Electromagnetic wave propagation in non-linear dielectric media

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

“…with c defined by (3). This is a system of one-dimensional wave equations, which couple only through the wave speed c. Analytical solutions for the wave propagation have been found in [18,22] for some special constitutive relations. These solutions could be used to benchmark an algorithm for the wave propagation, although this is not performed in this work.…”

Ermakov-Modulated Nonlinear Schrödinger Models. Integrable Reduction

“…In a more general situation wherein J(σ ) is such that 33) an elliptic integral representation for σ may be obtained directly via…”

“…[2] connection was made between termination of wave front expansions and the iterated action of Bäcklund-Darboux type transformations. This termination of Bergman series approach has also been applied in the setting of electromagnetic wave propagation in nonlinear dielectric media [33] to isolate D(E) and B(H) constitutive laws for which associated 'modulation' hodograph systems admit integration. In a nonlinear elastodynamic context, an analogous procedure may be used to isolate the constitutive laws introduced by Cekirge and Varley in Ref.…”

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

“…Some early works are summarized in [2], and especially the papers on wave propagation in nonlinear dielectrics [5,6,17,21,29] are worthy of attention. A prominent feature of nonlinear wave propagation, where the nonlinearity acts as an amplitude-dependent wave speed, is the formation of shock waves.…”