Pole expansion of the Lorenz-Mie coefficients

Vadim A. Markel

doi:10.1117/1.3332549

1 February 2010 Pole expansion of the Lorenz-Mie coefficients

Vadim A. Markel

Author Affiliations +

Journal of Nanophotonics, Vol. 4, Issue 1, 041555 (February 2010). https://doi.org/10.1117/1.3332549

Abstract

A spectral approach to the Lorenz-Mie problem was adopted to obtain a pole expansion of the Lorenz-Mie coefficients in the complex variable z = 4π=(n² - 1), where n² is the dielectric permittivity of the scatterer. In the absence of magnetic properties (which is assumed), n is the refractive index of the scatterer. It is shown that the Lorenz-Mie coefficients are meromorphic functions of z with simple poles. The poles and the residues are functions of the size parameter x = ka = 2πa/λ and of the order of the Lorenz-Mie coefficient, l, but are independent of the material properties. This leads to a numerically efficient representation of the Lorenz-Mie coefficients.

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Vadim A. Markel "Pole expansion of the Lorenz-Mie coefficients," Journal of Nanophotonics 4(1), 041555 (1 February 2010). https://doi.org/10.1117/1.3332549

Published: 1 February 2010

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