Nonlinear tunneling of electromagnetic wave through a plasma layer

Background and Objectives: The propagation of a strong plane electromagnetic wave from a vacuum through a limited plasma layer is considered, taking into account non-linearity under tunneling and transparency conditions. The temperature dependence is not taken into account. The non-linearity is taken into account phenomenologically as the dependence of the plasma frequency and collision frequency on the field averaged over the period squared. Conclusion: Coupled stationary nonlinear integral equations for the field harmonics, as well as a nonlinear integral equation for a non-stationary process, are obtained. The speed 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 of a transparent layer, and the process of nonlinear tunneling is a longer process compared to linear, while in all cases the time of the wave passage is longer when passing the structure at the speed of light.