Modulational instability and beam splitting in the nonlinear light propagation in sodium vapour

Abstract

A linearly polarized laser beam propagating through sodium vapour is known to break up into its circular polarization components (`beam splitting'). We clarify the underlying mechanism by showing that spatially periodic perturbations of the polarization state of a plane wave will be amplified exponentially during propagation due to a modulational instability. For a Gaussian beam in one transverse spatial dimension we find even as well as odd active eigenmodes for polarization perturbations. Their two-dimensional generalizations elucidate the reason for the radial and lateral splitting that is observed in a number of experiments. In the limiting case of a cubic nonlinearity the splitting can also be expected from a variational approach.