Jump method for optical thin film design

Lei Li; Qiong-Hua Wang; Da-Hai Li; Hua-Rong Peng

doi:10.1364/OE.17.016920

Abstract

This paper proposes a method called Jump method for optimization of optical thin films. The method is the combination of local search strategy using modified Coordinate-Wise Algorithm and global search strategy using modified Evolutionary Algorithm. Jump method can evolve the designs of optical thin films for good performances. The design of a dielectric beam splitter and an edge filter as examples is carried out and the results indicate that Jump method is a very robust algorithm for optical thin film designs.

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References

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J. A. Dobrowolski, F. C. Ho, A. Belkind, and V. A. Koss, “Merit function for more effective thin film calculations,” Appl. Opt. 28(14), 2824–2831 (1989).
[Crossref] [PubMed]
A. V. Tikhonravov and M. K. Trubetskov, “Modern status and prospects of the development of methods of designing multilayer optical coatings,” J. Opt. Technol. 74, 845–850 (2007).
[Crossref]
J. A. Dobrowolski and R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29(19), 2876–2893 (1990).
[Crossref] [PubMed]
J. A. Dobrowolski, “Numerical methods for optical thin films,” Opt. Photonics News 8, 24–33 (1997).
[Crossref]
A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46(5), 704–710 (2007).
[Crossref] [PubMed]
T. Bäck and H. P. Schwefel, “An overview of evolution algorithms for parameter optimization,” Evol. Comput. 1(1), l–23 (1993).
[Crossref]
J. M. Yang and C. Y. Kao, “A robust evolutionary algorithm for optical thin-film designs,” Evol. Comput. 2, 978–985 (2000).
V. Yakovlev and G. Tempea, “Optimization of chirped mirrors,” Appl. Opt. 41(30), 6514–6520 (2002).
[Crossref] [PubMed]
Q. H. Wang, D. H. Li, B. J. Peng, Y. H. Tao, and W. X. Zhao, “Multi-layer dielectric color filters for optically written display using up-conversion of near infrared light,” J. Disp. Technol. 4(2), 250–253 (2008).
[Crossref]
H.-P. Schwefel, “Numerical Optimization of Computer Models,” (Wiley, New York, 1981).

2008 (1)

Q. H. Wang, D. H. Li, B. J. Peng, Y. H. Tao, and W. X. Zhao, “Multi-layer dielectric color filters for optically written display using up-conversion of near infrared light,” J. Disp. Technol. 4(2), 250–253 (2008).
[Crossref]

2007 (2)

A. V. Tikhonravov and M. K. Trubetskov, “Modern status and prospects of the development of methods of designing multilayer optical coatings,” J. Opt. Technol. 74, 845–850 (2007).
[Crossref]

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46(5), 704–710 (2007).
[Crossref] [PubMed]

2002 (1)

V. Yakovlev and G. Tempea, “Optimization of chirped mirrors,” Appl. Opt. 41(30), 6514–6520 (2002).
[Crossref] [PubMed]

2000 (1)

J. M. Yang and C. Y. Kao, “A robust evolutionary algorithm for optical thin-film designs,” Evol. Comput. 2, 978–985 (2000).

1997 (1)

J. A. Dobrowolski, “Numerical methods for optical thin films,” Opt. Photonics News 8, 24–33 (1997).
[Crossref]

1993 (1)

T. Bäck and H. P. Schwefel, “An overview of evolution algorithms for parameter optimization,” Evol. Comput. 1(1), l–23 (1993).
[Crossref]

1990 (1)

J. A. Dobrowolski and R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29(19), 2876–2893 (1990).
[Crossref] [PubMed]

1989 (1)

J. A. Dobrowolski, F. C. Ho, A. Belkind, and V. A. Koss, “Merit function for more effective thin film calculations,” Appl. Opt. 28(14), 2824–2831 (1989).
[Crossref] [PubMed]

Bäck, T.

T. Bäck and H. P. Schwefel, “An overview of evolution algorithms for parameter optimization,” Evol. Comput. 1(1), l–23 (1993).
[Crossref]

Belkind, A.

J. A. Dobrowolski, F. C. Ho, A. Belkind, and V. A. Koss, “Merit function for more effective thin film calculations,” Appl. Opt. 28(14), 2824–2831 (1989).
[Crossref] [PubMed]

DeBell, G. W.

