Nonlinear polarization dynamics. III. Spatial polarization chaos in counterpropagating beams

Abstract

The steady-state spatial polarization distribution of counterpropagating plane waves in a ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ medium is numerically investigated using a Stokes vector formalism. We consider all those material symmetry classes whose equations of motion are thought to be nonintegrable. Poincaré plots indicate that all these cases exhibit chaotic behavior. We also identify new analytic solutions for certain initial conditions. This completes the classification of the polarization dynamics of counterpropagating beams for all rotation symmetries about the axis of propagation, in parity- and non-parity-invariant media.