Abstract

Thin-film gradient-index profiles have been analyzed and new profiles have been synthesized for broadband antireflection coatings on dielectric surfaces. It is shown that the control of the index gradient as a design parameter can significantly enhance the performance of interference coatings.

© 1983 Optical Society of America

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References

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  1. 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).
    [CrossRef]
  2. R. Jacobson, “Inhomogeneous and coevaporated homogeneous films for optical applications,” in Physics of Thin Films, G. Haas, M. Francombe, R. Hoffman, eds. (Academic, New York, 1975), Vol. 8, p. 51.
  3. C. G. Snedaker, “New numerical thin-film synthesis technique,” J. Opt. Soc. Am. 72, 1732 (A) (1982).

1982 (1)

C. G. Snedaker, “New numerical thin-film synthesis technique,” J. Opt. Soc. Am. 72, 1732 (A) (1982).

1976 (1)

Jacobson, R.

R. Jacobson, “Inhomogeneous and coevaporated homogeneous films for optical applications,” in Physics of Thin Films, G. Haas, M. Francombe, R. Hoffman, eds. (Academic, New York, 1975), Vol. 8, p. 51.

Minot, M. J.

Snedaker, C. G.

C. G. Snedaker, “New numerical thin-film synthesis technique,” J. Opt. Soc. Am. 72, 1732 (A) (1982).

J. Opt. Soc. Am. (2)

Other (1)

R. Jacobson, “Inhomogeneous and coevaporated homogeneous films for optical applications,” in Physics of Thin Films, G. Haas, M. Francombe, R. Hoffman, eds. (Academic, New York, 1975), Vol. 8, p. 51.

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Figures (8)

Fig. 1
Fig. 1

Index profile and reflectivity of a 1-μm gradient-index layer between two dielectric media with n = 1.6 and n = 2.4. Without the layer the reflectivity is 4 × 10−2. The curves shown are for the following index profiles: a, linear; b, cubic; and c, quintic.

Fig. 2
Fig. 2

Index profile results produced by optimization after 30 passes beginning with the quintic distribution shown in Fig. 1.

Fig. 3
Fig. 3

Index profile (curve a) initially, (curve b) after one pass, and (curve c) after 216 passes. This is apparently a local minimum for the problem posed in Figs. 1 and 2.

Fig. 4
Fig. 4

Index profiles after the first few optimization passes for layers of different thicknesses. The index profile after each of eight passes is shown for fixed total thickness of 0.5, 0.25, and 0.125 μm after starting from a quintic distribution.

Fig. 5
Fig. 5

Index profiles for a layer 0.1 μm thick. (Top) Quintic starting profile and profile after 30 passes. (Bottom) Constant starting profile and profile after 30 passes. The average reflectivity for this configuration is 1.99 × 10−4.

Fig. 6
Fig. 6

(a) Linear index profile between n = 1.1 and the substrate n = 1.52 and its corresponding reflectivity. The incident medium has index n = 1. (b) Optimized index profile and its corresponding reflectivity after 60 passes.

Fig. 7
Fig. 7

Three-layer antireflection coating of the quarter–half–quarter-wave type optimized in index for the nine-wavelength merit function.

Fig. 8
Fig. 8

With the three-layer design of Fig. 7 as a starting point, this index profile and its corresponding reflectivity are the result of optimization with 600 passes. (The index profile in this figure shows the discrete nature of each incremental layer. Other plots in this Letter connect midpoints of all incremental layers, thereby showing the continuous nature of the index profiles.)

Equations (3)

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n = n i + ( n s n i ) t , 0 t 1 ,
n = n 2 + ( n s n i ) ( 3 t 2 2 t 3 ) ,
n = n i + ( n s n i ) ( 10 t 3 15 t 4 + 6 t 5 ) .

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