Resonant scattering and generation of waves. Cubically polarizable layers (Q1662965)

The authors tackle the problem of resonant processes occurring during propagation of linear electromagnetic waves through non-uniform media in presence of excited polarization nonlinearities. Detailed theoretical derivations and various numerical applications are performed for a specific model of layered structures in plane geometry with inclusion of the third-order nonlinear perturbations of the dielectric medium induced by propagating incident waves. As a result, phase synchronism conditions can be achieved yielding resonant generation and scattering of higher harmonic waves which influence the propagation characteristics of electromagnetic waves in the considered nonlinear media that can also be of significance in practical applications. For this reason, the book is a useful reference work, not only for professional theoreticians dealing with problems of nonlinear electrodynamics, but also for graduate students who can widely benefit from it. \par The text is divided into eight chapters, each followed by a list of references, two appendices and an index. Chapter 1 describes the mathematical model and provides the necessary introduction on the essential physical properties related to electromagnetic waves in media with nonlinear electric polarizability. Among other things, this includes descriptions of phase synchronism, generation of wave-packets and wave scattering, and conservation laws. The problem of nonlinear boundary conditions and the existence of weak solutions is treated in detail in Chapter 2, while Chapter 3 contains a mathematical treatment of the problem by using integral equations. Chapter 4 is devoted to details of the spectral analysis method in treating scattering and generation of electromagnetic waves. Chapters 5--7 provide details of numerical procedures for solving the considered equations with nonlinear boundary conditions, using the finite element method. In this sense, Chapter 5 gives essentials on solving a problem with nonlinear boundary conditions by the finite element method, including discussions on existence and uniqueness of solutions error estimates. Chapter 6 is devoted to numerical procedures of solving integral equations, including numerical quadrature, iterative solutions, and spectral analysis, while Chapter 7 is of basic importance as it deals with various examples of numerical experiments with configurations that can be encountered in practical applications. The final Chapter 8 contains a summary of the issues treated in the book and gives suggestions for future extension of the work. The two appendices provide numerical parameters of cubic polarization and some elements of functional analysis, respectively.