Abstract

Refinement techniques usually calculate an optimized local solution, which is strongly dependent on the initial formula used for the thin film design. In the present study, a clustering global optimization method is used which can iteratively change this initial formula, thereby progressing further than in the case of local optimization techniques. A wide panel of local solutions is found using this procedure, resulting in a large range of optical thicknesses. The efficiency of this technique is illustrated by two thin film design problems, in particular an infrared antireflection coating, and a solar-selective absorber coating.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Baumeister, “Design of multilayer filters by successive approximations,” J. Opt. Soc. Am. 48(12), 955–957 (1958).
    [CrossRef]
  2. C. J. Laan, H. J. Frankena, “Fast computation method for derivatives of multilayer stack reflectance,” Appl. Opt. 17(4), 538–541 (1978).
    [CrossRef] [PubMed]
  3. J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29(19), 2876–2893 (1990).
    [CrossRef] [PubMed]
  4. J. A. Dobrowolski, “Automatic refinement of optical multilayer assemblies,” J. Opt. Soc. Am. 51, 1475 (1961).
  5. Sh. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems, Ed Frontieres, Gif sur-Yvette, France (1992).
  6. A. V. Tikhonravov, M. K. Trubetskov, G. W. Debell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35(28), 5493–5508 (1996).
    [CrossRef] [PubMed]
  7. A. V. Tikhonravov, M. K. Trubetskov, “Modern design tools and a new paradigm in optical coating design,” Appl. Opt. 51(30), 7319–7332 (2012).
    [CrossRef] [PubMed]
  8. W. H. Southwell, “Flip-flop coating synthesis revisited,” Appl. Opt. 53(4), A179–A185 (2014).
    [CrossRef] [PubMed]
  9. S. Larouche, L. Martinu, “Step method: a new synthesis method for the design of optical filters with intermediate refractive indices,” Appl. Opt. 47(24), 4321–4330 (2008).
    [CrossRef] [PubMed]
  10. P. G. Verly, “Fourier transform technique with refinement in the frequency domain for the synthesis of optical thin films,” Appl. Opt. 35(25), 5148–5154 (1996).
    [CrossRef] [PubMed]
  11. K. Hendrix, J. Oliver, “Optical interference coatings design contest 2010: solar absorber and Fabry-Perot etalon,” Appl. Opt. 50(9), C286–C300 (2011).
    [CrossRef] [PubMed]
  12. S. F. Masri, G. A. Bekey, F. B. Safford, “A global optimization algorithm using adaptive random search,” Appl. Math. Comput. 7(4), 353–375 (1980).
    [CrossRef]
  13. R. Fletcher, Practical Methods of Optimization, Second Edition (John Wiley & Sons, 1987).
  14. J. A. Aguilera, J. Aguilera, P. Baumeister, A. Bloom, D. Coursen, J. A. Dobrowolski, F. T. Goldstein, D. E. Gustafson, R. A. Kemp, “Antireflection coatings for germanium IR optics: a comparison of numerical design methods,” Appl. Opt. 27(14), 2832–2840 (1988).
    [CrossRef] [PubMed]
  15. C. G. E. Boender, A. H. G. Rinnooy Kan, L. Strougie, G. T. Timmer, “A stochastic method for global optimization,” Math. Program. 22(1), 125–140 (1982).
    [CrossRef]
  16. T. Csendes, “Nonlinear parameter estimation by global optimization - efficiency and reliability,” Acta Cybernetica 8, 361–370 (1989).
  17. T. Csendes, L. Pál, J. Oscar, H. Sendín, J. R. Banga, “The global optimization method revisited,” Optim. Lett. 2(4), 445–454 (2088).
    [CrossRef]
  18. M. Mongeau, H. Karsenty, V. Rouzé, J.-B. Hiriart-Urruty, “Comparison of public-domain software for black-box global optimization,” Optim. Methods Softw. 13(3), 203–226 (2000).
    [CrossRef]
  19. http://link.springer.com/content/pdf/10.1007%2Fs11590-007-0072-3.pdf
  20. J. R. Banga, C. G. Moles, and A. A. Alonso, “Global optimization of bioprocesses using stochastic and hybrid methods,” in C.A. Floudas and P.M. Pardalos, eds., Frontiers in Global Optimization (Springer, (2003), pp. 45–70.
  21. C. G. Moles, J. R. Banga, K. Keller, “Solving non convex climate control problems: pitfalls and algorithm performances,” Appl. Soft Comput. 5(1), 35–44 (2004).
    [CrossRef]
  22. C. G. Moles, G. Gutierrez, A. A. Alonso, J. R. Banga, “Integrated process design and control via global optimization -A wastewater treatment plant case study,” Chem. Eng. Res. Des. 81(5), 507–517 (2003).
    [CrossRef]
  23. http://www.inf.u-szeged.hu/~csendes/index_en.html
  24. W. C. Davidon, “Variable metric method for minimization,” SIAM J. Optim. 1(1), 1–17 (1991).
    [CrossRef]
  25. T. E. Shoup and F. Mistree, Optimization Methods with Applications to Personal Computers (Springer Verlag, 1985), pp. 110–118.

