A tanh substitution technique for the analysis of abrupt and graded interface multilayer dielectric stacks

The authors report a new analytical technique for estimating the peak reflectivity of lossless dielectric stacks with combinations of quarter and/or half-wave thicknesses. A simple variable substitution is used to transform the standard formula for the reflectivity of a Fabry-Perot resonator into a remarkably simplified form. The resulting expressions for reflectivity are intuitively appealing, allowing use of additive algebra to calculate the peak reflectivity of a multilayer dielectric stack.<
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