Abstract

A simple method of calculating the reflectance R, absorptance from the substrate, absorptance from arbitrarily distributed losses in the coating material or interfaces, and the phase distortion resulting from small wavelength changes, from heating, and from deviations in the thicknesses and indices of all or any one or more of the layers is given for normal-incidence multilayer-dielectric reflectors with 1 − <i>R</i> ≪ 1. The method is employed to derive useful expressions for absorptance, reflectance, and phase distortion that are not easily obtained by other methods. The key is the use of the simple zeroth-order (<i>R</i> = 1) electric field distribution in the coating (sinusoidal standing wave whose amplitude is reduced by a factor <i>n</i><sub>0</sub>/<i>n</i><sub><i>H</i></sub> at the coating surface and by a factor of <i>n</i><sub><i>L</i></sub>/<i>n</i><sub><i>H</i></sub> at every <i>LH</i> interface, and is unchanged at every <i>HL</i> interface) to obtain first-order results.

© 1977 Optical Society of America

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  1. M. Sparks, Theoretical Studies of High-Power Ultraviolet and Infrared Materials, Xonics, Inc., Eighth Technical Report, 31 Dec. 1976, under Defense Advanced Research Projects, Agency Contract No. DAHC 15–73-C-0127.
  2. M. Flannery, M. Sparks, and E. Loh, Jr. (unpublished).
  3. D. H. Rank and H. E. Bennett, J. Opt. Soc. Am. 45, 69–73 (1955).
  4. Jean M. Bennett, J. Opt. Soc. Am. 54, 612–624 (1964).
  5. P. H. Lissberger, Rep. Prog. Phys. 33, 197–268 (1970).
  6. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).
  7. G. Koppelmann, Ann. Phys. (Leip.) 7, 388–396 (1960).
  8. M. Sparks, in Laser Induced Damage in Optical Materials: 1976, edited by A. J. Glass and A. H. Guenther, NBS Special Publication 462, Proceedings of a Symposium at Boulder, Colo., July 13–15, 1976, 203–213; Theoretical Studies of Materials for High-Power Infrared Coatings, Xonics, Inc., Sixth Technical Report, 31 Dec. 1975, under Defense Advanced Research Projects Agency Contract No. DAHC 15–73-C-0127.
  9. Dr. S. J. Holmes, Northrop Corporation (private communication).
  10. Joesph W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chaps. 3 and 4.
  11. C. Dufour, Rev. d'Opt. 31, 1 (1952).
  12. P. Baumeister and O. Arnon, Appl. Opt. 16, 439–444 (1977).

Arnon, O.

P. Baumeister and O. Arnon, Appl. Opt. 16, 439–444 (1977).

Baumeister, P.

P. Baumeister and O. Arnon, Appl. Opt. 16, 439–444 (1977).

Bennett, H. E.

D. H. Rank and H. E. Bennett, J. Opt. Soc. Am. 45, 69–73 (1955).

Bennett, Jean M.

Jean M. Bennett, J. Opt. Soc. Am. 54, 612–624 (1964).

Dufour, C.

C. Dufour, Rev. d'Opt. 31, 1 (1952).

Flannery, M.

M. Flannery, M. Sparks, and E. Loh, Jr. (unpublished).

Goodman, Joesph W.

Joesph W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chaps. 3 and 4.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

Holmes, Dr. S. J.

Dr. S. J. Holmes, Northrop Corporation (private communication).

Koppelmann, G.

G. Koppelmann, Ann. Phys. (Leip.) 7, 388–396 (1960).

Lissberger, P. H.

P. H. Lissberger, Rep. Prog. Phys. 33, 197–268 (1970).

Loh, Jr., E.

M. Flannery, M. Sparks, and E. Loh, Jr. (unpublished).

Rank, D. H.

D. H. Rank and H. E. Bennett, J. Opt. Soc. Am. 45, 69–73 (1955).

Sparks, M.

M. Flannery, M. Sparks, and E. Loh, Jr. (unpublished).

M. Sparks, in Laser Induced Damage in Optical Materials: 1976, edited by A. J. Glass and A. H. Guenther, NBS Special Publication 462, Proceedings of a Symposium at Boulder, Colo., July 13–15, 1976, 203–213; Theoretical Studies of Materials for High-Power Infrared Coatings, Xonics, Inc., Sixth Technical Report, 31 Dec. 1975, under Defense Advanced Research Projects Agency Contract No. DAHC 15–73-C-0127.

M. Sparks, Theoretical Studies of High-Power Ultraviolet and Infrared Materials, Xonics, Inc., Eighth Technical Report, 31 Dec. 1976, under Defense Advanced Research Projects, Agency Contract No. DAHC 15–73-C-0127.

Other (12)

M. Sparks, Theoretical Studies of High-Power Ultraviolet and Infrared Materials, Xonics, Inc., Eighth Technical Report, 31 Dec. 1976, under Defense Advanced Research Projects, Agency Contract No. DAHC 15–73-C-0127.

M. Flannery, M. Sparks, and E. Loh, Jr. (unpublished).

D. H. Rank and H. E. Bennett, J. Opt. Soc. Am. 45, 69–73 (1955).

Jean M. Bennett, J. Opt. Soc. Am. 54, 612–624 (1964).

P. H. Lissberger, Rep. Prog. Phys. 33, 197–268 (1970).

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

G. Koppelmann, Ann. Phys. (Leip.) 7, 388–396 (1960).

M. Sparks, in Laser Induced Damage in Optical Materials: 1976, edited by A. J. Glass and A. H. Guenther, NBS Special Publication 462, Proceedings of a Symposium at Boulder, Colo., July 13–15, 1976, 203–213; Theoretical Studies of Materials for High-Power Infrared Coatings, Xonics, Inc., Sixth Technical Report, 31 Dec. 1975, under Defense Advanced Research Projects Agency Contract No. DAHC 15–73-C-0127.

Dr. S. J. Holmes, Northrop Corporation (private communication).

Joesph W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chaps. 3 and 4.

C. Dufour, Rev. d'Opt. 31, 1 (1952).

P. Baumeister and O. Arnon, Appl. Opt. 16, 439–444 (1977).

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