Relativistic Propagation of Linearly/Circularly Polarized Laser Radiation in Plasmas

Paraxial theory of relativistic self-focusing of Gaussian laser beams in plasmas for arbitrary magnitude of intensity of the beam has been presented in this paper. The nonlinearity in the dielectric constant arises on account of relativistic variation of mass. An appropriate expression for the nonlinear dielectric constant has been used to study laser beam propagation for linearly/circularly polarized wave. The variation of beamwidth parameter with distance of propagation, self-trapping condition, and critical power has been evaluated. The saturating nature of nonlinearity yields two values of critical power of the beam ( and ) for self-focusing. When the beam diverges. When the beam first converges then diverges and so on. When the beam first diverges and then converges and so on. Numerical estimates are made for linearly/circularly polarized wave applicable for typical values of relativistic laser-plasma interaction process in underdense and overdense plasmas. Since the relativistic mechanism is instantaneous, this theory is applicable to understanding of self-focusing of laser pulses. 1. Introduction The interaction of ultrahigh-power laser beams with plasmas is not only of technological importance but also rich in a variety of nonlinear phenomena. These phenomena become particularly interesting and involved when the laser power is sufficiently intense to cause the electron oscillation (quiver) velocity to become relativistic [1]. An important process that can affect the size of the focused spot of the radiation is self-focusing. In recent years the field of laser plasma interaction in the relativistic regime has been identified as an emerging area and is often referred to as high-field science. Several complex phenomena are included in the area of high-field science. These phenomena (on account of their nonlinear nature) are all significantly affected by the field distribution in the beam, and hence, self-focusing occupies a unique position in the field as it affects all other phenomena. Relativistic electron motion in a plasma due to an intense laser pulse modifies the refractive index and leads to two effects: relativistic induced transparency and relativistic self-focusing. In dense plasma with , light cannot propagate and is reflected from the surface. However, for relativistic intensities generating large factors, the plasma becomes transparent. The dependence of the electron mass on intensity causes significant change of characteristic properties of the plasma and its nonlinear processes; the increase in effective electron mass decreases the