Abstract

Useful features of an efficient thin-film synthesis technique based on the refinement of inhomogeneous films are adapted to the needle method. As in the former approach, all the layer refractive indices and thicknesses are refined simultaneously, and special attention is given to computation speed and accuracy. In particular, key parameters are calculated from analytical formulas, namely, the gradients used in the optimization routines and the optimum needle positions and refractive indices. Inhomogeneous as well as multilayer solutions are possible. The efficiency of the modified approach is demonstrated by the solution of a complex nonpolarizing, wide-angle antireflection coating problem. The results are compared with those obtained in the past by the conventional needle method and by refinement of inhomogeneous films.

© 2001 Optical Society of America

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References

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  1. A. V. Tikhonravov, “On the synthesis of optical thin films using optimality conditions,” Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91–93 (1982).
  2. A. V. Tikhonravov, M. K. Trubetskov, G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
    [CrossRef] [PubMed]
  3. B. T. Sullivan, J. A. Dobrowolski, “Implementation of a numerical needle method for thin-film design,” Appl. Opt. 35, 5484–5492 (1996).
    [CrossRef] [PubMed]
  4. P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement algorithm for the synthesis of inhomogeneous optical coatings,” Appl. Opt. 36, 1487–1495 (1997).
    [CrossRef] [PubMed]
  5. P. G. Verly, “Optical coating synthesis by simultaneous refractive-index and thickness refinement of inhomogeneous films,” Appl. Opt. 37, 7327–7333 (1998).
    [CrossRef]
  6. P. G. Verly, “Iterative correction process for optical thin film synthesis with the Fourier transform method,” Appl. Opt. 29, 3672–3684 (1990).
    [CrossRef] [PubMed]
  7. P. G. Verly, “Design of inhomogeneous and quasi-inhomogeneous optical coatings at the NRC,” in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J. A. Dobrowolski, P. G. Verly, eds., Proc. SPIE2046, 36–45 (1993).
    [CrossRef]
  8. A. V. Tikhonravov, M. K. Trubetskov, “Advanced thin film optical coatings, evaluation and design,” presented at the Fourth OptiLayer Conference, ENEA Research Center, Rome, 13–15 March 2000.
  9. P. G. Verly, “Needle method with simultaneous thickness and refractive index refinement for optical thin film synthesis,” in Optical Interference Coatings, Vol. 9 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 271–272.

1998 (1)

1997 (1)

1996 (2)

1990 (1)

1982 (1)

A. V. Tikhonravov, “On the synthesis of optical thin films using optimality conditions,” Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91–93 (1982).

DeBell, G. W.

Dobrowolski, J. A.

Sullivan, B. T.

Tikhonravov, A. V.

P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement algorithm for the synthesis of inhomogeneous optical coatings,” Appl. Opt. 36, 1487–1495 (1997).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
[CrossRef] [PubMed]

A. V. Tikhonravov, “On the synthesis of optical thin films using optimality conditions,” Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91–93 (1982).

A. V. Tikhonravov, M. K. Trubetskov, “Advanced thin film optical coatings, evaluation and design,” presented at the Fourth OptiLayer Conference, ENEA Research Center, Rome, 13–15 March 2000.

Trubetskov, M. K.

Verly, P. G.

P. G. Verly, “Optical coating synthesis by simultaneous refractive-index and thickness refinement of inhomogeneous films,” Appl. Opt. 37, 7327–7333 (1998).
[CrossRef]

P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement algorithm for the synthesis of inhomogeneous optical coatings,” Appl. Opt. 36, 1487–1495 (1997).
[CrossRef] [PubMed]

P. G. Verly, “Iterative correction process for optical thin film synthesis with the Fourier transform method,” Appl. Opt. 29, 3672–3684 (1990).
[CrossRef] [PubMed]

P. G. Verly, “Needle method with simultaneous thickness and refractive index refinement for optical thin film synthesis,” in Optical Interference Coatings, Vol. 9 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 271–272.

P. G. Verly, “Design of inhomogeneous and quasi-inhomogeneous optical coatings at the NRC,” in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J. A. Dobrowolski, P. G. Verly, eds., Proc. SPIE2046, 36–45 (1993).
[CrossRef]

Appl. Opt. (5)

Vestn. Mosk. Univ. Fiz. Astronomiya (1)

A. V. Tikhonravov, “On the synthesis of optical thin films using optimality conditions,” Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91–93 (1982).

Other (3)

P. G. Verly, “Design of inhomogeneous and quasi-inhomogeneous optical coatings at the NRC,” in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J. A. Dobrowolski, P. G. Verly, eds., Proc. SPIE2046, 36–45 (1993).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, “Advanced thin film optical coatings, evaluation and design,” presented at the Fourth OptiLayer Conference, ENEA Research Center, Rome, 13–15 March 2000.

P. G. Verly, “Needle method with simultaneous thickness and refractive index refinement for optical thin film synthesis,” in Optical Interference Coatings, Vol. 9 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 271–272.

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Figures (5)

Fig. 1
Fig. 1

Typical variation of the merit-value perturbation ∂F produced by a needle as a function of its refractive index n. Curve A, original values; curves B–D, parabolic fits of ∂F(n), ∂F[log(n)], and ∂F(1/n). Curves A and D are essentially superposed.

Fig. 2
Fig. 2

Evolution of the solution and needle selection in the synthesis of a nonpolarizing antireflection coating for 0°, 30°, 45°, 60°, and 70° incidence. A, starting design and first series of needles. The needles are inserted at the deepest minima of the merit-value perturbation curve plotted on the right-hand Y axis. Dotted curve, variation of the optimum needle refractive index as a function of the needle position in the system. B, refined solution and next series of needles. C–F, progress at the end of the second to fifth iterations. G, final semi-inhomogeneous solution at the end of the seventh iteration. See text for details.

Fig. 3
Fig. 3

Multilayer solutions based on five prescribed materials. A, inhomogeneous and multilayer solutions obtained by the modified needle method. B, comparison with a solution obtained in Ref. 2 by the conventional needle method. C, solutions obtained by the Refinh method. See text for details.

Fig. 4
Fig. 4

Convergence of the merit value during the synthesis. Solid curve, modified needle approach. Filled squares, intermediate solutions shown in Fig. 2. Dotted curve, synthesis by the Refinh approach. Triangles, successive design stages. Dashed curve, accelerated synthesis by the modified needle approach. See text for details.

Fig. 5
Fig. 5

Evolution of the overall optical thickness during the synthesis. Solid curve, modified needle approach. Dotted curve, Refinh approach. Dashed curve, accelerated synthesis by the modified needle approach. Markers, successive design stages discussed in the text.

Equations (6)

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ϕ=2πλ nd  1,
Mj=ϕMj0icos θηjiη cos θj0+0ϕ2, j=1, 2,, J+1,
ηS=n cosθ,  s pol, ηP=ncosθ,  p pol,
rj=TrPostjMjPrejψr.
Prej=m=1j-1 Mj, Postj=m=j+1J Mj
ψr=t2nana1-r-1+rnans1-r-ns1+r.

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