Abstract

Design approaches for optical thin films that recognize the key role of a design's total optical thickness are presented. These approaches are based primarily on the needle optimization technique but also utilize other optimization procedures. Using the described design approaches, an optical coating engineer can obtain a set of theoretical designs with different combinations of principal design metrics (merit function value, number of layers, and total design optical thickness); this extends opportunities for choosing the most practical and manufacturable design. We also show that some design problems have multiple solutions with nearly the same combinations of principal design metrics.

© 2007 Optical Society of America

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    [CrossRef]
  2. H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).
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  5. J. A. Dobrowolski, Optical Properties of Films and Coatings (McGraw-Hill, 1994), Chap. 42, pp. 42.3-42.130.
  6. N. Kaiser and H. K. Pulker, Optical Interference Coatings (Springer-Verlag, 2003).
  7. P. W. Baumeister, Optical Coating Technology (SPIE Press, 2004).
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    [CrossRef]
  9. J. A. Dobrowolski and R. A. Kemp, "Refinement of optical multilayer systems with different optimization procedures," Appl. Opt. 29, 2876-2893 (1990).
    [CrossRef] [PubMed]
  10. J. Kruschwitz, "Software tools speed optical thin-film design," Laser Focus World 39, 157-166 (2003).
  11. A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov, "Second order optimization methods in the synthesis of multilayer coatings," Comp. Maths. Math. Phys. 33, 1339-1352 (1993).
  12. A. V. Tikhonravov, "Synthesis of optical coatings using optimality conditions," Vestn. Mosk. Univ. , Fiz, Astron. 23, 91-93 (1982).
  13. A. V. Tikhonravov, M. K. Trubetskov, and G. DeBell, "Application of the needle optimization technique to the design of optical coatings," Appl. Opt. 35, 5493-5508 (1996).
    [CrossRef] [PubMed]
  14. A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, "Key role of the coating total optical thickness in solving design problems," in Proc. SPIE 5250, 312-321 (2004).
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    [CrossRef]
  16. J. A. Dobrowolski and D. Lowe, "Optical thin-film synthesis program based on the use of Fourier transforms," Appl. Opt. 17, 3039-3050 (1978).
    [CrossRef] [PubMed]
  17. P. G. Verly, J. A. Dobrowolski, W. Wild, and R. Burton, "Synthesis of high rejection filters with the Fourier transform method," Appl. Opt. 28, 2864-2875 (1989).
    [CrossRef] [PubMed]
  18. P. G. Verly and J. A. Dobrowolski, "Iterative correction process for optical thin-film synthesis with the Fourier transform method," Appl. Opt. 29, 3672-3684 (1990).
    [CrossRef] [PubMed]
  19. P. G. Verly, J. A. Dobrowolski, and R. R. Willey, "Fourier-transform method for the design of wideband antireflection coatings," Appl. Opt. 31, 3836-3846 (1992).
    [CrossRef] [PubMed]
  20. P. G. Verly, "Fourier-transform technique with frequency filtering for optical thin-film design," Appl. Opt. 34, 688-694 (1995).
    [CrossRef] [PubMed]
  21. A. V. Tikhonravov, B. T. Sullivan, and M. V. Borisova, "Discrete Fourier-transform approach to inhomogeneous layer synthesis," Appl. Opt. 33, 5142-5150 (1994).
    [CrossRef] [PubMed]
  22. J. A. Dobrowolski, "Completely automatic synthesis of optical thin-film systems," Appl. Opt. 4, 937-946 (1965).
    [CrossRef]
  23. A. V. Tikhonravov and M. K. Trubetskov, OptiLayer Thin Film Software, http://www.optilayer.com.
  24. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, "Investigation of the effect of accumulation of thickness errors in optical coating production using broadband optical monitoring," Appl. Opt. 45, 7026-7034 (2006).
    [CrossRef] [PubMed]
  25. A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
    [CrossRef] [PubMed]
  26. A. V. Tikhonravov, "Virtual deposition plant," in Proc. SPIE 5870, 108-120 (2005).
  27. A. Tikhonravov and M. Trubetskov, "Stabilization of computational algorithms for the characterization of thin-film coatings," Numer. Methods Programming 6, 109-117 (2005).

2006 (1)

2005 (3)

A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
[CrossRef] [PubMed]

A. V. Tikhonravov, "Virtual deposition plant," in Proc. SPIE 5870, 108-120 (2005).

A. Tikhonravov and M. Trubetskov, "Stabilization of computational algorithms for the characterization of thin-film coatings," Numer. Methods Programming 6, 109-117 (2005).

2004 (1)

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, "Key role of the coating total optical thickness in solving design problems," in Proc. SPIE 5250, 312-321 (2004).

