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Use of Chebychev Polynomials in Thin Film Computations
From Herpin’s expression for the mth power of a multilayer matrix, very simple closed formulas are derived for the matrices and optical constants of any multilayer with a periodic structure. According to Epstein’s theorem, any symmetrical multilayer is equivalent to a fictitious monolayer. A simple...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
[Gaithersburg, MD] : U.S. Dept. of Commerce, National Institute of Standards and Technology
1959
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5287042/ https://www.ncbi.nlm.nih.gov/pubmed/31216138 http://dx.doi.org/10.6028/jres.063A.024 |
Sumario: | From Herpin’s expression for the mth power of a multilayer matrix, very simple closed formulas are derived for the matrices and optical constants of any multilayer with a periodic structure. According to Epstein’s theorem, any symmetrical multilayer is equivalent to a fictitious monolayer. A simple expression for the equivalent index and thickness of this monolayer is deduced for the case of a periodic and symmetrical sequence of equally thick films. As compared to any other method of numerical computation, the suggested formulation provides a considerable saving of time and work. In a numerical example, this saving amounts to about 80 percent. |
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