Abstract

An iterative correction process, recently incorporated into the National Research Council of Canada Fourier-transform thin-film synthesis program, is applied to the design of wideband antireflection coatings. This type of problem is different from those solved in the past by this method. It cannot be handled in a practical way without a correction process. We consider in detail the effects—critical for this application—of constraints on the refractive indices and overall thicknesses of the solutions. Our graded-index and multilayer designs have a remarkable resemblance in performance and refractive-index structure to results obtained by more conventional techniques. The Fourier-transform method is of interest because of its speed and versatility.

© 1992 Optical Society of America

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References

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  1. E. Delano, “Fourier synthesis of multilayer filters,” J. Opt. Soc. Am. 57, 1529–1533 (1967).
    [Crossref]
  2. L. Sossi, “A method for the synthesis of multilayer interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229–237 (1974). An English translation of this paper is available from Translation Services of the Canada Institute for Technical & Scientific Information, National Research Council of Canada, Ottawa, Ontario K1A 0R6, Canada.
  3. L. Sossi, “On the synthesis of interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 26, 28–36 (1977). An English translation is available; see Ref. 2.
  4. J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt. 17, 3039–3050 (1978).
    [Crossref] [PubMed]
  5. P. G. Verly, J. A. Dobrowolski, W. W. Wild, R. L. Burton, “Synthesis of high rejection filters with the Fourier transform method,” Appl. Opt. 28, 2864–2875 (1989).
    [Crossref] [PubMed]
  6. P. G. Verly, J. A. Dobrowolski, “Iterative correction process for optical thin film synthesis with the Fourier transform method,” Appl. Opt. 29, 3672–3684 (1990).
    [Crossref] [PubMed]
  7. R. R. Willey, P. G. Verly, J. A. Dobrowolski, “Synthesis of wide band AR coatings with the Fourier transform method,” in Optical Thin Films and Applications, R. Herrman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 36–44 (1990).
  8. B. G. Bovard, “Fourier transform technique applied to quarter wave optical coatings,” Appl Opt. 27, 3062–3063 (1988).
    [Crossref] [PubMed]
  9. B. G. Bovard, “Derivation of a matrix describing a rugate dielectric film,” Appl. Opt. 27, 1998–2005 (1988).
    [Crossref] [PubMed]
  10. B. G. Bovard, “Rugate filter design: the modified Fourier transform technique,” Appl. Opt. 29, 24–30 (1990).
    [Crossref] [PubMed]
  11. J. A. Aguilera, J. Aguilera, P. Baumeister, A. Bloom, D. Coursen, J. A. Dobrowolski, F. T. Goldstein, D. E. Gustafson, R. A. Kemp, “Antireflection coatings for germanium IR optics: a comparison of numerical design methods,” Appl. Opt. 27, 2832–2840 (1988).
    [Crossref] [PubMed]
  12. J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
    [Crossref] [PubMed]
  13. L. Young, “Synthesis of multiple antireflection films over a prescribed frequency band,” J. Opt. Soc. Am. 51, 967–974 (1961).
    [Crossref]
  14. W. H. Southwell, “Gradient index antireflection coatings,” Opt. Lett. 8, 584–586 (1983).
    [Crossref] [PubMed]
  15. R. W. Bertram, M. F. Ouellette, P. Y. Tse, “Inhomogeneous optical coatings: an experimental study of a new approach,” Appl. Opt. 28, 2935–2939 (1989).
    [Crossref] [PubMed]
  16. J. A. Dobrowolski, F. C. Ho, “High performance step-down AR coatings for high refractive-index IR materials,” Appl. Opt. 21, 288–292 (1982).
    [Crossref] [PubMed]
  17. R. R. Willey, “Rugate broadband antireflection coating design,” in Current Developments in Optical Engineering and Commercial Optics, R. E. Fischer, H. M. Pollicove, W. J. Smith, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1168, 224–228 (1989).
  18. R. R. Willey, “Another viewpoint on antireflection coating design,” in Optical Systems for Space and Defence, A. H. Lettington, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1191, 181–188 (1989).

1990 (3)

1989 (2)

1988 (3)

1983 (1)

1982 (1)

1978 (1)

1977 (1)

L. Sossi, “On the synthesis of interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 26, 28–36 (1977). An English translation is available; see Ref. 2.

1974 (1)

L. Sossi, “A method for the synthesis of multilayer interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229–237 (1974). An English translation of this paper is available from Translation Services of the Canada Institute for Technical & Scientific Information, National Research Council of Canada, Ottawa, Ontario K1A 0R6, Canada.

1967 (1)

1961 (1)

Aguilera, J.

Aguilera, J. A.

Baumeister, P.

Bertram, R. W.

Bloom, A.

Bovard, B. G.

Burton, R. L.

Coursen, D.

Delano, E.

Dobrowolski, J. A.

Goldstein, F. T.

Gustafson, D. E.

Ho, F. C.

Kemp, R. A.

Lowe, D.

Ouellette, M. F.

Sossi, L.

L. Sossi, “On the synthesis of interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 26, 28–36 (1977). An English translation is available; see Ref. 2.

L. Sossi, “A method for the synthesis of multilayer interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229–237 (1974). An English translation of this paper is available from Translation Services of the Canada Institute for Technical & Scientific Information, National Research Council of Canada, Ottawa, Ontario K1A 0R6, Canada.

Southwell, W. H.

Tse, P. Y.

Verly, P. G.

Wild, W. W.

Willey, R. R.

R. R. Willey, P. G. Verly, J. A. Dobrowolski, “Synthesis of wide band AR coatings with the Fourier transform method,” in Optical Thin Films and Applications, R. Herrman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 36–44 (1990).

