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Research on resonance wave scattering has made important progress in recent years thanks to a series of profound analytical studies on some general issues and widespread implementation of a new methodology of scientific search based on adequate mathematical modeling and computational experiment. Some physical effects and phenomena discovered and studied in the course of analyzing various resonance structures have become a guide for scientific instrument-making. However, most of the results still remain within the realm of theory. One of the reasons is the complexity of the primary modeling of the problem that should take into account the most complete number of the functionally relevant electromagnetic characteristics of separate elements and allow an estimate of the effectiveness of the system or performance of the device as a whole. As for the resonance quasioptic devices, the problem becomes even more complicated due to the substantial difference (by an order or more) in the characteristic dimensions of the scatterers that jointly create the electromagnetic field with the given parameters. [ABSTRACT FROM AUTHOR]

Transient resonance wave scattering by gratings is rather complicated phenomenon; it depends on numerous parameters and has not been studied thoroughly yet. The numerical simulation that takes into account diverse properties of the spectrum (various eigenmodes: natural oscillations and eigenwaves) may serve as the most reliable tool for such investigation. The components of the grating's spectrum may be found through analytical continuation of the solutions to diffraction problems into the domain of complex values of the real physical parameters (such as frequency, propagation constants, and geometrical dimensions). When the parameters vary within the domain of real values (diffraction theory in the frequency domain) properties of complex spectrum usually stay out of the focus of intrest. However, it turns out that spectral properties play the principal role in the formation of the response of an electromagnetic structure to every external excitation. The approach, based on the study of the singularities (spectrum) of resolvent operators of boundary value problems in the frequency domain, allows us to consider and treat various mathematical, electromagnetic, and applied problems of resonant wave scattering using the same methodological background. In this chapter we apply this approach to the analysis of regularities in transient resonance wave scatterings and for the description and treatment of irregular effects and anomalous phenomena associated with the ability of a grating to support regimes with complicated nonclassical dispersion laws. [ABSTRACT FROM AUTHOR]

The approach presented in this chapter is based on the description of the scattering properties of the discontinuities in free space and regular wave-guiding structures in terms of transform operators. These transform operators are qualitatively the same for all scatterers that are characterized by the discrete spatial spectrum of the signal's evolutionary basis. By the notion of scatterers with discrete spectrum we imply such electromagnetic objects that have solutions of the corresponding boundary value problems in the form of a series of spherical or cylindrical harmonics, or of plane wave or waveguide modes. In FD this approach is known as the generalized scattering-matrix technique and is widely used nowadays in the context of automatic simulation and design. [ABSTRACT FROM AUTHOR]

The analysis of pattern-forming structures (PFSs) with compact elements (whose parameters are given by the functions ε (g), σ (g), and the boundaries S) excited by compact current and momentary sources (the functions F (g, t), φ (g), and ψ (g) are finite) is reduced to the solution of the initial boundary value problems considered in Chapter 3. [ABSTRACT FROM AUTHOR]

Proceeding with the discussion started in the previous chapters, let us consider model scalar and vector initial boundary value problems typical for the theory of the scattering of transient waves from compact (bounded) inhomogeneities in R2-space (E- and H-polarization) and R3-space. The geometry of the problems (the shape of metal and dielectric inclusions, the supports of momentary and current sources) may be of a rather general nature. However, it is essential that for all of these geometries there exists a regular region LQ, where the outgoing signal U (g, t) propagates freely. This point is of utmost importance in the algorithms suggested below for truncating the analysis domain. [ABSTRACT FROM AUTHOR]

In this and subsequent chapters, we discuss scalar and vector initial boundary-value model problems for two- and three-dimensional telegraphy andwave equations describing the scattering of electromagnetic waves by compact objects in unbounded domains Q of the spaces R2 and R3. The central problem arising in the course of the solution of such problems by finite-difference methods is caused by the progressively expanding support of the scalar or vector function U(g, t), g ∈ Q, t ≥ 0, which determines the resulting field for the increasing observation times t. The analysis domain can be bounded by introducing anywhere in Q the artificial boundary L (see Fig. 1.1C) and supplementing the original initial boundary value problem with the condition [ABSTRACT FROM AUTHOR]

In this chapter, we describe the state of the art in the development of general approaches and algorithms that serve as bases for solving fundamental and applied problems in the theory of transient electromagnetic fields. [ABSTRACT FROM AUTHOR]