Analysis of self-trapping using the wave equation with high-order nonlinear electric permittivity

The self-trapping of light pulses is considered using the classical nonlinear wave equation of Chiao, Garmire, and Townes, modified to include nonlinearities up to sixth order in electric field. A phenomenological approach is adopted in which the nonlinear coefficients are considered without reference to a specific molecular self-trapping mechanism. It is found that filament formation can occur only over a narrow range of values of the nonlinear coefficients. The method can be used as a criterion to test the validity of various self-trapping mechanisms.