solution clearly shows that there exists an inherent limit of the induced transparency on the density of the overdense plasma in order to obtain a stationary physical solution. Furthermore, it is found that the striction nonlinearity tends to create a strong peaking of the plasma electron density, which suppresses the laser penetration and significantly enhances the threshold intensity for induced transparency.