2003 (1)

J. Kruschwitz, "Software tools speed optical thin-film design," Laser Focus World 39, 157-166 (2003).

1997 (1)

J. A. Dobrowolski, "Numerical methods for optical thin films," Opt. Photonics News 8, 24-33 (1997).
[CrossRef]

1996 (1)

1995 (1)

1994 (1)

1993 (1)

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov, "Second order optimization methods in the synthesis of multilayer coatings," Comp. Maths. Math. Phys. 33, 1339-1352 (1993).

1992 (1)

1990 (2)

1989 (1)

1986 (1)

J. A. Dobrowolski, "Comparison of the Fourier transform and flip-flop thin-film synthesis methods," Appl. Opt. 33, 1966-1972 (1986).
[CrossRef]

1982 (1)

A. V. Tikhonravov, "Synthesis of optical coatings using optimality conditions," Vestn. Mosk. Univ. , Fiz, Astron. 23, 91-93 (1982).

1978 (1)

1965 (1)

1958 (1)

Amotchkina, T. V.

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, "Investigation of the effect of accumulation of thickness errors in optical coating production using broadband optical monitoring," Appl. Opt. 45, 7026-7034 (2006).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, "Key role of the coating total optical thickness in solving design problems," in Proc. SPIE 5250, 312-321 (2004).

Baumeister, P.

Baumeister, P. W.

P. W. Baumeister, Optical Coating Technology (SPIE Press, 2004).

Borisova, M. V.

Burton, R.

DeBell, G.

Dobrowolski, J. A.

Furman, S.

S. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette, 1992).

Kaiser, N.

N. Kaiser and H. K. Pulker, Optical Interference Coatings (Springer-Verlag, 2003).

Kemp, R. A.

Kokarev, M. A.

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, "Key role of the coating total optical thickness in solving design problems," in Proc. SPIE 5250, 312-321 (2004).

Kruschwitz, J.

J. Kruschwitz, "Software tools speed optical thin-film design," Laser Focus World 39, 157-166 (2003).

Lowe, D.

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).

Pulker, H. K.

N. Kaiser and H. K. Pulker, Optical Interference Coatings (Springer-Verlag, 2003).

Sullivan, B. T.

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1988).

Tikhonov, A. N.

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov, "Second order optimization methods in the synthesis of multilayer coatings," Comp. Maths. Math. Phys. 33, 1339-1352 (1993).

Tikhonravov, A.

A. Tikhonravov and M. Trubetskov, "Stabilization of computational algorithms for the characterization of thin-film coatings," Numer. Methods Programming 6, 109-117 (2005).

Tikhonravov, A. V.

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, "Investigation of the effect of accumulation of thickness errors in optical coating production using broadband optical monitoring," Appl. Opt. 45, 7026-7034 (2006).
[CrossRef] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
[CrossRef] [PubMed]

A. V. Tikhonravov, "Virtual deposition plant," in Proc. SPIE 5870, 108-120 (2005).

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, "Key role of the coating total optical thickness in solving design problems," in Proc. SPIE 5250, 312-321 (2004).

A. V. Tikhonravov, M. K. Trubetskov, and G. DeBell, "Application of the needle optimization technique to the design of optical coatings," Appl. Opt. 35, 5493-5508 (1996).
[CrossRef] [PubMed]

A. V. Tikhonravov, B. T. Sullivan, and M. V. Borisova, "Discrete Fourier-transform approach to inhomogeneous layer synthesis," Appl. Opt. 33, 5142-5150 (1994).
[CrossRef] [PubMed]

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov, "Second order optimization methods in the synthesis of multilayer coatings," Comp. Maths. Math. Phys. 33, 1339-1352 (1993).

A. V. Tikhonravov, "Synthesis of optical coatings using optimality conditions," Vestn. Mosk. Univ. , Fiz, Astron. 23, 91-93 (1982).

S. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette, 1992).

Trubetskov, M.

A. Tikhonravov and M. Trubetskov, "Stabilization of computational algorithms for the characterization of thin-film coatings," Numer. Methods Programming 6, 109-117 (2005).

Trubetskov, M. K.

Verly, P. G.

Wild, W.

Willey, R. R.

Appl. Opt. (12)

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

J. A. Dobrowolski and D. Lowe, "Optical thin-film synthesis program based on the use of Fourier transforms," Appl. Opt. 17, 3039-3050 (1978).
[CrossRef] [PubMed]

P. G. Verly, J. A. Dobrowolski, W. Wild, and R. Burton, "Synthesis of high rejection filters with the Fourier transform method," Appl. Opt. 28, 2864-2875 (1989).
[CrossRef] [PubMed]

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

P. G. Verly and J. A. Dobrowolski, "Iterative correction process for optical thin-film synthesis with the Fourier transform method," Appl. Opt. 29, 3672-3684 (1990).
[CrossRef] [PubMed]

