Special Section on Nanostructures Honoring Craig F. Bohren

Pole expansion of the Lorenz-Mie coefficients

[+] Author Affiliations
Vadim A. Markel

Departments of Radiology and Bioengineering, University of Pennsylvania, 3320 Smith Walk, Philadelphia, PA 19104

J. Nanophoton. 4(1), 041555 (February 4, 2010). doi:10.1117/1.3332549
History: Received November 18, 2009; Revised December 21, 2009; Accepted December 21, 2009; February 4, 2010; Online February 04, 2010
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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.

© 2010 Society of Photo-Optical Instrumentation Engineers

Citation

Vadim A. Markel
"Pole expansion of the Lorenz-Mie coefficients", J. Nanophoton. 4(1), 041555 (February 4, 2010). ; http://dx.doi.org/10.1117/1.3332549


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