2088 (1)

T. Csendes, L. Pál, J. Oscar, H. Sendín, J. R. Banga, “The global optimization method revisited,” Optim. Lett. 2(4), 445–454 (2088).
[CrossRef]

2014 (1)

2012 (1)

2011 (1)

2008 (1)

2004 (1)

C. G. Moles, J. R. Banga, K. Keller, “Solving non convex climate control problems: pitfalls and algorithm performances,” Appl. Soft Comput. 5(1), 35–44 (2004).
[CrossRef]

2003 (1)

C. G. Moles, G. Gutierrez, A. A. Alonso, J. R. Banga, “Integrated process design and control via global optimization -A wastewater treatment plant case study,” Chem. Eng. Res. Des. 81(5), 507–517 (2003).
[CrossRef]

2000 (1)

M. Mongeau, H. Karsenty, V. Rouzé, J.-B. Hiriart-Urruty, “Comparison of public-domain software for black-box global optimization,” Optim. Methods Softw. 13(3), 203–226 (2000).
[CrossRef]

1996 (2)

1991 (1)

W. C. Davidon, “Variable metric method for minimization,” SIAM J. Optim. 1(1), 1–17 (1991).
[CrossRef]

1990 (1)

1989 (1)

T. Csendes, “Nonlinear parameter estimation by global optimization - efficiency and reliability,” Acta Cybernetica 8, 361–370 (1989).

1988 (1)

1982 (1)

C. G. E. Boender, A. H. G. Rinnooy Kan, L. Strougie, G. T. Timmer, “A stochastic method for global optimization,” Math. Program. 22(1), 125–140 (1982).
[CrossRef]

1980 (1)

S. F. Masri, G. A. Bekey, F. B. Safford, “A global optimization algorithm using adaptive random search,” Appl. Math. Comput. 7(4), 353–375 (1980).
[CrossRef]

1978 (1)

1961 (1)

J. A. Dobrowolski, “Automatic refinement of optical multilayer assemblies,” J. Opt. Soc. Am. 51, 1475 (1961).

1958 (1)

Aguilera, J.

Aguilera, J. A.

Alonso, A. A.

C. G. Moles, G. Gutierrez, A. A. Alonso, J. R. Banga, “Integrated process design and control via global optimization -A wastewater treatment plant case study,” Chem. Eng. Res. Des. 81(5), 507–517 (2003).
[CrossRef]

Banga, J. R.

T. Csendes, L. Pál, J. Oscar, H. Sendín, J. R. Banga, “The global optimization method revisited,” Optim. Lett. 2(4), 445–454 (2088).
[CrossRef]

C. G. Moles, J. R. Banga, K. Keller, “Solving non convex climate control problems: pitfalls and algorithm performances,” Appl. Soft Comput. 5(1), 35–44 (2004).
[CrossRef]

C. G. Moles, G. Gutierrez, A. A. Alonso, J. R. Banga, “Integrated process design and control via global optimization -A wastewater treatment plant case study,” Chem. Eng. Res. Des. 81(5), 507–517 (2003).
[CrossRef]

Baumeister, P.

