Relativistic nonlinear frequency shift of laser pulse on reflection from critical layer in inhomogeneous plasma

Abstract

An analytical formalism is developed for the nonlinear frequency shift of intense laser pulse, due to relativistic mass nonlinearity (in the sub-relativistic regime), on reflection from the critical layer in an inhomogeneous plasma. As a higher and higher intensity front of the pulse approaches the critical layer, the reflection layer moves forward to higher densities, due to the relativistic increase in the electron mass, causing a red shift in the reflected wave frequency. The frequency shift increases with shortening laser pulse duration and laser intensity. For the rear portion of the pulse, the critical layer moves backward, causing a blue shift. The effect is more pronounced for shorter pulses and longer density scale lengths, consistent with recent experiments.