## Abstract

This paper applies two different techniques to the problem of scattering by two spheres in contact:modal analysis, which is an exact method, and the discrete-dipole approximation (DDA). Good agreement is obtained, which further demonstrates the utility of the DDA to scattering problems for irregular particles. The choice of the DDA polarizability scheme is discussed in detail. We show that the lattice dispersion relation provides excellent improvement over the Clausius–Mossoti polarizability parameterization.

© 1993 Optical Society of America

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### Equations (7)

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(1)
$${\mathbf{a}}^{i}+\sum _{j=1,j\ne i}^{{N}_{3}}{\mathbf{T}}^{ij}{\mathbf{a}}^{j}={\mathbf{p}}^{i},$$
(2)
$$\mathrm{\alpha}=\frac{{\mathrm{\alpha}}^{(nr)}}{1-(2/3)i[{\mathrm{\alpha}}^{(nr)}/{d}^{3}]{({k}_{0}d)}^{3}},$$
(3)
$${\mathrm{\alpha}}^{(nr)}\approx \frac{{\mathrm{\alpha}}^{(0)}}{1+[{\mathrm{\alpha}}^{(0)}/{d}^{3}]({b}_{1}+{m}^{2}{b}_{2}+{m}^{2}{b}_{3}S){({k}_{0}d)}^{2}},$$
(4)
$${b}_{1}={c}_{1}/\mathrm{\pi}=-1.8915316,$$
(5)
$${b}_{2}={c}_{2}/\mathrm{\pi}=0.1648469,$$
(6)
$${b}_{3}=-(3{c}_{2}+{c}_{3})/\mathrm{\pi}=-1.7700004,$$
(7)
$${{\mathrm{\alpha}}_{\text{i}}}^{(0)}\equiv \frac{3{d}^{3}}{4\mathrm{\pi}}\left(\frac{{{m}_{i}}^{2}-1}{{{m}_{i}}^{2}+2}\right).$$