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46(5), 704–710 (2007).
[Crossref] [PubMed]

Dobrowolski, J. A.

J. A. Dobrowolski, “Numerical methods for optical thin films,” Opt. Photonics News 8, 24–33 (1997).
[Crossref]

J. A. Dobrowolski and R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29(19), 2876–2893 (1990).
[Crossref] [PubMed]

J. A. Dobrowolski, F. C. Ho, A. Belkind, and V. A. Koss, “Merit function for more effective thin film calculations,” Appl. Opt. 28(14), 2824–2831 (1989).
[Crossref] [PubMed]

Ho, F. C.

J. A. Dobrowolski, F. C. Ho, A. Belkind, and V. A. Koss, “Merit function for more effective thin film calculations,” Appl. Opt. 28(14), 2824–2831 (1989).
[Crossref] [PubMed]

Kao, C. Y.

J. M. Yang and C. Y. Kao, “A robust evolutionary algorithm for optical thin-film designs,” Evol. Comput. 2, 978–985 (2000).

Kemp, R. A.

J. A. Dobrowolski and R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29(19), 2876–2893 (1990).
[Crossref] [PubMed]

Koss, V. A.

J. A. Dobrowolski, F. C. Ho, A. Belkind, and V. A. Koss, “Merit function for more effective thin film calculations,” Appl. Opt. 28(14), 2824–2831 (1989).
[Crossref] [PubMed]

Li, D. H.

Q. H. Wang, D. H. Li, B. J. Peng, Y. H. Tao, and W. X. Zhao, “Multi-layer dielectric color filters for optically written display using up-conversion of near infrared light,” J. Disp. Technol. 4(2), 250–253 (2008).
[Crossref]

Peng, B. J.

Q. H. Wang, D. H. Li, B. J. Peng, Y. H. Tao, and W. X. Zhao, “Multi-layer dielectric color filters for optically written display using up-conversion of near infrared light,” J. Disp. Technol. 4(2), 250–253 (2008).
[Crossref]

Schwefel, H. P.

T. Bäck and H. P. Schwefel, “An overview of evolution algorithms for parameter optimization,” Evol. Comput. 1(1), l–23 (1993).
[Crossref]

Tao, Y. H.

Q. H. Wang, D. H. Li, B. J. Peng, Y. H. Tao, and W. X. Zhao, “Multi-layer dielectric color filters for optically written display using up-conversion of near infrared light,” J. Disp. Technol. 4(2), 250–253 (2008).
[Crossref]

Wang, Q. H.

Q. H. Wang, D. H. Li, B. J. Peng, Y. H. Tao, and W. X. Zhao, “Multi-layer dielectric color filters for optically written display using up-conversion of near infrared light,” J. Disp. Technol. 4(2), 250–253 (2008).
[Crossref]

Yakovlev, V.

V. Yakovlev and G. Tempea, “Optimization of chirped mirrors,” Appl. Opt. 41(30), 6514–6520 (2002).
[Crossref] [PubMed]

Yang, J. M.

J. M. Yang and C. Y. Kao, “A robust evolutionary algorithm for optical thin-film designs,” Evol. Comput. 2, 978–985 (2000).

Zhao, W. X.

Q. H. Wang, D. H. Li, B. J. Peng, Y. H. Tao, and W. X. Zhao, “Multi-layer dielectric color filters for optically written display using up-conversion of near infrared light,” J. Disp. Technol. 4(2), 250–253 (2008).
[Crossref]

Appl. Opt. (4)

J. A. Dobrowolski, F. C. Ho, A. Belkind, and V. A. Koss, “Merit function for more effective thin film calculations,” Appl. Opt. 28(14), 2824–2831 (1989).
[Crossref] [PubMed]

J. A. Dobrowolski and R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29(19), 2876–2893 (1990).
[Crossref] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46(5), 704–710 (2007).
[Crossref] [PubMed]

V. Yakovlev and G. Tempea, “Optimization of chirped mirrors,” Appl. Opt. 41(30), 6514–6520 (2002).
[Crossref] [PubMed]

Evol. Comput. (2)

T. Bäck and H. P. Schwefel, “An overview of evolution algorithms for parameter optimization,” Evol. Comput. 1(1), l–23 (1993).
[Crossref]

J. M. Yang and C. Y. Kao, “A robust evolutionary algorithm for optical thin-film designs,” Evol. Comput. 2, 978–985 (2000).

