Direct and Inverse Scattering of Electromagnetic Waves in Nonlinear Media

Abstract: 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.