Bekey, G. A.

S. F. Masri, G. A. Bekey, F. B. Safford, “A global optimization algorithm using adaptive random search,” Appl. Math. Comput. 7(4), 353–375 (1980).
[CrossRef]

Bloom, A.

Boender, C. G. E.

C. G. E. Boender, A. H. G. Rinnooy Kan, L. Strougie, G. T. Timmer, “A stochastic method for global optimization,” Math. Program. 22(1), 125–140 (1982).
[CrossRef]

Coursen, D.

Csendes, T.

T. Csendes, L. Pál, J. Oscar, H. Sendín, J. R. Banga, “The global optimization method revisited,” Optim. Lett. 2(4), 445–454 (2088).
[CrossRef]

T. Csendes, “Nonlinear parameter estimation by global optimization - efficiency and reliability,” Acta Cybernetica 8, 361–370 (1989).

Davidon, W. C.

W. C. Davidon, “Variable metric method for minimization,” SIAM J. Optim. 1(1), 1–17 (1991).
[CrossRef]

Debell, G. W.

Dobrowolski, J. A.

Frankena, H. J.

Goldstein, F. T.

Gustafson, D. E.

Gutierrez, G.

C. G. Moles, G. Gutierrez, A. A. Alonso, J. R. Banga, “Integrated process design and control via global optimization -A wastewater treatment plant case study,” Chem. Eng. Res. Des. 81(5), 507–517 (2003).
[CrossRef]

Hendrix, K.

Hiriart-Urruty, J.-B.

M. Mongeau, H. Karsenty, V. Rouzé, J.-B. Hiriart-Urruty, “Comparison of public-domain software for black-box global optimization,” Optim. Methods Softw. 13(3), 203–226 (2000).
[CrossRef]

Karsenty, H.

M. Mongeau, H. Karsenty, V. Rouzé, J.-B. Hiriart-Urruty, “Comparison of public-domain software for black-box global optimization,” Optim. Methods Softw. 13(3), 203–226 (2000).
[CrossRef]

Keller, K.

C. G. Moles, J. R. Banga, K. Keller, “Solving non convex climate control problems: pitfalls and algorithm performances,” Appl. Soft Comput. 5(1), 35–44 (2004).
[CrossRef]

Kemp, R. A.

Laan, C. J.

Larouche, S.

Martinu, L.

Masri, S. F.

S. F. Masri, G. A. Bekey, F. B. Safford, “A global optimization algorithm using adaptive random search,” Appl. Math. Comput. 7(4), 353–375 (1980).
[CrossRef]

Moles, C. G.

C. G. Moles, J. R. Banga, K. Keller, “Solving non convex climate control problems: pitfalls and algorithm performances,” Appl. Soft Comput. 5(1), 35–44 (2004).
[CrossRef]

C. G. Moles, G. Gutierrez, A. A. Alonso, J. R. Banga, “Integrated process design and control via global optimization -A wastewater treatment plant case study,” Chem. Eng. Res. Des. 81(5), 507–517 (2003).
[CrossRef]

Mongeau, M.

M. Mongeau, H. Karsenty, V. Rouzé, J.-B. Hiriart-Urruty, “Comparison of public-domain software for black-box global optimization,” Optim. Methods Softw. 13(3), 203–226 (2000).
[CrossRef]

Oliver, J.

Oscar, J.

T. Csendes, L. Pál, J. Oscar, H. Sendín, J. R. Banga, “The global optimization method revisited,” Optim. Lett. 2(4), 445–454 (2088).
[CrossRef]

Pál, L.

T. Csendes, L. Pál, J. Oscar, H. Sendín, J. R. Banga, “The global optimization method revisited,” Optim. Lett. 2(4), 445–454 (2088).
[CrossRef]

Rinnooy Kan, A. H. G.

C. G. E. Boender, A. H. G. Rinnooy Kan, L. Strougie, G. T. Timmer, “A stochastic method for global optimization,” Math. Program. 22(1), 125–140 (1982).
[CrossRef]

Rouzé, V.

