Progressive algorithm for the scattering of electromagnetic waves by a multilayered eccentric sphere

This paper presents a general progressive algorithm for the computational study of electromagnetic wave scattering by a multilayered eccentric nanoparticle. The presented methodology is based on a combination of the vector addition theorem for spherical wave functions and an efficient progressive algorithm that matches the boundary conditions of every two adjacent shell layers from the outmost to the innermost layer. As a result, only a solution of small-sized matrices is required rather than solving a large set of system equations as reported in other works. With the developed approach, explicit expressions of the Mie scattering coefficients of the eccentric particle can be obtained. Moreover, the Mie coefficients of a specific inner layer could be calculated selectively, instead of having to compute those of all layers of the entire particle as required by other algorithms. The presented methodology can be used to study practically any type of spherical particle inclusions and the most widely studied cases such as scattering by solid particles, concentric particles, and inclusions with centers displaced along a straight line are just special cases of the algorithm presented. Computed results are also presented, illustrating that the eccentric structure allows extra freedom in the design of multilayered nanoparticles for optical applications.