Abstract

Normal incidence measurements of single-layer gradient refractive-index antireflection films, produced by a chemical etch-leach process on glass sensitized by a phase-separating heat treatment, indicate very low reflection over a broad wavelength regime, 0.35–2.5 μm. First-surface measurements of the reflectance of the gradient index films have now been made, in the visible regime, at off-normal incidence (to 70°) using polarized light. These measurements show that significant reflection reduction is obtained even at high angles of incidence—5.7% reflectance from the filmed glass at 70° compared to 16.4% for the unfilmed glass. Furthermore, although the films exhibit a weak wavelength dependence at high angles, they continue to be effective over a broad spectral region. The optical properties observed are in good agreement with computations based on a gradient refractive-index film with a step at the air-film interface. The optical properties of the film offer considerable advantage over conventional interference films in many applications.

© 1977 Optical Society of America

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References

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  1. M. J. Minot, J. Opt. Soc. Am. 66, 515–519 (1976).
    [Crossref]
  2. Krylon®Paint, Borden, Inc., Columbus, Ohio.
  3. Harrick Scientific Corp., Ossining, N. Y.
  4. W. Konig, Handbuch der Physik, Vol. 20 (Springer, Berlin, 1928), p. 66.
  5. G. Hass and J. E. Waylonis, J. Opt. Soc. Am. 50, 1133 (1960).
  6. R. Jacobsson, Progress in Optics V, edited by E. Wolf (North-Holland, Amsterdam, 1966), p. 249.
  7. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 55–61.

1976 (1)

1960 (1)

G. Hass and J. E. Waylonis, J. Opt. Soc. Am. 50, 1133 (1960).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 55–61.

Hass, G.

G. Hass and J. E. Waylonis, J. Opt. Soc. Am. 50, 1133 (1960).

Jacobsson, R.

R. Jacobsson, Progress in Optics V, edited by E. Wolf (North-Holland, Amsterdam, 1966), p. 249.

Konig, W.

W. Konig, Handbuch der Physik, Vol. 20 (Springer, Berlin, 1928), p. 66.

Minot, M. J.

Waylonis, J. E.

G. Hass and J. E. Waylonis, J. Opt. Soc. Am. 50, 1133 (1960).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 55–61.

J. Opt. Soc. Am. (2)

M. J. Minot, J. Opt. Soc. Am. 66, 515–519 (1976).
[Crossref]

G. Hass and J. E. Waylonis, J. Opt. Soc. Am. 50, 1133 (1960).

Other (5)

R. Jacobsson, Progress in Optics V, edited by E. Wolf (North-Holland, Amsterdam, 1966), p. 249.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 55–61.

Krylon®Paint, Borden, Inc., Columbus, Ohio.

Harrick Scientific Corp., Ossining, N. Y.

W. Konig, Handbuch der Physik, Vol. 20 (Springer, Berlin, 1928), p. 66.

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Figures (9)

FIG. 1
FIG. 1

Computed reflectance for an aluminum mirror as a function of angle and wavelength. These curves were computed on the basis of optical constants listed in Table I.

FIG. 2
FIG. 2

Wavelength dependence of the experimental reflectance data, at an angle of 20°, for the aluminum mirror, Corning Glass Works (CGW) Code No. 7740 glass, and CGW Code No. 7740 glass coated with the gradient index antireflection film. Data for both S and P components are shown. A scale expansion of 1 × or 10 × is used as indicated.

FIG. 3
FIG. 3

Wavelength dependence of the experimental reflectance data, at an angle of 60°, for the aluminum mirror, CGW Code No. 7740 glass, and CGW Code No. 7740 glass coated with the gradient index antireflection film. Data for both S and P components are shown. A scale expansion of 1 × or 10 × is used as indicated.

FIG. 4
FIG. 4

Wavelength dependence of the experimental reflectance data, at an angle of 70°, for the aluminum mirror, CGW Code No. 7740 glass, and CGW Code No. 7740 glass coated with the gradient index antireflection film. Data for both S and P components are shown. A scale expansion of 1 × or 10 × is used as indicated.

FIG. 5
FIG. 5

Plot of corrected average reflectance [ R ¯ = 1 2 ( R s + R p ) ] vs wavelength vs angle for CGW Code No. 7740 glass (no film) and CGW Code No. 7740 coated with the gradient-type anti-reflection film.

FIG. 6
FIG. 6

Comparison of the reflectance as a function of angle, at λ = 5000 Å, of CGW Code No. 7740 glass with and without the gradient index antireflection film.

FIG. 7
FIG. 7

Geometrical representation of a thin inhomogeneous film whose refractive index changes linearly with film thickness. The dotted step profile, offset for ease of illustration, shows the inhomogeneous film approximated by a series of thin homogeneous films.

FIG. 8
FIG. 8

Computer-calculated reflectance, for both the S and P polarization, as a function of angle, plotted against d/λ for the case of an antireflection film characterized by a linear gradient refractive-index profile where η1 = 1, η2 = 1.118, and η 2 = η 3 = 1.474.

FIG. 9
FIG. 9

Computer-calculated average reflectance R ¯ = 1 2 ( R s + R p ) as a function of angle, plotted against d/λ for the same film as shown in Fig. 8.

Tables (3)

Tables Icon

TABLE I Optical constants of pure aluminum thin films (Ref. 5).

Tables Icon

TABLE II Corrected reflectance of Code No. 7740 glass with and without gradient index antireflection film as a function of wavelength and angle of incidence.

Tables Icon

TABLE III Computed reflectance versus angle.

Equations (7)

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R S = a 2 + b 2 2 a cos i + cos 2 i a 2 + b 2 + 2 a cos i + cos 2 i , R P = R s a 2 + b 2 2 a sin i tan i + sin 2 i tan 2 i a 2 + b 2 + 2 a sin i tan i + sin 2 i tan 2 i ,
R ¯ = 1 2 ( R s + R p ) ,
a 2 = ( 1 / 2 n 0 2 ) { [ ( n 2 K 2 n 0 2 sin 2 i ) 2 + 4 n 2 K 2 ] 1 / 2 + n 2 K 2 n 0 2 sin 2 i } , b 2 = ( 1 / 2 n 0 2 ) { [ ( n 2 K 2 n 0 2 sin 2 i ) + 4 n 2 K 2 ] 1 / 2 n 2 + K 2 + n 0 2 sin 2 i } .
M = i = 1 P M i ( Z ( i ) Z ( i 1 ) ) .
R ¯
R ¯
R ¯ ( % ) = 1 2 ( R S + R P )