Abstract

The effects on reflectivity of a statistical variation in the thickness of layers in a multilayered Bragg reflector are studied. Analytic expressions are obtained for 〈ρ〉 and 〈ρρ*〉, the expected value of the reflection and reflectivity coefficients as a function of σ, the standard deviation in layer thickness. These expressions are then compared with values obtained using a computer routine which "builds" a reflector with the desired parameters and σ value, and then calculates the reflection. The results of the computer experiment are presented in the form of <i>p</i>(ρρ*), the probability distribution function of a statistical Bragg reflector. Finally, simple phenomenological expressions are presented for the reflectivity probability distribution.

© 1978 Optical Society of America

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