J. Disp. Technol. (1)

Q. H. Wang, D. H. Li, B. J. Peng, Y. H. Tao, and W. X. Zhao, “Multi-layer dielectric color filters for optically written display using up-conversion of near infrared light,” J. Disp. Technol. 4(2), 250–253 (2008).
[Crossref]

J. Opt. Technol. (1)

A. V. Tikhonravov and M. K. Trubetskov, “Modern status and prospects of the development of methods of designing multilayer optical coatings,” J. Opt. Technol. 74, 845–850 (2007).
[Crossref]

Opt. Photonics News (1)

J. A. Dobrowolski, “Numerical methods for optical thin films,” Opt. Photonics News 8, 24–33 (1997).
[Crossref]

Other (1)

H.-P. Schwefel, “Numerical Optimization of Computer Models,” (Wiley, New York, 1981).

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Fig. 1

The structure of the thin film

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Fig. 2

Flow chart of Jump method.

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Fig. 3

The wavelength-dependent transmittance of the dielectric beam splitter for different number of layers using Jump method.

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Fig. 4

The transmittance of the edge filter using Jump method.

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Tables (3)

Table 1 Parameters of Jump method used for the simulation of the dielectric beam splitter.

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Table 2 Some parameters of the dielectric beam splitter using Jump method.

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Table 3 Some parameters of the edge filter using Jump method.

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Equations (12)

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

F = {\sum_{K = 1}^{W} {{[R (η, d, λ_{K}) - R (λ_{K})]}^{2}}}^{1 / 2},

T^{'} = T (i f f^{'} < f),

T^{'} = T + 1 (i f f^{'} > f),

d_{i}^{'} = d_{i} + u (i f T^{'} = 0),

d_{i}^{'} = d_{i} - u (i f T^{'} = 1),

u^{'} = C u

d_{i}^{c} = d_{i}^{a} (w i t h t h e p r o b a b i l i t y P_{c}),

d_{i}^{c} = d_{i}^{b} (w i t h t h e p r o b a b i l i t y 1 - P_{c}),

v_{i}^{c} = v_{i}^{a} \exp [τ N (0, 1) + τ^{'} N_{i} (0, 1)],

d_{i}^{c} = d_{i}^{a} + v_{i}^{c} N_{i} (0, 1),

τ = {(\sqrt{2 n})}^{- 1},

τ^{'} = {(\sqrt{2 \sqrt{n}})}^{- 1} .

Procedure	Parameters
Modified Coordinate-Wise Procedure	C = 0.97, u = 2 nm.
Modified Evolutionary Procedure	P_c =0.4, v = 0.05 nm, n = 10.

Number of layers	Total thickness (nm)	Merit function
11	440.8	0.3571
17	608.1	0.3410
24	831.9	0.3379

Procedure	Parameters
Modified Coordinate-Wise Procedure	C = 0.97, u = 2 nm.
Modified Evolutionary Procedure	P_c =0.4, v = 0.05 nm, n = 10.

Number of layers	Total thickness (nm)	Merit function
11	440.8	0.3571
17	608.1	0.3410
24	831.9	0.3379

Abstract

References

2008 (1)

2007 (2)

2002 (1)

2000 (1)

1997 (1)

1993 (1)

1990 (1)

1989 (1)

Bäck, T.

Belkind, A.

DeBell, G. W.

Dobrowolski, J. A.

Ho, F. C.

Kao, C. Y.

Kemp, R. A.

Koss, V. A.

Li, D. H.

Peng, B. J.

Schwefel, H. P.

Tao, Y. H.

Tempea, G.

Tikhonravov, A. V.

Trubetskov, M. K.

Wang, Q. H.

Yakovlev, V.

Yang, J. M.

Zhao, W. X.

Appl. Opt. (4)

Evol. Comput. (2)

J. Disp. Technol. (1)

J. Opt. Technol. (1)

Opt. Photonics News (1)

Other (1)

Cited By

Figures (4)

Tables (3)

Equations (12)

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