Abstract

A new design technique for multilayer reflectors is presented: It is useful when slight absorption by one or both of the coating materials limits the performance of the reflector. The basic procedure is to add layers to a given substrate or multilayer system one pair at a time. The thickness of each layer is chosen to give the maximum increase in reflectance for each pair of layers added. In general, the optical thicknesses of the layers in each pair are not quarter waves, but depend on the optical constants of the materials, as well as the starting reflectance of the subsystem. By using such optimized pairs, it is possible to exceed the reflectance limit usually imposed on quarter-wave stack reflectors by absorption. Expressions for the optimum design and the ultimate reflectance for a high reflector made with a given set of coating materials are given. Other design techniques found in the literature require more layers to achieve the same level of reflectance as the present method.

© 1980 Optical Society of America

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References

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  1. G. Koppelmann, "On the theory of multilayers consisting of weakly absorbing materials and their use as interferometer mirrors," (in German) Ann. Phys. (Leipzig) 5, 388–396 (1960).
  2. P. Baumeister and O. Arnon, "Use of hafnium dioxide in multilayer dielectric reflectors for the near UV," Appl. Opt. 16, 439–444 (1977).
  3. M. Sparks and M. Flannery, "Simplified description of multilayer dielectric reflectors," J. Opt. Soc. Am. 69, 993–1006 (1979).
  4. P. H. Lissberger, "The ultimate reflectance of multilayer dielectric mirrors," Opt. Acta 25, 291–298 (1978).
  5. G. W. DeBell, "The design and measurement of low absorptance optical interference coatings," Ph.D. thesis, Institute of Optics,. University of Rochester, 1972 (unpublished).
  6. Joseph H. Apfel, "Optical coating design with reduced electric field intensity," Appl. Opt. 16, 1880–1885 (1977); Eberhard Spiller, "Reflective multilayer coatings for the far uv region," Appl. Opt. 15, 2333–2338 (1976).
  7. Leo Young, "Prediction of absorption loss in multilayer interference filters," J. Opt. Soc. Am. 52, 753–761 (1962).
  8. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).
  9. When a term in δij occurs with a coefficient of the form (1 — r2j), it is considered to be of order higher than k/n. This is strictly true only as rj → 1. In Eq. (27) the coefficient is (1 — r212) and is not small.

1979 (1)

1978 (1)

P. H. Lissberger, "The ultimate reflectance of multilayer dielectric mirrors," Opt. Acta 25, 291–298 (1978).

1977 (2)

1962 (1)

1960 (1)

G. Koppelmann, "On the theory of multilayers consisting of weakly absorbing materials and their use as interferometer mirrors," (in German) Ann. Phys. (Leipzig) 5, 388–396 (1960).

Apfel, Joseph H.

Arnon, O.

Baumeister, P.

DeBell, G. W.

G. W. DeBell, "The design and measurement of low absorptance optical interference coatings," Ph.D. thesis, Institute of Optics,. University of Rochester, 1972 (unpublished).

Flannery, M.

Heavens, O. S.

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

Koppelmann, G.

G. Koppelmann, "On the theory of multilayers consisting of weakly absorbing materials and their use as interferometer mirrors," (in German) Ann. Phys. (Leipzig) 5, 388–396 (1960).

Lissberger, P. H.

P. H. Lissberger, "The ultimate reflectance of multilayer dielectric mirrors," Opt. Acta 25, 291–298 (1978).

Sparks, M.

Young, Leo

Ann. Phys. (1)

G. Koppelmann, "On the theory of multilayers consisting of weakly absorbing materials and their use as interferometer mirrors," (in German) Ann. Phys. (Leipzig) 5, 388–396 (1960).

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

Opt. Acta (1)

P. H. Lissberger, "The ultimate reflectance of multilayer dielectric mirrors," Opt. Acta 25, 291–298 (1978).

Other (3)

G. W. DeBell, "The design and measurement of low absorptance optical interference coatings," Ph.D. thesis, Institute of Optics,. University of Rochester, 1972 (unpublished).

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

When a term in δij occurs with a coefficient of the form (1 — r2j), it is considered to be of order higher than k/n. This is strictly true only as rj → 1. In Eq. (27) the coefficient is (1 — r212) and is not small.

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