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 t hat understanding. An inverse transmission problem is posed; it is one of reconstructing the medium parameters, by measurement of a wave tha t has been propagated through the nonlinear medium. The nonlinear medi um is assumed to be homogeneous and isotropic. The methods have applic ation to nonlinear optics, and the numerical results for both the dire ct and inverse problems presented are based on the nonlinear Kerr effe ct, which is observed in the optical wavelength band. However, the mat hematical techniques that are developed are applicable to any set of n onlinear first-order equations. The method is therefore model independ ent.