Yu. A. Eremin

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.

Simulation of light scattering from a particle upon a wafer surface.

We simulated light scattering from a particle located on a smooth surface. We developed a new approach utilizing the discrete sources method based on a strict mathematical model for this scattering problem. The main features of the corresponding numerical algorithm are presented. The results of modeling and comparisons with other theoretical results and experimental data are shown as well.

Scattering of evanescent waves by a particle on or near a plane surface

The paper is devoted to semi-analytical approaches for analyzing the evanescent wave scattering by penetrable scatterers on a plane surface. On the basis of the discrete sources method and the T-matrix method numerical schemes were developed and implemented in computer programs. Numerical results related to the influence of the plane surface on the scattering characteristics are discussed.

Convergence of the T-matrix method for light scattering from a particle on or near a surface

Convergence of the T-matrix approach for analyzing the scattering light from a particle located on a smooth surface is investigated. Numerical experiments are performed for oblate spheroids by choosing the discrete source method as reference. The results show that instability and convergence problems occur when the sphere enclosing the singularities of the scattered field intersects the interface.

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.

Non-axisymmetric models for light scattering from a particle on or near a plane surface

The communication is devoted to semi-analytical approaches for analyzing the scattering by a non-axisymmetric structure consisting of a nonspherical particle and a plane surface. On the basis of the discrete sources method and the T-matrix method, numerical schemes were developed and implemented in computer programs. Numerical results related to the influence of particle shape on the scattering characteristics are discussed. We will show that even for particles much smaller than the wavelength the scattering characteristics are still sensitive to the particle shape.

MODELING OF LIGHT SCATTERING BY NON-SPHERICAL INHOMOGENEOUS PARTICLES

Abstract An improved volume integral equation method for computing electromagnetic scattering by particles in the free space or imbedded in layered media is introduced. We apply method of moment with rooftop expansion and test function for the solution of volume integral equation. The singularity of Green’s function is reduced by moving derivatives to test and expansion functions. Comparison with Mie theory and other numerical codes are made.

Modeling of light scattering by non-spherical particles based on discrete sources method

Abstract Light scattering from a smooth axi-symmetrical particle has been simulated. The scattering problem has been analyzed through a strict mathematical model based on Maxwell equations. Implementation of the Discrete Sources Method (DSM) produced a compact efficient numericafl algorithm enabling to compute light scattering in a real-time regime on PC. Both polarizations of an exciting plane wave and all incidences are computed in parallel. A built-in residual criterion enables to control the accuracy of results. Examples of numerical simulation and comparisons with other techniques are presented.

Scattering of evanescent waves by a sensor tip near a plane surface

The paper is devoted to the application of a rigorous approach for analyzing the evanescent wave scattering by sensor tip near a plane surface. On the basis of the discrete sources method a numerical schemes was developed and implemented in computer program. Numerical results related to the influence of the position of the sensor tip on the scattering characteristics are discussed.

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.