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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  1. M. Born and E. Wolf, Principles of Optics (MacMillan, New York, 1964).
  2. P. Yeh, A. Yariv and C. Hong, J. Opt. Soc. Am. 67, 423 (1977).
  3. A. Ashkin and A. Yariv, Bell Labs. Tech. Memo MM-61-124-46 (13 November 1961) (unpublished).
  4. N. Bloembergen and A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).
  5. C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
  6. S. M. Rytov, Zh. Eksp. Teor. Fiz. 29, 605 (1955) [Sov. Phys.-JETP 2, 466 (1956)].
  7. J. P. Vander Ziel, M. Illegems, and R. M. Mikulyak, Appl. Phys. (to be published).
  8. Private communication with Wess Icenogle of Spectra Physics, Mountain View, Calif.
  9. Private communication with Steve Silver of OCLI, Santa Rosa, Calif.
  10. K. O. Hill, Appl. Opt. 13, 1853 (1974).
  11. A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).
  12. C. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, and A. Katzir, Appl. Phys. Lett. 31, 276 (1977).
  13. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1971), p. 85.
  14. Petr Beckmann, The Scattering of Electromagnetic Waves From Rough Surfaces (MacMillan, New York, 1963), p. 81.
  15. H. Kogelnik, Bell. Syst. Tech. J. 55, 109–126 (1976).
  16. A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
  17. W. Streifer, D. R. Scifres, and R. D. Burnham, J. Opt. Soc. Am. 66, 1359 (1976).
  18. H. W. Harman, Principles of the Statistical Theory of Communication, (McGraw-Hill, New York, 1963), p. 75.

Ashkin, A.

A. Ashkin and A. Yariv, Bell Labs. Tech. Memo MM-61-124-46 (13 November 1961) (unpublished).

Beckmann, Petr

Petr Beckmann, The Scattering of Electromagnetic Waves From Rough Surfaces (MacMillan, New York, 1963), p. 81.

Bey, P. P.

C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).

Bloembergen, N.

N. Bloembergen and A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).

Born, M.

M. Born and E. Wolf, Principles of Optics (MacMillan, New York, 1964).

Burnham, R. D.

W. Streifer, D. R. Scifres, and R. D. Burnham, J. Opt. Soc. Am. 66, 1359 (1976).

Harman, H. W.

H. W. Harman, Principles of the Statistical Theory of Communication, (McGraw-Hill, New York, 1963), p. 75.

Hill, K. O.

K. O. Hill, Appl. Opt. 13, 1853 (1974).

Hong, C.

P. Yeh, A. Yariv and C. Hong, J. Opt. Soc. Am. 67, 423 (1977).

C. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, and A. Katzir, Appl. Phys. Lett. 31, 276 (1977).

Illegems, M.

J. P. Vander Ziel, M. Illegems, and R. M. Mikulyak, Appl. Phys. (to be published).

Katzir, A.

A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).

C. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, and A. Katzir, Appl. Phys. Lett. 31, 276 (1977).

Kittel, C.

C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1971), p. 85.

Kogelnik, H.

H. Kogelnik, Bell. Syst. Tech. J. 55, 109–126 (1976).

Livanos, A. C.

C. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, and A. Katzir, Appl. Phys. Lett. 31, 276 (1977).

A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).

Mikulyak, R. M.

J. P. Vander Ziel, M. Illegems, and R. M. Mikulyak, Appl. Phys. (to be published).

Rytov, S. M.

S. M. Rytov, Zh. Eksp. Teor. Fiz. 29, 605 (1955) [Sov. Phys.-JETP 2, 466 (1956)].

Scifres, D. R.

W. Streifer, D. R. Scifres, and R. D. Burnham, J. Opt. Soc. Am. 66, 1359 (1976).

Shellan, J. B.

C. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, and A. Katzir, Appl. Phys. Lett. 31, 276 (1977).

A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).

Sievers, A. J.

N. Bloembergen and A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).

Streifer, W.

W. Streifer, D. R. Scifres, and R. D. Burnham, J. Opt. Soc. Am. 66, 1359 (1976).

Tang, C. L.

C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).

Vander Ziel, J. P.

J. P. Vander Ziel, M. Illegems, and R. M. Mikulyak, Appl. Phys. (to be published).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (MacMillan, New York, 1964).

Yariv, A.

P. Yeh, A. Yariv and C. Hong, J. Opt. Soc. Am. 67, 423 (1977).

A. Ashkin and A. Yariv, Bell Labs. Tech. Memo MM-61-124-46 (13 November 1961) (unpublished).

A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).

C. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, and A. Katzir, Appl. Phys. Lett. 31, 276 (1977).

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).

Yeh, P.

P. Yeh, A. Yariv and C. Hong, J. Opt. Soc. Am. 67, 423 (1977).

Other

M. Born and E. Wolf, Principles of Optics (MacMillan, New York, 1964).

P. Yeh, A. Yariv and C. Hong, J. Opt. Soc. Am. 67, 423 (1977).

A. Ashkin and A. Yariv, Bell Labs. Tech. Memo MM-61-124-46 (13 November 1961) (unpublished).

N. Bloembergen and A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).

C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).

S. M. Rytov, Zh. Eksp. Teor. Fiz. 29, 605 (1955) [Sov. Phys.-JETP 2, 466 (1956)].

J. P. Vander Ziel, M. Illegems, and R. M. Mikulyak, Appl. Phys. (to be published).

Private communication with Wess Icenogle of Spectra Physics, Mountain View, Calif.

Private communication with Steve Silver of OCLI, Santa Rosa, Calif.

K. O. Hill, Appl. Opt. 13, 1853 (1974).

A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).

C. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, and A. Katzir, Appl. Phys. Lett. 31, 276 (1977).

C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1971), p. 85.

Petr Beckmann, The Scattering of Electromagnetic Waves From Rough Surfaces (MacMillan, New York, 1963), p. 81.

H. Kogelnik, Bell. Syst. Tech. J. 55, 109–126 (1976).

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).

W. Streifer, D. R. Scifres, and R. D. Burnham, J. Opt. Soc. Am. 66, 1359 (1976).

H. W. Harman, Principles of the Statistical Theory of Communication, (McGraw-Hill, New York, 1963), p. 75.

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