Analytic expressions for the reflection delay, penetration depth, and absorptance of quarter-wave dielectric mirrors

The authors analyze the operation of high-reflectivity quarter-wave (QW) dielectric mirrors at the band-stop center (Bragg) frequency, relevant for the design of small-cavity optoelectronic structures. The energy penetration depth concept is used to determine a first-order linear approximation for the reduction of the mirror peak reflectivity of the QE mirror as a function of the mirror material parameters and the number of layers. The expression can be applied in the limit of small loss. The mathematical analysis and expressions for the absorptance and the peak reflectivity of a dielectric mirror with weak material absorption are presented. The use of the results is illustrated for a typical vertical cavity surface-emitting laser structure.<
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