Direct and Inverse Scattering of Electromagnetic Waves in Nonlinear Media

by Sjöberg, Daniel

Models for materials with nonlinear electromagnetic response are examined. Three simple physical causes for nonlinear behavior are presented: electronic polarization, molecular direction and electrostriction. Some introductory results and approximations for nonlinear, dispersive media are given, such as the phase-matching criterion, Miller's rule, the Born approximation and the slowly varying amplitude approximation. However, the emphasis is on instantaneously reacting media, that is, materials with no or negligible memory. For these models, the inverse scattering problem of determining the field dependent permittivity and permeability from the scattered field is solved.