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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 27, Iss. 10 — May. 15, 1988
  • pp: 1998–2005

Derivation of a matrix describing a rugate dielectric thin film

Bertrand G. Bovard  »View Author Affiliations


Applied Optics, Vol. 27, Issue 10, pp. 1998-2005 (1988)
http://dx.doi.org/10.1364/AO.27.001998


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Abstract

In optical coating calculations, a 2 × 2 matrix formalism is generally used to describe the effect of each layer on the electromagnetic field. In current applications, the layers are considered homogeneous, and, therefore, the matrix used is restricted to this particular case. In this paper, a 2 × 2 matrix describing an inhomogeneous dielectric thin film is derived from Maxwell’s equations. The inhomogeneity is assumed to vary along the direction perpendicular to the film plane. No restriction is made on the amplitude of its variation. The matrix is illustrated in the case of a rugate filter designed according to Sossi’s Fourier transform technique. An improved approximation for the Fourier transform technique is then introduced.

© 1988 Optical Society of America

History
Original Manuscript: August 3, 1987
Published: May 15, 1988

Citation
Bertrand G. Bovard, "Derivation of a matrix describing a rugate dielectric thin film," Appl. Opt. 27, 1998-2005 (1988)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-27-10-1998


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References

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  2. H. A. Macleod, Thin-Film Optical Filters (Macmillan, New York, 1986). [CrossRef]
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  15. W. H. Southwell, “Use of Gradient Index for Spectral Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 464, 110 (1984).

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