Direct and inverse scattering for transient electromagnetic waves in nonlinear media

Nonlinear propagation of electromagnetic waves is an important problem in optics. Often the properties of the nonlinear media are not fully understood. The solution of an inverse problem can provide an aid to that understanding. An inverse transmission problem is posed; it is one of reconstructing the medium parameters, by measurement of a wave that has been propagated through the nonlinear medium. The nonlinear medium is assumed to be homogeneous and isotropic. The methods have application to nonlinear optics, and the numerical results for both the direct and inverse problems presented are based on the nonlinear Kerr effect, which is observed in the optical wavelength band. However, the mathematical techniques that are developed are applicable to any set of nonlinear first-order equations. The method is therefore model independent.