OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 23 — Aug. 10, 2006
  • pp: 5910–5922

Global optimization and modeling techniques for planar multilayered dielectric structures

R. F. Oulton and C. S. Adjiman  »View Author Affiliations

Applied Optics, Vol. 45, Issue 23, pp. 5910-5922 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (623 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a multilevel global optimization strategy for synthesizing planar multilayered dielectric structures. A low discrepancy sequence of sample points with uniform variable space coverage allows a global-level search while systematic refinement using gradient-based techniques identifies optima at the local level. Since efficient local optimization is important for this method, a fast calculation approach based on mode matching is presented; this also facilitates the compact derivation of analytical gradients. The approach is compared with genetic and simulated annealing algorithms through an antireflection coating design. The method proves to be competitive in terms of its performance, nonadaptive algorithm, and ability to track local solutions.

© 2006 Optical Society of America

OCIS Codes
(230.4170) Optical devices : Multilayers
(310.0310) Thin films : Thin films

Original Manuscript: December 15, 2005
Revised Manuscript: February 13, 2006
Manuscript Accepted: March 6, 2006

R. F. Oulton and C. S. Adjiman, "Global optimization and modeling techniques for planar multilayered dielectric structures," Appl. Opt. 45, 5910-5922 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Born and E. Wolf, Principles of Optics, 6th (revised) ed. (Cambridge U. Press, 1999).
  2. H. A. McLeod, Thin Film Optical Filters, 3rd ed. (Adam Hilger, 2001). [CrossRef]
  3. J. A. Dobrowolski and R. A. Kemp, "Refinement of optical multilayer systems with different optimization procedures," Appl. Opt. 29, 2876-2892 (1990). [CrossRef] [PubMed]
  4. E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, "Optimization of multilayer integrated optics waveguides," J. Lightwave Technol. 12, 512-517 (1994). [CrossRef]
  5. S. Martin, J. Rivory, and M. Schoenauer, "Synthesis of optical multilayer systems using genetic algorithms," Appl. Opt. 34, 2247-2254 (1995). [CrossRef] [PubMed]
  6. V. Yakovelev and G. Tempea, "Optimization of chirped mirrors," Appl. Opt. 41, 6514-6520 (2002). [CrossRef]
  7. C.-L. Lee and Y. Lai, "Optical narrowband dispersionless fiber Bragg grating filter with short grating length and smooth dispersion profile," Opt. Commun. 235, 99-106 (2004). [CrossRef]
  8. T. Boudet, P. Chaton, L. Herault, G. Gonon, L. Jouanet, and P. Keller, "Thin-film designs by simulated annealing," Appl. Opt. 35, 6219-6222 (1996). [CrossRef] [PubMed]
  9. L. Liberti and S. Kucherenko, "Comparison of deterministic and stochastic approaches to global optimization," Int. Trans. Oper. Res. 12, 263-281 (2005). [CrossRef]
  10. J. H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, 1975).
  11. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983). [CrossRef] [PubMed]
  12. A. H. G. Rinnooy Kan and G. T. Timmer, "Stochastic global optimisation methods, part i, clustering methods," Math. Program. 39, 27-56 (1987). [CrossRef]
  13. A. H. G. Rinnooy Kan and G. T. Timmer, "Stochastic global optimisation methods, part ii, multilevel methods," Math. Program. 39, 57-78 (1987). [CrossRef]
  14. S. Kucherenko and Y. Sytsko, "Application of deterministic low-discrepancy sequences in global optimization," Comput. Optim. Appl. 30, 297-318 (2005). [CrossRef]
  15. I. M. Sobol, "On the distribution of points in a cube and the approximate evaluation of integrals," Comput. Math. Phys. 7, 86-112 (1992). [CrossRef]
  16. P. Bratley, B. L. Fox, and H. Neiderreiter, "Implementation and tests of low discrepancy sequences," ACM Trans. Model. Comput. Simul. 2, 195-213 (1992). [CrossRef]
  17. P. J. B. Clarricoats and K. R. Slinn, "Numerical method for the solution of waveguide discontinuity problems," Electron. Lett. 2, 226-239 (1966). [CrossRef]
  18. P. J. B. Clarricoats and K. R. Slinn, "Numerical solution of waveguide discontinuity problems," Proc. IEEE 114, 878-886 (1967).
  19. A. Wexler, "Solution of waveguide discontinuities by modal analysis," IEEE Trans. MTT 9, 508-516 (1967). [CrossRef]
  20. K.-O. Peng and M. R. de la Fonteijne, "Derivatives of transmittance and reflectance for an absorbing multilayer stack," Appl. Opt. 24, 501-503 (1985). [CrossRef] [PubMed]
  21. T. I. Oh, "Broadband AR coatings on germanium substrates using ion assisted deposition," Appl. Opt. 27, 4255-4259 (1988). [CrossRef] [PubMed]
  22. J. H. Holton, "On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals," Numer. Math. 2, 84-90 (1960). [CrossRef]
  23. H. Niederreiter, "Point sets and sequences with small discrepancy," Monatsh. Math. 104, 273-337 (1987). [CrossRef]
  24. R. Fletcher and M. J. D. Powell, "A rapidly convergent descent method for minimization," Comput. J. 6, 163-168 (1963).
  25. T. F. Coleman and Y. Li, "An interior, trust region approach for non-linear minimization subject to bounds," SIAM J. Optim. 6, 418-445 (1996). [CrossRef]
  26. J. A. Dobrowolski, A. V. Tikhonaravov, M. K. Trubetskov, B. T. Sullivan, and P. G. Verly, "Refinement of optical multilayer systems with different optimization procedures," Appl. Opt. 35, 644-658 (1996). [CrossRef] [PubMed]
  27. A. V. Tikhonaravov and J. A. Dobrowolski, "A new, quasi-optimal synthesis method for antireflection coatings," Appl. Opt. 32, 4265-4275 (1993). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited