OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 7 — Jul. 1, 1978
  • pp: 964–972

Use of Fourier coefficients in multilayer synthesis computations

J. P. Borgogno and E. Pelletier  »View Author Affiliations


JOSA, Vol. 68, Issue 7, pp. 964-972 (1978)
http://dx.doi.org/10.1364/JOSA.68.000964


View Full Text Article

Acrobat PDF (1079 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The objective of our synthesis technique is to find the refractive indices ni and the thicknesses ei of the layers in a nonabsorbing multilayer stack with prescribed properties. By introducing the constraint that each layer should have an optical thickness niei = ki λ0/4, where ki is an integer and λ0 a simple parameter as small as we wish, we have developed a calculation method for the optical properties, expressed as R/T, which is particularly advantageous. The form of the solution is a series of cosine terms. Given the reflectance R0 and the transmittance T0 of the filter to be synthesized, its R0/T0 curve is expanded in a Fourier series over a given frequency interval. The integers ki and the refractive indices of the layers are then adjusted until the coefficients of the cosine terms approximate those of the Fourier series of the filter being synthesized. The technique is demonstrated in the synthesis of a beamsplitter and a dichroic mirror.

© 1978 Optical Society of America

Citation
J. P. Borgogno and E. Pelletier, "Use of Fourier coefficients in multilayer synthesis computations," J. Opt. Soc. Am. 68, 964-972 (1978)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-68-7-964


Sort:  Author  |  Journal  |  Reset

References

  1. H. Pohlack, Jenaer Jahrb. 5, 181–221(1952); A. Vasicek, Optics of Thin Films (North-Holland, Amsterdam, 1960); Z. Knittl, Optics of Thin Films (Wiley, New York, 1976).
  2. E. Delano, J. Opt. Soc. Am. 57, 1529–1533(1967); (b) E. Delano and R. J. Pegis, in Progress in Optics, edited by E. Wolf (Wiley, New York, 1969), Vol. 7, p 67.
  3. P. H. Berning, in Physics of Thin Films, Vol. 1, edited by G. Hass (Academic London, 1963); P. Baumeister, Optical Interference Coating Technology. Course given at the University of California, Los Angeles, June 27-July 1, 1977.
  4. P. Baumeister, Opt. Acta 8, 105–109(1961).
  5. J. A. Nelder and R. Mead, Comput. J. 7, 308–313(1965).
  6. E. Ritter in Physics of Thin Films, Vol. 8, edited by G. Hass (Academic, London, 1975); E. Ritter, in Laser Handbook, edited by F. T. Arrechi and E. O. Schulz-Dubois (North-Holland, Amsterdam, 1972).
  7. C. Dufour and A. Herpin, Opt. Acta 1, 1–8(1954); H. A. Macleod, Thin Film Optical Filters (Hilger, London, 1969).
  8. A. F. Turner and P. W. Baumeister, Appl. Opt. 5, 69–76(1966).
  9. O. S. Heavens and H. M. Liddell, Appl. Opt. 5, 373–376(1966).
  10. E. Pelletier, M. Klapish, and P. Giacomo, Nouv. Rev. Opt. Appl. 2, 247–259(1971); P. Baumeister, J. Opt. Soc. Am. 48, 955–958(1958); O. S. Heavens and H. M. Liddell, Opt. Acta 15, 129–138(1968).
  11. J. P. Borgogno and E. Pelletier, Thin Solid Films 34, 357–361(1976).
  12. E. Pelletier, P. Roche, and B. Vidal, Nouv. Rev. Opt. 7, 353–362(1976).

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