The authors have identified three regimes of propagation of circularly polarized laser beams in plasmas, taking into account the relativistic laser plasma interaction. An appropriate expression for the nonlinear dielectric constant has been used in the analysis of laser-beam propagation in the paraxial approximation. Three regimes of propagation in a homogeneous plasma have been identified, viz.

I. In this regime the beam keeps on diverging.

II. In this regime the beam travels in a guided oscillatory and diverging mode, with the width lying between the original value and a maximum value.

III. In this regime the beam becomes self-focused, with the width lying between the original value and a minimum value.

For a given value of $\omega _{\rm p}/\omega $ the regimes are characterized by dimensionless power and dimensional beam width. The variation of beam width with distance of propagation has also been obtained for typical values of parameters in the three regimes.

The variation of beam-width parameter with distance of propagation has also been studied for inhomogeneous plasma and penetration in overdense plasmas is indicated.