Abstract

The objective of our synthesis technique is to find the refractive indices <i>n</i><sub>i</sub> and the thicknesses <i>e</i><sub>i</sub> of the layers in a nonabsorbing multilayer stack with prescribed properties. By introducing the constraint that each layer should have an optical thickness <i>n</i><sub>i</sub><i>e</i><sub>i</sub> = <i>k</i><sub>i</sub> λ<sub>0</sub>/4, where <i>k</i><sub>i</sub> is an integer and λ<sub>0</sub> a simple parameter as small as we wish, we have developed a calculation method for the optical properties, expressed as <i>R</i>/<i>T</i>, which is particularly advantageous. The form of the solution is a series of cosine terms. Given the reflectance <i>R</i><sub>0</sub> and the transmittance <i>T</i><sub>0</sub> of the filter to be synthesized, its <i>R</i><sub>0</sub>/<i>T</i><sub>0</sub> curve is expanded in a Fourier series over a given frequency interval. The integers <i>k</i><sub>i</sub> 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

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  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).

Baumeister, P.

P. Baumeister, Opt. Acta 8, 105–109(1961).

Baumeister, P. W.

A. F. Turner and P. W. Baumeister, Appl. Opt. 5, 69–76(1966).

Berning, P. H.

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.

Borgogno, J. P.

J. P. Borgogno and E. Pelletier, Thin Solid Films 34, 357–361(1976).

Delano, E.

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.

Dufour, C.

C. Dufour and A. Herpin, Opt. Acta 1, 1–8(1954); H. A. Macleod, Thin Film Optical Filters (Hilger, London, 1969).

Giacomo, P.

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).

Heavens, O. S.

O. S. Heavens and H. M. Liddell, Appl. Opt. 5, 373–376(1966).

Herpin, A.

C. Dufour and A. Herpin, Opt. Acta 1, 1–8(1954); H. A. Macleod, Thin Film Optical Filters (Hilger, London, 1969).

Klapish, M.

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).

Liddell, H. M.

O. S. Heavens and H. M. Liddell, Appl. Opt. 5, 373–376(1966).

Mead, R.

J. A. Nelder and R. Mead, Comput. J. 7, 308–313(1965).

Nelder, J. A.

J. A. Nelder and R. Mead, Comput. J. 7, 308–313(1965).

Pelletier, E.

E. Pelletier, P. Roche, and B. Vidal, Nouv. Rev. Opt. 7, 353–362(1976).

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).

J. P. Borgogno and E. Pelletier, Thin Solid Films 34, 357–361(1976).

Pohlack, H.

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).

Ritter, E.

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).

Roche, P.

E. Pelletier, P. Roche, and B. Vidal, Nouv. Rev. Opt. 7, 353–362(1976).

Turner, A. F.

A. F. Turner and P. W. Baumeister, Appl. Opt. 5, 69–76(1966).

Vidal, B.

E. Pelletier, P. Roche, and B. Vidal, Nouv. Rev. Opt. 7, 353–362(1976).

Other (12)

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).

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.

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.

P. Baumeister, Opt. Acta 8, 105–109(1961).

J. A. Nelder and R. Mead, Comput. J. 7, 308–313(1965).

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).

C. Dufour and A. Herpin, Opt. Acta 1, 1–8(1954); H. A. Macleod, Thin Film Optical Filters (Hilger, London, 1969).

A. F. Turner and P. W. Baumeister, Appl. Opt. 5, 69–76(1966).

O. S. Heavens and H. M. Liddell, Appl. Opt. 5, 373–376(1966).

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).

J. P. Borgogno and E. Pelletier, Thin Solid Films 34, 357–361(1976).

E. Pelletier, P. Roche, and B. Vidal, Nouv. Rev. Opt. 7, 353–362(1976).

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