Exact solution of slowly varying envelope approximation equations for plane wave propagation of light in lossy isotropic nonlinear medium

Nonlinear coupled differential equations for Stokes parameters for plane wave propagation of light in an isotropic medium having third-order nonlinearity are obtained in slowly varying envelope approximation and solved exactly for arbitrary linear and nonlinear losses. Numerical solution in general and analytic solutions in special cases exist. Vibration ellipse is seen to rotate and change in shape. Only plane and circular polarizations are stable and others change. This change is large when absorption is mainly nonlinear, and for purely nonlinear absorption, polarization tends asymptotically to either plane or circular. An example of analytic exact solution is discussed.