Generalization of the separation of variables method for non-spherical scattering on dielectric objects

During the last years, the T-matrix approach based on the Extended Boundary Condition Method (EBCM) has become a powerful technique for solving the problem of plane wave scattering by non-spherical particles. It can be applied to different geometries and to large size parameters. For certain scattering configurations this method is able to bridge the gap between the resonance region and the geometric optics approximation. Despite these advantages it still remains a difficult method for practitioners. It is accompanied by loss of simplicity in concept and execution caused by the formulation in terms of integrals and related problems like the formulation of the non-local EBC, and the open question if it suffers from a restricted range of applicability of the Rayleigh hypothesis. In this paper, a new method will be presented which offers a much simpler way to derive a T-matrix without running into these problems. This is achieved by a generalization of the Separation of Variables Method (SVM) which uses the differential formulation of the scattering process. In this way, we are able to remove the mistake that SVM can be applied only if the boundary surface of the scatterer coincides with a constant coordinate line. Additional advantages of this approach are the possibility to consolidate different methods into a common mathematical body, thus allowing a better estimation of the accuracy of different numerical techniques, and the possibility to find an answer to the problem of the Rayleigh hypothesis. To formulate this new approach the method of lines (MoL) is used as a starting point. The Mot is a mathematical tool for solving partial differential equations, and it has been applied very successfully in guided wave theories. It also forms the mathematical basis of the Discretized Mie-formalism (DMF) which has been recently developed for plane wave scattering. With this contribution, there will be discussed interesting new aspects of the Mot. (C) 1998 Elsevier Science Ltd. All rights reserved.