Abstract

A variant of the powerful thin-film needle design technique, which was first described by Tikhonravov and his co-workers, is described. In this method thin layers are introduced at optimum positions within the refractive-index profile of a given multilayer system. In the original method the optimum locations for the layer insertions are calculated analytically, whereas in this variant of the method they are determined numerically. This approach, although somewhat slower, is very flexible. With the numerical needle method it is easy to define a merit function that consists of quite complex spectral quantities, such as Commission Internationale de l’Eclairage color coordinates or custom spectral properties that are defined at run time. In the program described, three different absorbing or nonabsorbing materials can be used for the needle layers and one or more needles can be inserted into the system at any given time. Multilayer solutions can also be sought in which the system is defined in terms of repeating groups of layers. It is also possible to calculate automatically a series of solutions to a particular problem with increasing overall thicknesses or to perform simultaneous calculations on several different systems. Examples are given that illustrate these various points.

© 1996 Optical Society of America

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References

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  1. J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
    [CrossRef] [PubMed]
  2. L. Li, J. A. Dobrowolski, “Computation speeds of different optical thin-film synthesis methods,” Appl. Opt. 31, 3790–3799 (1992).
    [CrossRef] [PubMed]
  3. A. V. Tikhonravov, “On the synthesis of optical coatings using optimality conditions,” Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91–93 (1982).
  4. A. N. Baskakov, A. V. Tikhonravov, “Synthesis of two-component optical coatings,” Opt. Spectrosc. (USSR) 56, 559–562 (1984).
  5. A. V. Tikhonravov, “Optical coating synthesis using optimal conditions,” Vestn. Mosk. Univ. Fiz. Astromiya 23, 91–93 (1982).
  6. A. V. Tikhonravov, “On the optimality of thin film optical coating design,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. SPIE1270, 28–35 (1990).
  7. A. V. Tikhonravov, M. K. Trubetskov, “Thin film coating design using second order optimization methods,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. SPIE1782, 156–164 (1992).
  8. A. V. Tikhonravov, “Some theoretical aspects of thin-film optics and their applications,” Appl. Opt. 32, 4265–4275 (1993).
    [CrossRef] [PubMed]
  9. G. W. DeBell, A. V. Tikhonravov, M. K. Trubetskov, “Use of a new synthesis algorithm to design polarization insensitive optical coatings,” in Optical Thin Films IV: New Developments, J. D. Rancourt, ed., Proc. SPIE2262, 187–197 (1994).
  10. A. V. Tikhonravov, M. K. Trubetskov, “Development of the needle optimization technique and new features of “Optilayer” design software,” in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE2253, 10–20 (1994).
  11. J. A. Dobrowolski, “Completely automatic synthesis of optical thin film systems,” Appl. Opt. 4, 937–946 (1965).
    [CrossRef]
  12. S. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Editions Frontieres, Gif-sur-Yvette, France, 1992).
  13. C. J. van der Laan, H. J. Frankena, “Fast computation method for derivatives of multilayer stack reflectance,” Appl. Opt. 17, 538–541 (1978).
    [CrossRef]
  14. K.-O. Peng, M. R. de la Fonteijne, “Derivatives of transmittance and reflectance for an absorbing multilayer stack,” Appl. Opt. 24, 501–503 (1985).
    [CrossRef] [PubMed]
  15. D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminum,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–406.
  16. H. R. Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 749–764.
  17. D. W. Lynch, W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 275–367.
  18. J. A. Dobrowolski, J. R. Pekelsky, R. Pelletier, M. Ranger, B. T. Sullivan, A. J. Waldorf, “A practical magnetron sputtering system for the deposition of optical multilayer coatings,” Appl. Opt. 31, 3784–3789 (1992).
    [CrossRef] [PubMed]
  19. J. A. Dobrowolski, B. T. Sullivan, “Universal antireflection coatings for the visible spectral region,” Appl. Opt. 35, 4993–4997 (1996).
    [CrossRef] [PubMed]
  20. B. T. Sullivan, J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. II. Experimental results—sputtering system,” Appl. Opt. 32, 2351–2360 (1993).
    [CrossRef] [PubMed]

1996

1993

1992

1990

1985

1984

A. N. Baskakov, A. V. Tikhonravov, “Synthesis of two-component optical coatings,” Opt. Spectrosc. (USSR) 56, 559–562 (1984).

1982

A. V. Tikhonravov, “Optical coating synthesis using optimal conditions,” Vestn. Mosk. Univ. Fiz. Astromiya 23, 91–93 (1982).

A. V. Tikhonravov, “On the synthesis of optical coatings using optimality conditions,” Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91–93 (1982).

1978

1965

Baskakov, A. N.