R. R. Willey, “Rugate broadband antireflection coating design,” in Current Developments in Optical Engineering and Commercial Optics, R. E. Fischer, H. M. Pollicove, W. J. Smith, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1168, 224–228 (1989).

R. R. Willey, “Another viewpoint on antireflection coating design,” in Optical Systems for Space and Defence, A. H. Lettington, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1191, 181–188 (1989).

Young, L.

Appl Opt. (1)

B. G. Bovard, “Fourier transform technique applied to quarter wave optical coatings,” Appl Opt. 27, 3062–3063 (1988).
[Crossref] [PubMed]

Appl. Opt. (9)

B. G. Bovard, “Derivation of a matrix describing a rugate dielectric film,” Appl. Opt. 27, 1998–2005 (1988).
[Crossref] [PubMed]

B. G. Bovard, “Rugate filter design: the modified Fourier transform technique,” Appl. Opt. 29, 24–30 (1990).
[Crossref] [PubMed]

J. A. Aguilera, J. Aguilera, P. Baumeister, A. Bloom, D. Coursen, J. A. Dobrowolski, F. T. Goldstein, D. E. Gustafson, R. A. Kemp, “Antireflection coatings for germanium IR optics: a comparison of numerical design methods,” Appl. Opt. 27, 2832–2840 (1988).
[Crossref] [PubMed]

J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
[Crossref] [PubMed]

J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt. 17, 3039–3050 (1978).
[Crossref] [PubMed]

P. G. Verly, J. A. Dobrowolski, W. W. Wild, R. L. Burton, “Synthesis of high rejection filters with the Fourier transform method,” Appl. Opt. 28, 2864–2875 (1989).
[Crossref] [PubMed]

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

R. W. Bertram, M. F. Ouellette, P. Y. Tse, “Inhomogeneous optical coatings: an experimental study of a new approach,” Appl. Opt. 28, 2935–2939 (1989).
[Crossref] [PubMed]

J. A. Dobrowolski, F. C. Ho, “High performance step-down AR coatings for high refractive-index IR materials,” Appl. Opt. 21, 288–292 (1982).
[Crossref] [PubMed]

Eesti NSV Tead. Akad. Toim. Fuus. Mat. (2)

L. Sossi, “A method for the synthesis of multilayer interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229–237 (1974). An English translation of this paper is available from Translation Services of the Canada Institute for Technical & Scientific Information, National Research Council of Canada, Ottawa, Ontario K1A 0R6, Canada.

L. Sossi, “On the synthesis of interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 26, 28–36 (1977). An English translation is available; see Ref. 2.

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Other (3)

R. R. Willey, P. G. Verly, J. A. Dobrowolski, “Synthesis of wide band AR coatings with the Fourier transform method,” in Optical Thin Films and Applications, R. Herrman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 36–44 (1990).

R. R. Willey, “Rugate broadband antireflection coating design,” in Current Developments in Optical Engineering and Commercial Optics, R. E. Fischer, H. M. Pollicove, W. J. Smith, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1168, 224–228 (1989).

R. R. Willey, “Another viewpoint on antireflection coating design,” in Optical Systems for Space and Defence, A. H. Lettington, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1191, 181–188 (1989).

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Figures (9)

Fig. 1
Fig. 1

Step-down AR coatings obtained in the absence of refractive-index constraints: curve 1, exponential sine graded-index profile; curve 2, multilayer designed with Young’s method13; curve 3, result obtained with the Fourier-transform method; curve 4, low spatial frequency content of the latter.

Fig. 2
Fig. 2

Variation of the merit function values with thickness in the absence of refractive-index constraints: △, Young’s step-down AR multilayers13; + and ×, graded-index coatings that evolved from constant index and exponential sine starting designs.

Fig. 3
Fig. 3

Multicycle refractive-index profiles obtained in the absence of refractive-index constraints.

Fig. 4
Fig. 4

Performance of the graded-index design shown as curve 3 in Fig. 1 before and after thickness adjustments. The asterisks indicate the AR range.

Fig. 5
Fig. 5

Graded-index and multilayer designs obtained under the same thickness and refractive-index constraints. The multilayers are from Refs. 11 and 12.

Fig. 6
Fig. 6

Variation of the merit function values with thickness in the presence of refractive-index constraints. The curves correspond to graded-index solutions obtained with different starting designs (see text): □ and ○, multilayer solutions from Refs. 11 and 12, respectively; △, optimized graded-index design (see text).

Fig. 7
Fig. 7

Intermediate solutions produced by the thickness adjustments during the design of the systems shown in Figs. 5(b) and 5(c) (see text).

Fig. 8
Fig. 8

Examples of 2 1/2 cycle refractive-index profiles: (a) similar to Figs. 5(a) but shown on a different scale; (b) similar to (a) but obtained with the Shah option (thick curve) and transformed into a two-material system by a Herpin effective-index approximation and refinement; (c) similar to (a) but for a difforont AR bandwidth.

Fig. 9
Fig. 9

Comparison of graded-index designs obtained by the Fourier-transform method (thick line) and by refinement15 (thin line).

Equations (6)

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ln ( n ( x ) n 0 ) = j π - Q ˜ ( T , σ ) σ exp ( - j 2 π σ x ) d σ ,
Δ Q ˜ ( σ ) = w [ Q ˜ ( T D , σ ) - Q ˜ ( T C , σ ) ] ,
n ( x ) = n A ( x ) n B ( x ) .
T = n M n S t 2
ln [ n ( x ) n 0 ] = 2 p m = - l F Q ( m p ) ,             l p x l + 1 p ,
Q ˜ ( - σ ) = Q ˜ * ( σ ) ,

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