Nonlinear Tunneling of an Electromagnetic Wave through a Plasma Layer

The propagation of a strong plane electromagnetic wave from vacuum through a bounded plasma layer is considered taking into account nonlinearity under tunneling and transparency conditions. The plasma is considered to be cold and nonmagnetic, and the electromagnetic pulse to be quasi-monochromatic, but short (i.e., not heating the plasma layer during its passage through it). The temperature dependence is not taken into account. The nonlinearity is taken into account phenomenologically as a dependence of the plasma frequency and collision rate on the field square averaged over the period. Associated stationary nonlinear integral equations for field harmonics, as well as a nonlinear integral equation for a nonstationary process, are obtained. The rate and time of tunneling in linear and nonlinear cases, the field distribution, and the third harmonic generation coefficient are determined. It is shown that tunneling takes longer than the passage through a transparent layer, and the nonlinear tunneling is a longer process compared to linear tunneling, while in all cases the time of the wave passage is longer when the time of passage through the equivalent length in vacuum at the speed of light.