P. G. Verly, J. A. Dobrowolski, and R. R. Willey, "Fourier-transform method for the design of wideband antireflection coatings," Appl. Opt. 31, 3836-3846 (1992).
[CrossRef] [PubMed]

A. V. Tikhonravov, B. T. Sullivan, and M. V. Borisova, "Discrete Fourier-transform approach to inhomogeneous layer synthesis," Appl. Opt. 33, 5142-5150 (1994).
[CrossRef] [PubMed]

P. G. Verly, "Fourier-transform technique with frequency filtering for optical thin-film design," Appl. Opt. 34, 688-694 (1995).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and G. DeBell, "Application of the needle optimization technique to the design of optical coatings," Appl. Opt. 35, 5493-5508 (1996).
[CrossRef] [PubMed]

J. A. Dobrowolski, "Comparison of the Fourier transform and flip-flop thin-film synthesis methods," Appl. Opt. 33, 1966-1972 (1986).
[CrossRef]

A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, "Investigation of the effect of accumulation of thickness errors in optical coating production using broadband optical monitoring," Appl. Opt. 45, 7026-7034 (2006).
[CrossRef] [PubMed]

Comp. Maths. Math. Phys. (1)

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov, "Second order optimization methods in the synthesis of multilayer coatings," Comp. Maths. Math. Phys. 33, 1339-1352 (1993).

J. Opt. Soc. Am. (1)

Laser Focus World (1)

J. Kruschwitz, "Software tools speed optical thin-film design," Laser Focus World 39, 157-166 (2003).

Numer. Methods Programming (1)

A. Tikhonravov and M. Trubetskov, "Stabilization of computational algorithms for the characterization of thin-film coatings," Numer. Methods Programming 6, 109-117 (2005).

Opt. Photonics News (1)

J. A. Dobrowolski, "Numerical methods for optical thin films," Opt. Photonics News 8, 24-33 (1997).
[CrossRef]

Vestn. Mosk. Univ. (1)

A. V. Tikhonravov, "Synthesis of optical coatings using optimality conditions," Vestn. Mosk. Univ. , Fiz, Astron. 23, 91-93 (1982).

Other (9)

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, "Key role of the coating total optical thickness in solving design problems," in Proc. SPIE 5250, 312-321 (2004).

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1988).

S. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette, 1992).

J. A. Dobrowolski, Optical Properties of Films and Coatings (McGraw-Hill, 1994), Chap. 42, pp. 42.3-42.130.

N. Kaiser and H. K. Pulker, Optical Interference Coatings (Springer-Verlag, 2003).

P. W. Baumeister, Optical Coating Technology (SPIE Press, 2004).

A. V. Tikhonravov and M. K. Trubetskov, OptiLayer Thin Film Software, http://www.optilayer.com.

A. V. Tikhonravov, "Virtual deposition plant," in Proc. SPIE 5870, 108-120 (2005).

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Figures (8)

Fig. 1
Fig. 1

Schematic of the gradual evolution approach enhanced with the needle optimization technique.

Fig. 2
Fig. 2

Achieved merit function values versus design total optical thicknesses: Each circle corresponds to one of the designs obtained in the course of the gradual evolution procedure; the four dark triangles correspond to the designs with spectral transmittances shown in Fig. 3.

Fig. 3
Fig. 3

Spectral transmittances of several designs obtained in the course of the gradual evolution process. Principal design metrics are MF, merit function value; N, number of design layers; and TOT, design total optical thickness in nanometers.

Fig. 4
Fig. 4

Transmittance of the 93-layer design obtained with the design cleaning process from the 146-layer design with spectral characteristic depicted in Fig. 3(d).

Fig. 5
Fig. 5

Refractive index profiles of three partitioned reflector–transmitter designs. Design metrics for these designs are presented in Table 2.

Fig. 6
Fig. 6

Transmittances of two partitioned reflector–transmitter designs: solid curve, transmittance of the design with the refractive index profile a in Fig. 5; dotted curve, transmittance of the design with the refractive index profile b in Fig. 5.

Fig. 7
Fig. 7

Refractive index profiles of three hot-mirror designs. Design metrics for these designs are presented in Table 3.

Fig. 8
Fig. 8

Transmittance of the hot-mirror design with the refractive index profile shown in Fig. 7(a).

Tables (3)

Tables Icon

Table 1 Principal Design Metrics of the Ten Best Designs a

Tables Icon

Table 2 Principal Design Metrics of the Three Partitioned Reflector–Transmitter Designs with Refractive Index Profiles Shown in Fig. 5

Tables Icon

Table 3 Principal Design Metrics of the Three Hot Mirror Designs with Refractive Index Profiles Shown in Fig. 7

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

MF = { 1 L j = 1 L [ T ( λ j ) T ^ ( λ j ) Δ T j ] 2 } 1 / 2 ,

Metrics