OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 13 — May. 1, 2008
  • pp: C124–C130

Estimation of the average residual reflectance of broadband antireflection coatings

Alexander V. Tikhonravov, Michael K. Trubetskov, Tatiana V. Amotchkina, and J. A. Dobrowolski  »View Author Affiliations

Applied Optics, Vol. 47, Issue 13, pp. C124-C130 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (575 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We deal with optimal two-material antireflection (AR) coatings for the visible and adjacent spectral regions. It has been shown before that, for a given set of input parameters (refractive indices of the substrate, ambient medium and high- and low-index coating materials, and for a given spectral width of the AR coating), such designs consist of one or more clusters of layers of approximately constant optical thickness and number of layers. We show that, through the analysis of many different optimal coatings, it is possible to derive two parameters for a simple empirical expression that relates the residual average reflectance in the AR region to the number of clusters. These parameters are given for all possible combinations of relative spectral bandwidth equal to 2, 3, and 4; low-index to ambient-medium index ratio equal to 1.38 and 1.45; and high-to-low index ratio equal to 1.4, 1.5, and 1.7. The agreement between the numerically and the empirically calculated values of residual average reflectance is excellent. From the information presented the optical thin-film designer can quickly calculate the required number of layers and the overall optical thickness of an AR coating having the desired achievable residual average reflectance.

© 2008 Optical Society of America

OCIS Codes
(310.1210) Thin films : Antireflection coatings
(310.6805) Thin films : Theory and design

Original Manuscript: September 18, 2007
Revised Manuscript: October 23, 2007
Manuscript Accepted: October 24, 2007
Published: November 29, 2007

Alexander V. Tikhonravov, Michael K. Trubetskov, Tatiana V. Amotchkina, and J. A. Dobrowolski, "Estimation of the average residual reflectance of broadband antireflection coatings," Appl. Opt. 47, C124-C130 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. N. Kaiser, "Optical coatings road-map," presented at the International Workshop on Optical Coatings, Ottawa, Canada, 11 May 2006.
  2. I. V. Grebenshchikov, L. G. Vlasov, B. S. Neporent, and N. V. Suikovskaya, Antireflection Coating of Optical Surfaces (State Publishers of Technical and Theoretical Literature, 1946) (in Russian).
  3. J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, and P. G. Verly, "Optimal single-band normal-incidence antireflection coatings," Appl. Opt. 35, 644-658 (1996). [CrossRef] [PubMed]
  4. J. A. Dobrowolski, D. Poitras, P. Ma, H. Vakil, and M. Acree, "Toward perfect antireflection coatings: numerical investigation," Appl. Opt. 41, 3075-3083 (2002). [CrossRef] [PubMed]
  5. D. Poitras and J. A. Dobrowolski, "Toward perfect antireflection coatings. 2. Theory," Appl. Opt. 43, 1286-1295 (2004). [CrossRef] [PubMed]
  6. J. A. Dobrowolski, Y. Guo, T. Tiwald, P. Ma, and D. Poitras, "Toward perfect antireflection coatings. 3. Experimental results obtained with the use of Reststrahlen materials," Appl. Opt. 45, 1555-1562 (2006). [CrossRef] [PubMed]
  7. U. B.Schulz, U. B. Schallenberg, and N. Kaiser, "Symmetrical periods in antireflective coatings for plastic optics," Appl. Opt. 42, 1346-1351 (2003). [CrossRef] [PubMed]
  8. U. B. Schallenberg, "Antireflection design concepts with equivalent layers," Appl. Opt. 45, 1507-1514 (2006). [CrossRef] [PubMed]
  9. A. V. Tikhonravov, "Some theoretical aspects of thin film optics and their applications," Appl. Opt. 32, 5417-5426 (1993). [CrossRef] [PubMed]
  10. 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]
  11. A. V. Tikhonravov and J. A. Dobrowolski, "Quasi-optimal synthesis for antireflection coatings: a new method," Appl. Opt. 32, 4265-4275 (1993). [CrossRef] [PubMed]
  12. A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, "Application of the needle optimization technique to the design of optical coatings," Appl. Opt. 35, 5493-5508 (1996). [CrossRef] [PubMed]
  13. A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, "Optical coating design approaches based on the needle optimization technique," Appl. Opt. 46, 704-710 (2007). [CrossRef] [PubMed]
  14. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1988).
  15. J. A. Dobrowolski, "Comparison of the Fourier transform and flip-flop thin-film synthesis methods," Appl. Opt. 25, 1966-1972 (1986). [CrossRef] [PubMed]
  16. 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," Proc. SPIE 5250, 312-321 (2004). [CrossRef]
  17. R. Willey, "Predicting achievable design performance of broadband antireflection coatings," Appl. Opt. 32, 5447-5451 (1993). [CrossRef] [PubMed]
  18. A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and S. A. Yanshin, "Structural properties of antireflection coatings," in Proceedings of Optical Interference Coatings on CD-ROM, presentation WB5 (Optical Society of America, 2007).
  19. R. Willey, "Refined criteria for estimating limits of broad-band AR coatings," Proc. SPIE 5250, 393-399 (2004). [CrossRef]
  20. T. V. Amotchkina, "Analytical properties of spectral characteristics of antireflection optical coatings," Vestnik MGU Ser. 3 Fiz. Astron. (posted 16 July 2007, in press).
  21. A. V. Tikhonravov, P. W. Baumeister, and K. V. Popov, "Phase properties of multilayers," Appl. Opt. 36, 4382-4392 (1997). [CrossRef] [PubMed]

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited