Reconstruction of nonlinear material properties for homogeneous, isotropic slabs using electromagnetic waves

Abstract

This paper addresses the inverse problem of reconstructing a medium's instantaneous, nonlinear response to electromagnetic excitation. Using reflection and transmission data for an almost arbitrary incident field on a homogeneous slab, we are able to obtain the nonlinear constitutive relations for both electric and magnetic fields, with virtually no assumptions made on the specific form of the relations. It is shown that, for a non-magnetic material, reflection data suffice to obtain the electrical nonlinear response. We also show that the algorithms are well posed. Numerical examples illustrate the analysis presented in this paper.

Nonlinear waveguides

“…For the Kerr medium, where F e ( E 2 ) = 1 + E 2 (after scaling to dimensionless fields), we have It is easy to show that for a medium where F e can be expanded in a polynomial series, the energy density can be expressed in a related series. Another medium which has been used is the saturated Kerr medium [ Kristensson and Wall , 1998; Sjöberg , 1999; Tikhonenko et al , 1996], where F e ( E 2 ) = 1 + E 2 /(1 + E 2 ). The energy density for this medium is Integrating over z and 0 ≤ t ≤ T , we have since the integral of the z derivative correspond to the field values at infinity, and can be assumed to disappear for finite times T .…”

“…It is easy to show that for a medium where F e can be expanded in a polynomial series, the energy density can be expressed in a related series. Another medium which has been used is the saturated Kerr medium [Kristensson and Wall, 1998;Sjöberg, 1999;Tikhonenko et al, 1996], where F e (E 2 ) = 1 + E 2 /(1 + E 2 ). The energy density for this medium is…”

Simple wave solutions for the Maxwell equations in bianisotropic, nonlinear media, with application to oblique incidence

“…We have scaled the fields to obtain dimensionless field strengths and substantial nonlinearities for field strengths of a few units, see e.g., [23,30]. The constitutive relation is characterized by the dyadic ε, which is represented in the xyz-coordinate system as…”

An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods

“…Extensive work has been done on inverse problems for linear materials [4,5,7,9,12]. However, the literature on inverse problems for nonlinear rods is sparse [8,13,18,22,24], especially in the time domain (although there has been recent activity in nonlinear electromagnetic scattering problems using wave splitting [1,6,16,25]). But the time domain is the natural place to study the propagation of short duration pulses, nonperiodic waves and transients, which are important in many applications.…”