An Integral Equation Solution To the Scattering of Electromagnetic Radiation By a Linear Chain of Interacting Triaxial Dielectric Ellipsoids. the Case of a Red Blood Cell Rouleau

Abstract

A mathematical formalism describing plane electromagnetic wave scattering by a linear chain of N triaxial dielectric ellipsoids of complex index of refraction is presented. The Fredholm integral equation theory is employed. As a first approximation, electromagnetic coupling between only neighbouring scatterers is taken into account. The case of non-negligible coupling between any pairs of scatterers is a straightforward extension of the present treatment. However, the computing time demands in that case are particularly high. The analysis is based on the Lippman-Schwinger integral equation for the electric field. The corresponding integral equation for the scattering, which contains N singular kernels, is transformed into N non-singular integral equations for the angular Fourier transform of the field indide each scatterer. The latter equations are solved by reducing them by quadrature into a matrix equation. The resulting solutions are used to calculate the scattering amplitude. As a numerical application, the case of a red blood cell rouleau consisting of three adjacent oblate spheroidal models of erythrocytes is considered. Typical values of the appropriate discretization parameters which are sufficient for achieving convergence, as well as certain validity tests are provided. The effect of electromagnetic coupling between neighbouring scatterers is demonstrated. Efficient techniques for reducing the rather high computing requirements of the analysis, such as parallel processing, are both suggested and applied.