Light-induced nonreciprocity, field invariants, and nonlinear eigenpolarizations

It is shown that the magnitude of nonlinear nonreciprocity, self-induced by counterpropagating laser beams, is related to the anisotropic properties on the nonlinear third-order susceptibility (resulting in the light-induced birefringence and gyrotropy) and therefore is sensitive to the mutual arrangement of polarization of both of the beams. The invariants of nonlinear wave equations suggest an existence of mutual eigenarrangements of polarization with different relevant eigennonreciprocities. By using this effect, a nonreciprocal spectrocopy of the anisotropic nonlinear susceptibility may be developed.