M. Mongeau, H. Karsenty, V. Rouzé, J.-B. Hiriart-Urruty, “Comparison of public-domain software for black-box global optimization,” Optim. Methods Softw. 13(3), 203–226 (2000).
[CrossRef]

Safford, F. B.

S. F. Masri, G. A. Bekey, F. B. Safford, “A global optimization algorithm using adaptive random search,” Appl. Math. Comput. 7(4), 353–375 (1980).
[CrossRef]

Sendín, H.

T. Csendes, L. Pál, J. Oscar, H. Sendín, J. R. Banga, “The global optimization method revisited,” Optim. Lett. 2(4), 445–454 (2088).
[CrossRef]

Southwell, W. H.

Strougie, L.

C. G. E. Boender, A. H. G. Rinnooy Kan, L. Strougie, G. T. Timmer, “A stochastic method for global optimization,” Math. Program. 22(1), 125–140 (1982).
[CrossRef]

Tikhonravov, A. V.

Timmer, G. T.

C. G. E. Boender, A. H. G. Rinnooy Kan, L. Strougie, G. T. Timmer, “A stochastic method for global optimization,” Math. Program. 22(1), 125–140 (1982).
[CrossRef]

Trubetskov, M. K.

Verly, P. G.

Acta Cybernetica (1)

T. Csendes, “Nonlinear parameter estimation by global optimization - efficiency and reliability,” Acta Cybernetica 8, 361–370 (1989).

Appl. Math. Comput. (1)

S. F. Masri, G. A. Bekey, F. B. Safford, “A global optimization algorithm using adaptive random search,” Appl. Math. Comput. 7(4), 353–375 (1980).
[CrossRef]

Appl. Opt. (9)

C. J. Laan, H. J. Frankena, “Fast computation method for derivatives of multilayer stack reflectance,” Appl. Opt. 17(4), 538–541 (1978).
[CrossRef] [PubMed]

J. A. Aguilera, J. Aguilera, P. Baumeister, A. Bloom, D. Coursen, J. A. Dobrowolski, F. T. Goldstein, D. E. Gustafson, R. A. Kemp, “Antireflection coatings for germanium IR optics: a comparison of numerical design methods,” Appl. Opt. 27(14), 2832–2840 (1988).
[CrossRef] [PubMed]

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

P. G. Verly, “Fourier transform technique with refinement in the frequency domain for the synthesis of optical thin films,” Appl. Opt. 35(25), 5148–5154 (1996).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, G. W. Debell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35(28), 5493–5508 (1996).
[CrossRef] [PubMed]

S. Larouche, L. Martinu, “Step method: a new synthesis method for the design of optical filters with intermediate refractive indices,” Appl. Opt. 47(24), 4321–4330 (2008).
[CrossRef] [PubMed]

K. Hendrix, J. Oliver, “Optical interference coatings design contest 2010: solar absorber and Fabry-Perot etalon,” Appl. Opt. 50(9), C286–C300 (2011).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, “Modern design tools and a new paradigm in optical coating design,” Appl. Opt. 51(30), 7319–7332 (2012).
[CrossRef] [PubMed]

W. H. Southwell, “Flip-flop coating synthesis revisited,” Appl. Opt. 53(4), A179–A185 (2014).
[CrossRef] [PubMed]

Appl. Soft Comput. (1)

C. G. Moles, J. R. Banga, K. Keller, “Solving non convex climate control problems: pitfalls and algorithm performances,” Appl. Soft Comput. 5(1), 35–44 (2004).
[CrossRef]

Chem. Eng. Res. Des. (1)

C. G. Moles, G. Gutierrez, A. A. Alonso, J. R. Banga, “Integrated process design and control via global optimization -A wastewater treatment plant case study,” Chem. Eng. Res. Des. 81(5), 507–517 (2003).
[CrossRef]

J. Opt. Soc. Am. (2)

J. A. Dobrowolski, “Automatic refinement of optical multilayer assemblies,” J. Opt. Soc. Am. 51, 1475 (1961).

P. Baumeister, “Design of multilayer filters by successive approximations,” J. Opt. Soc. Am. 48(12), 955–957 (1958).
[CrossRef]

Math. Program. (1)

