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Analytic solution for the peak reflectivity of an asymmetric mirror.

Asymmetric Bragg reflectors have been shown to optimize mirror performance in strained-layer material systems. Although the theory behind the reflectivity of symmetric mirrors has been well studied, little is known about asymmetric mirror designs. We present a closed-form solution for the peak reflectivity of an asymmetric mirror that results from applying a tanh substitution. This elegant technique has been shown to yield a markedly simplified calculation of the peak reflectivity of a symmetric mirror. These analytic expressions will be useful in mirror design by providing a straightforward way to compare the trade-offs between asymmetric and symmetric mirror designs.