Multiple Electromagnetic Scattering from a Cluster of Spheres. I. Theory

Abstract

A method for calculating the electromagnetic scattering for the truncation of the multipolar expansions describproperties of a cluster of spheres of arbitrary radii and ing the scattered field. The convergence of the expan-(possibly complex) refractive indexes is proposed. The sions is tested through the application to the simple but approach takes proper account of multiple scattering significant system of two spheres with varying interpareffects and does not require any approwinlation except ticle separation.

Calculation of total cross sections of multiple-sphere clusters

“…Nevertheless, it will be advantageous to retain the sphere-centered formulation of the T matrix in formulating the orientation-averaged cross sections of the cluster. The representation of the scattered field from the cluster in a single expansion has been discussed by Borghese et al 3 and Mackowski. 8 The first step in the process is to identify an origin of the cluster.…”

“…Developed first by Brunning and Lo 2 and later independently obtained by Borghese et al, 3 this analysis constructs the scattered field from the cluster as a superposition of individual fields scattered from each of the spheres. The individual fields, in turn, are expressed in terms of expansions of vector spherical harmonics written about the origin of the sphere.…”

Multiple Electromagnetic Scattering from a Cluster of Spheres. II. Symmetrization

“…(2)-(3) of MESI (Borghese et al, 1984) can be written in symmetrized form as (Hamermesh, 1962;Knox and Gold, 1964) Decomposition of the incident field [Eq. (la)] of MESI (Borghese et al, 1984) into parts belonging to the rows of the irreducible representations of 9 yields where W,,, is defined by Eq.…”

“…In a previous paper (Borghese et al, 1984) we proposed a method for studying the scattering properties of a cluster of spheres. Our approach, aimed at improving the Rayleigh-Debye theory (Rayleigh, 1881(Rayleigh, , 1910(Rayleigh, , 1914(Rayleigh, , 1918Debye, 1915) for the scattering of electromagnetic waves from molecules, is quite general in that it does not imply any restriction on either the effective index of refraction or the size and geometry of the cluster.…”

“…The multipoles transform according to the rows of the irreducible representations of the symmetry group. The symmetrization need not be applied to the Aerosol Sc~ence and Technology 3.237-243 (1984) field withn the spheres for, as shown in Section 4 of MESI (Borghese et al, 1984), the expansion coefficients of the internal field can be eliminated from the final equations.…”