A. N. Baskakov, A. V. Tikhonravov, “Synthesis of two-component optical coatings,” Opt. Spectrosc. (USSR) 56, 559–562 (1984).

de la Fonteijne, M. R.

DeBell, G. W.

G. W. DeBell, A. V. Tikhonravov, M. K. Trubetskov, “Use of a new synthesis algorithm to design polarization insensitive optical coatings,” in Optical Thin Films IV: New Developments, J. D. Rancourt, ed., Proc. SPIE2262, 187–197 (1994).

Dobrowolski, J. A.

Frankena, H. J.

Furman, S. A.

S. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Editions Frontieres, Gif-sur-Yvette, France, 1992).

Hunter, W. R.

D. W. Lynch, W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 275–367.

Inokuti, M.

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminum,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–406.

Kemp, R. A.

Li, L.

Lynch, D. W.

D. W. Lynch, W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 275–367.

Pekelsky, J. R.

Pelletier, R.

Peng, K.-O.

Philipp, H. R.

H. R. Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 749–764.

Ranger, M.

Shiles, E.

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminum,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–406.

Smith, D. Y.

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminum,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–406.

Sullivan, B. T.

Tikhonravov, A. V.

A. V. Tikhonravov, “Some theoretical aspects of thin-film optics and their applications,” Appl. Opt. 32, 4265–4275 (1993).
[CrossRef] [PubMed]

A. N. Baskakov, A. V. Tikhonravov, “Synthesis of two-component optical coatings,” Opt. Spectrosc. (USSR) 56, 559–562 (1984).

A. V. Tikhonravov, “Optical coating synthesis using optimal conditions,” Vestn. Mosk. Univ. Fiz. Astromiya 23, 91–93 (1982).

A. V. Tikhonravov, “On the synthesis of optical coatings using optimality conditions,” Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91–93 (1982).

A. V. Tikhonravov, “On the optimality of thin film optical coating design,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. SPIE1270, 28–35 (1990).

A. V. Tikhonravov, M. K. Trubetskov, “Thin film coating design using second order optimization methods,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. SPIE1782, 156–164 (1992).

S. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Editions Frontieres, Gif-sur-Yvette, France, 1992).

G. W. DeBell, A. V. Tikhonravov, M. K. Trubetskov, “Use of a new synthesis algorithm to design polarization insensitive optical coatings,” in Optical Thin Films IV: New Developments, J. D. Rancourt, ed., Proc. SPIE2262, 187–197 (1994).

A. V. Tikhonravov, M. K. Trubetskov, “Development of the needle optimization technique and new features of “Optilayer” design software,” in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE2253, 10–20 (1994).

Trubetskov, M. K.

A. V. Tikhonravov, M. K. Trubetskov, “Development of the needle optimization technique and new features of “Optilayer” design software,” in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE2253, 10–20 (1994).

G. W. DeBell, A. V. Tikhonravov, M. K. Trubetskov, “Use of a new synthesis algorithm to design polarization insensitive optical coatings,” in Optical Thin Films IV: New Developments, J. D. Rancourt, ed., Proc. SPIE2262, 187–197 (1994).

A. V. Tikhonravov, M. K. Trubetskov, “Thin film coating design using second order optimization methods,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. SPIE1782, 156–164 (1992).

van der Laan, C. J.

Waldorf, A. J.

Appl. Opt.

J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
[CrossRef] [PubMed]

L. Li, J. A. Dobrowolski, “Computation speeds of different optical thin-film synthesis methods,” Appl. Opt. 31, 3790–3799 (1992).
[CrossRef] [PubMed]

A. V. Tikhonravov, “Some theoretical aspects of thin-film optics and their applications,” Appl. Opt. 32, 4265–4275 (1993).
[CrossRef] [PubMed]

C. J. van der Laan, H. J. Frankena, “Fast computation method for derivatives of multilayer stack reflectance,” Appl. Opt. 17, 538–541 (1978).
[CrossRef]

K.-O. Peng, M. R. de la Fonteijne, “Derivatives of transmittance and reflectance for an absorbing multilayer stack,” Appl. Opt. 24, 501–503 (1985).
[CrossRef] [PubMed]

J. A. Dobrowolski, “Completely automatic synthesis of optical thin film systems,” Appl. Opt. 4, 937–946 (1965).
[CrossRef]

J. A. Dobrowolski, J. R. Pekelsky, R. Pelletier, M. Ranger, B. T. Sullivan, A. J. Waldorf, “A practical magnetron sputtering system for the deposition of optical multilayer coatings,” Appl. Opt. 31, 3784–3789 (1992).
[CrossRef] [PubMed]

J. A. Dobrowolski, B. T. Sullivan, “Universal antireflection coatings for the visible spectral region,” Appl. Opt. 35, 4993–4997 (1996).
[CrossRef] [PubMed]

B. T. Sullivan, J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. II. Experimental results—sputtering system,” Appl. Opt. 32, 2351–2360 (1993).
[CrossRef] [PubMed]

Opt. Spectrosc. (USSR)

A. N. Baskakov, A. V. Tikhonravov, “Synthesis of two-component optical coatings,” Opt. Spectrosc. (USSR) 56, 559–562 (1984).