C. G. E. Boender, A. H. G. Rinnooy Kan, L. Strougie, G. T. Timmer, “A stochastic method for global optimization,” Math. Program. 22(1), 125–140 (1982).
[CrossRef]

Optim. Lett. (1)

T. Csendes, L. Pál, J. Oscar, H. Sendín, J. R. Banga, “The global optimization method revisited,” Optim. Lett. 2(4), 445–454 (2088).
[CrossRef]

Optim. Methods Softw. (1)

M. Mongeau, H. Karsenty, V. Rouzé, J.-B. Hiriart-Urruty, “Comparison of public-domain software for black-box global optimization,” Optim. Methods Softw. 13(3), 203–226 (2000).
[CrossRef]

SIAM J. Optim. (1)

W. C. Davidon, “Variable metric method for minimization,” SIAM J. Optim. 1(1), 1–17 (1991).
[CrossRef]

Other (6)

T. E. Shoup and F. Mistree, Optimization Methods with Applications to Personal Computers (Springer Verlag, 1985), pp. 110–118.

R. Fletcher, Practical Methods of Optimization, Second Edition (John Wiley & Sons, 1987).

http://link.springer.com/content/pdf/10.1007%2Fs11590-007-0072-3.pdf

J. R. Banga, C. G. Moles, and A. A. Alonso, “Global optimization of bioprocesses using stochastic and hybrid methods,” in C.A. Floudas and P.M. Pardalos, eds., Frontiers in Global Optimization (Springer, (2003), pp. 45–70.

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

http://www.inf.u-szeged.hu/~csendes/index_en.html

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Reflectance vs wavelength (left), and refractive index profile vs optical thickness (right), for six thin-film designs. (a) DesA, MF = 10.58, initial design given by Baumeister. (b) DesB, MF = 0.94, resulting from the refinement of DesA using Hooke and Jeeves pattern search optimization procedure. (c) DesC, MF = 1.12, first local minimum using DesA as starting design. (d) DesD, MF = 0.55, best solution with DesA as starting design. (e) DesE, MF = 0.61, and (f) DesF, MF = 0.70, compromise between a good MF and a relatively small OT.Nota: DesA and DesB formula are given by [14], DesC, DesD, DesE, and DesF are calculated using CGO.

Fig. 2
Fig. 2

Merit Function as a function of the thicknesses of layers 20 and 21.

Fig. 3
Fig. 3

Absorbance vs wavenumber (cm−1) given by the winning design. M F s o l a r a b s o r b a n c e > 94 % , M F b b e m i t t a n c e < 10 % , with a minimal number of layers (6) and minimal total thickness (265 nm).

Tables (2)

Tables Icon

Table 1 Ten 6-layer Designs, Each Having a Total Thickness ≤ 320 nm, M F s o l a r a b s o r b a n c e > 94 % , and M F b b e m i t t a n c e < 10 %

Tables Icon

Table 2 Seven- and eight-layer designs with a total thickness ≤ 230 nm, M F s o l a r a b s o r b a n c e > 94 % , and M F b b e m i t t a n c e < 10 %

Equations (6)

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

M F ( d 1 , ... d n ) = [ 1 N d a t a i = 1 N d a t a [ O P i T g t O P i C a l ] 2 Δ i ] 1 / 2
M F ( d 1 , ... d ) n = 100 [ 1 N d a t a i = 1 N d a t a R i 2 ( λ i ) ] 1 / 2
L B ( i ) = max [ 0 ; d i 1.3 4 n i ] U B ( i ) = d i + 1.3 4 n i
M F = M F s o l a r a b s o r b a n c e M F b b e m i t t a n c e
M F s o l a r a b s o r b a n c e = 1 2480 σ i 35720 A S T M 173 ( σ i ) σ i 2 2480 σ i 35720 A S T M 173 ( σ i ) [ A ( σ i ) σ i 2 ] ,
M F e m i t t a n c e = 1 400 σ i 35720 B B 450 C ( σ i ) σ i 2 400 σ i 35720 B B 450 C ( σ i ) [ A ( σ i ) σ i 2 ] ,

Metrics