A New Regime of Anomalous Penetration of Relativistically Strong Laser Radiation into an Overdense Plasma

It is shown that penetration of relativistically intense laser light into an overdense plasma, accessible by self-induced transparency, occurs over a finite length only. The penetration length depends crucially on the overdense plasma parameter and increases with increasing incident intensity after exceeding the threshold for self-induced transparency. Exact analytical solutions describing the plasma-field distributions are presented. PACS number(s): 52.40.Nk, 52.35.Mw, 52.60.+h, 52.58.Ns In the past few years there has been much research devoted to the nonlinear interaction of superintense laser pulses with plasmas [1]. At intensities where electrons quiver with relativistic velocities, the interaction can be characterized as nonlinear optics in relativistic plasmas, and new regimes, not evident at nonrelativistic intensities, may appear. As was previously shown, superintense electromagnetic radiation can propagate through a classically overdense plasma due to the relativistic correction to the electron mass, the so called induced transparency effect, [2]-[10]. The present work has resulted in the identification of a new fundamental process in relativistic laser overdense plasma interaction. In order to understand the nonlinear regime of interaction of superintense laser light with an overdense plasma, it is enough, without loss of generality, to consider a stationary model. We present here a new class of exact analytical solutions describing the penetration of an electromagnetic wave normally incident onto a cold, overdense plasma with a sharp boundary. In particular, we show that, when the incident intensity exceeds the threshold for self-induced transparency, the laser energy penetrates into the dense plasma without any losses, but over a finite length only. At the same time, the electron density distribution becomes structured as a sequence of electron layers separated by about half a wavelength wide depleted regions, so that this strongly nonlinear plasma structure acts as a distributed Bragg reflector. The ultrahigh intensity laser-plasma interaction is described by the relativistic equation of motion and the equation of continuity for the electrons together with Maxwell’s equations. Ions are treated as a uniform neutralizing background. We will consider circularly polarized laser radiation with normalized amplitude of the vector potential eA/mc = (a/ √ 2)Re[(y + iz)exp(iωt)] normally incident from vacuum (x < 0) onto a semi-infinite plasma (x ≥ 0). Assuming a stationary regime, the basic equations may be written in the form φ′′ = no(n− 1), (1) a′′ + (1− no γ n)a = 0, (2) φ′ = γ′ if and only if n(x) 6= 0. (3) (where variables are normalized as x⇒ ωx/c, n⇒ n/no, no = ω p/ω, ω is the carrier frequency of the laser radiation, ωp is the plasma frequency of the initial unperturbed plasma, γ = (1+a) is the relativistic factor, n and φ are normalized electron density and scalar potential