Scattering coefficients for a multilayered sphere: analytic expressions and algorithms

MieLab: A Software Tool to Perform Calculations on the Scattering of Electromagnetic Waves by Multilayered Spheres

“…(i.e., multilayered) sphere [17][18][19][20]. Similar solutions have been found for homogeneous infinite circular cylinders [21], infinite elliptical cylinders [22], and homogeneous and coremantle spheroids [23].…”

Scattering of an electromagnetic plane wave by a Luneburg lens III Finely stratified sphere model

“…There are two procedures for computing the partial wave scattering amplitudes of a multilayer sphere: (i) the progressive iteration procedure [3][4][5][6][7][8][9] and (ii) the parallel iteration procedure [10]. The progressive procedure is valid for any number of layers M. One starts by calculating single-scattering partial wave amplitudes at the core, then iteratively progressing outward toward the sphere surface, adding on one layer at a time and recalculating the amplitudes.…”

“…Such computations are prone to numerical overflow and underflow problems, especially when these results are combined over and over again as the iteration progresses outward toward the sphere surface [3]. In spite of these potential numerical difficulties, stable and highly accurate progressive iteration computer programs have been written [3][4][5][6][7][8][9] that compute scattering by a multilayer sphere, carefully avoiding the overflow and underflow problems.…”

Debye series analysis of scattering of a plane wave by a spherical Bragg grating

“…The first successful attack on this problem in the context of Mie theory was Aden and Kerker's solution to scattering by a coated sphere, 3,4 i.e., M ϭ 2. Bhandari's solution for scattering by an M-layer sphere 5 proceeded by analogy to the calculation of transmission and reflection of a plane wave by a stack of flat slabs. 6,7 For the flat slab problem the transmission and reflection coefficients are obtained iteratively, beginning with the first slab, adding the second slab, the third, and so on, all the way to the last slab.…”