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

A mathematical formalism describing plane electromagnetic wave scatter ing by a linear chain of N triaxial dielectric ellipsoids of complex i ndex of refraction is presented. The Fredholm integral equation theory is employed. As a first approximation, electromagnetic coupling betwe en only neighbouring scatterers is taken into account. The case of non -negligible coupling between any pairs of scatterers is a straightforw ard extension of the present treatment. However, the computing time de mands in that case are particularly high. The analysis is based on the Lippman-Schwinger integral equation for the electric field. The corre sponding integral equation for the scattering, which contains N singul ar 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 matr ix equation. The resulting solutions are used to calculate the scatter ing amplitude. As a numerical application, the case of a red blood cel l rouleau consisting of three adjacent oblate spheroidal models of ery throcytes is considered. Typical values of the appropriate discretizat ion 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 t echniques for reducing the rather high computing requirements of the a nalysis, such as parallel processing, are both suggested and applied.