Vestn. Mosk. Univ. Fiz. Astromiya

A. V. Tikhonravov, “Optical coating synthesis using optimal conditions,” Vestn. Mosk. Univ. Fiz. Astromiya 23, 91–93 (1982).

Vestn. Mosk. Univ. Fiz. Astronomiya

A. V. Tikhonravov, “On the synthesis of optical coatings using optimality conditions,” Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91–93 (1982).

Other

G. W. DeBell, A. V. Tikhonravov, M. K. Trubetskov, “Use of a new synthesis algorithm to design polarization insensitive optical coatings,” in Optical Thin Films IV: New Developments, J. D. Rancourt, ed., Proc. SPIE2262, 187–197 (1994).

A. V. Tikhonravov, M. K. Trubetskov, “Development of the needle optimization technique and new features of “Optilayer” design software,” in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE2253, 10–20 (1994).

A. V. Tikhonravov, “On the optimality of thin film optical coating design,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. SPIE1270, 28–35 (1990).

A. V. Tikhonravov, M. K. Trubetskov, “Thin film coating design using second order optimization methods,” in Thin Films for Optical Systems, K. H. Guenther, ed., Proc. SPIE1782, 156–164 (1992).

S. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Editions Frontieres, Gif-sur-Yvette, France, 1992).

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminum,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–406.

H. R. Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 749–764.

D. W. Lynch, W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 275–367.

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Figures (6)

Fig. 1
Fig. 1

Beam splitter for s-polarized light incident at 45° that has a high transmittance in the 400–800-nm spectral region and a high reflectance at 1210 nm. Illustration of the use of the needle method with group-mode calculations: A, target and calculated performance; B, refractive-index profile.

Fig. 2
Fig. 2

CIE x ¯ λ filter for colorimetry. Illustration of the use of the needle method for the automatic generation of a series of solutions with increasing optical thicknesses. Rows A, B, C, and D represent the calculated performance and refractive-index profiles of solutions that have 600-, 1434-, 2470-, and 3982-nm total optical thicknesses, respectively. MF, merit function.

Fig. 3
Fig. 3

Filter with a low luminous reflectance and a high reflectance at 1500 nm. Illustration of the use of three different needle materials: a dielectric, a semiconductor, and a metal. A and B represent the calculated performance and the refractive-index profile, respectively, of a filter that meets the specifications.

Fig. 4
Fig. 4

Antireflection coating designed for use with six different substrates. Illustration of the use of the needle method in simultaneous calculations on several systems. A, the calculated reflectance before and after the coating of six substrates with different refractive indices; B, refractive-index profile of the antireflection coating.

Fig. 5
Fig. 5

Double-pass, broadband nonpolarizing beam splitter in which RpTp = RsTs. Illustration of the use of the needle method with custom quantities of interest defined at run time. A and B represent the calculated performance and the refractive-index profile, respectively, of a solution that meets the requirements.

Fig. 6
Fig. 6

Filter with a spectral reflectance that matches the silhouette of the Taj Mahal. Illustration of the insertion of more than one needle at a time: Solution obtained when, A, nine needles, B, one needle at a time was inserted into the system. Calculation time for the second example was approximately five times as long.

Tables (1)

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Table 1 Construction Parameters of Some of the Systemsa

Equations (9)

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f ( Q ) = { 1 m j = 1 m [ Q ( λ j , ϕ j ) - Q ˜ j Δ Q j ] 2 } 1 / 2 .
δ f ( t k ) = f [ Q ( t k ) - f ( Q ) ] ,             k = 1 , , N .
M = M pre M k M post ,
d M / d t i = M pre d M i / d t i M post .
M ( t i ) = M + d M / d t i Δ t i .
d Q / d t i = ( Q - Q ) / Δ t i .
Q = ( R s R p - T s T p ) / ( R s R p + T s T p ) .
SiO 2 , n = 1.455 + 3.816 × 10 3 λ 2 + 5.250 × 10 7 λ 4 ; Nb 2 O 5 , n = 2.177 + 3.293 × 10 4 λ 2 + 2.484 × 10 9 λ 4 .
( 0.5 H L 0.5 H ) 2 ( 0.5 H L 0.5 H ) 2 ( 0.5 H L 0.5 H ) 2 ,

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