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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 1 — Jan. 1, 1978
  • pp: 18–27

Statistical analysis of Bragg reflectors

J. B. Shellan, P. Agmon, P. Yeh, and A. Yariv  »View Author Affiliations

JOSA, Vol. 68, Issue 1, pp. 18-27 (1978)

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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 p(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

J. B. Shellan, P. Agmon, P. Yeh, and A. Yariv, "Statistical analysis of Bragg reflectors," J. Opt. Soc. Am. 68, 18-27 (1978)

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