Abstract

The angular reflectance of a graded-index layer, of arbitrary refractive-index profile, on the surface of a uniform substrate is calculated exactly by direct numerical integration of the wave equation for both states of polarization of the incident light. A study of the results for a number of selected profiles shows that (1) oscillations in reflectance versus wave-number graphs have an almost constant period, and (2) the period, when plotted against angle of incidence, gives a curve that is quite sensitive to the shape of the refractive-index profile. This sensitivity is the basis of a simple graphical procedure by means of which the inverse problem (i.e., deducing the index profile from reflectance measurements) can be solved. The procedure is applied to published reflectance data to determine both the thickness of a graded-index surface layer and the refractive-index profile.

© 1982 Optical Society of America

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References

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  1. S. F. Monaco, "Reflectance of an inhomogeneous thin film," J. Opt. Soc. Am. 51, 280–282 (1961).
  2. Z. Knittl, Optics of Thin Films (Wiley, London, 1976), pp. 429–479.
  3. M. Born and E. Wolf, Principles ot Optics (Pergamon, New York, 1964), pp. 51–55.
  4. T. H. Elmer and F. W. Martin, "Antireflection films on alkali-borosilicate glasses produced by chemical treatments," Am. Ceram. Soc. Bull. 58, 1092–1097 (1979).
  5. M. J. Minot, "The angular reflectance of single-layer gradient refractive index films," J. Opt. Soc. Am. 67,1046–1050 (1977).
  6. M. J. Minot, "Single-layer, gradient refractive index antireflection films effective from 0.35 µm to 2.5 µm," J. Opt. Soc. Am. 66, 515–519 (1976).
  7. A. Ralston and H. S. Wilf, Mathematical Methods for Digital Computers (Wiley, New York, 1967), Vol. 1, pp. 110–120.

1979 (1)

T. H. Elmer and F. W. Martin, "Antireflection films on alkali-borosilicate glasses produced by chemical treatments," Am. Ceram. Soc. Bull. 58, 1092–1097 (1979).

1977 (1)

1976 (1)

1961 (1)

Born, M.

M. Born and E. Wolf, Principles ot Optics (Pergamon, New York, 1964), pp. 51–55.

Elmer, T. H.

T. H. Elmer and F. W. Martin, "Antireflection films on alkali-borosilicate glasses produced by chemical treatments," Am. Ceram. Soc. Bull. 58, 1092–1097 (1979).

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, London, 1976), pp. 429–479.

Martin, F. W.

T. H. Elmer and F. W. Martin, "Antireflection films on alkali-borosilicate glasses produced by chemical treatments," Am. Ceram. Soc. Bull. 58, 1092–1097 (1979).

Minot, M. J.

Monaco, S. F.

Ralston, A.

A. Ralston and H. S. Wilf, Mathematical Methods for Digital Computers (Wiley, New York, 1967), Vol. 1, pp. 110–120.

Wilf, H. S.

A. Ralston and H. S. Wilf, Mathematical Methods for Digital Computers (Wiley, New York, 1967), Vol. 1, pp. 110–120.

Wolf, E.

M. Born and E. Wolf, Principles ot Optics (Pergamon, New York, 1964), pp. 51–55.

Am. Ceram. Soc. Bull. (1)

T. H. Elmer and F. W. Martin, "Antireflection films on alkali-borosilicate glasses produced by chemical treatments," Am. Ceram. Soc. Bull. 58, 1092–1097 (1979).

J. Opt. Soc. Am. (3)

Other (3)

Z. Knittl, Optics of Thin Films (Wiley, London, 1976), pp. 429–479.

M. Born and E. Wolf, Principles ot Optics (Pergamon, New York, 1964), pp. 51–55.

A. Ralston and H. S. Wilf, Mathematical Methods for Digital Computers (Wiley, New York, 1967), Vol. 1, pp. 110–120.

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