This paper presents an analysis of relativistic self-focusing of a Gaussian
laser beam incident normally on a plane interface of a linear medium and a
nonlinear, nonabsorbing plasma with an intensity dependent dielectric cons
tant. Considering the nonlinearity to arise from the relativistic variation
of mass and the Lorentz force on electrons. Following Wentzel-Kramers;Bril
louin (WKB) and paraxial ray approximation the phenomenon of relativistic s
elf-focusing of the transmitted laser radiation has been analyzed for the a
rbitrary magnitude of nonlinearity. Change in the intensity distribution al
ong the wavefront of the Gaussian beam, due to refraction at the interface
has also been taken into account. The variation of beamwidth parameter with
distance of propagation, self trapping condition and critical power has be
en evaluated. Numerical estimates for typical parameters of laser plasma in
teraction process indicate the refraction at the interface to have a signif
icant effect on self-focusing.