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Calculation of Lossy Dielectric Multilayer Filter Response

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Abstract

An algorithm for calculating the response of a multilayer optical filter to monochromatic plane wave radiation at arbitrary angles of incidence is developed and implemented. The layered media are assumed to be arranged in a planar stack, and each medium is assumed to be a scalar, linear, isotropic, homogeneous lossy dielectric characterized by generally complex values of the electrical permittivity, magnetic permeability and conductivity. Previously described techniques are less general, or are sometimes not clear about the degree of generality allowed in the parameters describing the wave and the media. Other descriptions focus on special cases which actually serve to complicate the mathematics and generate unwieldy mathematical expressions. This paper presents a more general derivation of the expressions for the total reflectance and transmittance of a multilayer optical filter, emphasizing the constraints placed upon the various parameters as a result of simplifying assumptions, and describing the algorithm in a simple and well-known 2× 2 matrix formulation. An implementation of the algorithm in the IDL programming language is provided.

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Authors and Affiliations

  1. Interferometrics Inc., 14120 Parke Long Court, Suite 103, Chantilly, VA, 20151, USA

    P. A. Reiser

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  1. P. A. Reiser
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Correspondence to P. A. Reiser.

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Reiser, P.A. Calculation of Lossy Dielectric Multilayer Filter Response. J Sci Comput 25, 499–513 (2005). https://doi.org/10.1007/s10915-004-4808-2

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  • DOI: https://doi.org/10.1007/s10915-004-4808-2

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