A. G. Sveshnikov

Models of Electromagnetic Scattering Problems Based on Discrete Sources Method

Publisher Summary This chapter reviews the Discrete Sources Method (DSM) as a basis for constructing mathematical models of electromagnetic wave scattering problems. The chapter concentrates on numerical schemes for investigating polarized scattering by a penetrable obstacle. Computer simulation of results associated with discrimination of smooth substrate defects is discussed. The analysis of scattering of electromagnetic waves by local obstacles and structures has a wide variety of applications in electromagnetics, optics, computerized tomography, and metrology. Mathematical modeling, operating with Boundary Value Scattering Problem (BVSPs), is a common tool for such an advanced analysis. From mathematical viewpoint BVSPs are classical problems of mathematical physics. The essential feature of BVSP under consideration is that the obstacle is far away from both the primary field sources and the region of the scattered field measurement. This allows the Quasi-Solution (QS) concept to be employed that enables one to avoid methods requiring the boundary conditions at the obstacle surface to be satisfied exactly, which obviously increases computational costs. The Discrete Sources Method (DSM) seems to be one of the most effective and flexible tools for QS construction. In the frame of DSM, the approximate solution is constructed as a finite linear combination of the fields of dipoles and multipoles.

Mathematical Models in Nanooptics and Biophotonics Based on the Discrete Sources Method

The state of the art of the discrete sources method is reviewed. The method can be used to construct effective numerical models for problems in nanooptics and biophotonics.

An optical theorem for local sources in diffraction theory

The optical theorem is generalized for the case of excitation of local structures by point sources. It is shown that an essential parameter, the Purcell factor, can be represented in analytical form. The results are generalized for the case of an interface between two semi-spaces. These results are of paramount importance for averaging of the coefficient of fluorescence amplification and the efficiency of an optical antenna by the position of an excitation source.

Optical theorem for multipole sources in wave diffraction theory

The optical theorem is generalized to the case of local body excitation by multipole sources. It is found that, to calculate the extinction cross section, it is sufficient to calculate the scattered field derivatives at a single point. It is shown that the Purcell factor, which is a rather important parameter, can be represented in analytic form. The result is generalized to the case of a local scatterer incorporated in a homogeneous halfspace.

Analysis of the effect of an extremal energy transmission through a conducting film with a nano-sized inset

The effect of an extremal transmission of electromagnetic energy through a film from a noble metal with a cylindrical inset is analyzed both in the spatial and spectral regions using the discrete-sources method. The results of computer simulation allow one to establish the mechanism by which this phenomenon occurs. A physical interpretation of this phenomenon is given.

Analysis of plasmon resonances of closely located particles by the discrete sources method

Based on a modification of the discrete sources method, a detailed analysis of plasmon resonances of closely located particles is performed. The numerical algorithm makes it possible to calculate the near field with a high degree of accuracy and to trace resonances at which both the cross section and the intensity of the near field increase by several orders of magnitude.

Sufficient conditions for the blowup of a solution to the Boussinesq equation subject to a nonlinear Neumann boundary condition

Sufficient blowup conditions are obtained for a solution to the generalized Boussinesq equation subject to a nonlinear Neumann boundary condition.

Sufficient close-to-necessary conditions for the blowup of solutions to a strongly nonlinear generalized Boussinesq equation

An initial boundary value problem for the generalized Boussinesq equation with allowance for linear dissipation and free electron sources is considered. The strong generalized time-local solvability of the problem is proved. Sufficient conditions are obtained for the blowup of the solution and for time-global solvability. Two-sided estimates of the blowup time are derived.

A Computer Technology for the Discrete Source Method in Scattering Problems

The latest achievements of the discrete source method are reviewed. The method constructs efficient numerical models for the scattering of electromagnetic waves by three-dimensional structures, including structures in the presence of a substrate. The proposed approach remains efficient for scatterers with extreme characteristics, both in free space and in the presence of a layered structure.

Discrete source method for analysis of fluorescence enhancement in the presence of plasmonic structures

A mathematical model of fluorescence enhancement in the presence of a plasmonic structure is examined by applying a modified discrete source method that takes into account the nonlocal interaction between the elements of the plasmonic structure. The fluorescence quantum yield is computed using a generalization of the optical theorem to the case of a local excitation source. The elements of the plasmonic structure are optimized in order to maximize the fluorescence enhancement factor.