Calculation of light scattering from a spherical particle on a surface by the multipole expansion method

The multipole expansion method for calculating light scattering from a spherical particle on or near a smooth surface is reviewed and presented with special attention to symmetry for reduction of the computational effort. Formulas for the scattering amplitude and the differential scattering cross section are presented. In addition, useful new formulas are derived for the absorption and extinction cross sections. The theory is exact in the limiting case in which the substrate is a perfect conductor, but an approximation is needed to handle problems with dielectric substrates. As a test of the approximation, a series of calculations for particles on dielectric substrates is carried out. The results of these tests are presented and compared with previously published calculations for the same problems.

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