Abstract

An optical thin-film synthesis technique combining a Fourier transform approach with the refinement of design parameters in the Fourier space is proposed. The theory and numerical examples are described.

© 1996 Optical Society of America

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References

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  1. W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
    [CrossRef] [PubMed]
  2. J. A. Dobrowolski, R. A. Kemp, “Flip-flop thin film design program with enhanced capabilities,” Appl. Opt. 31, 3807–3812 (1992).
    [CrossRef] [PubMed]
  3. B. G. Bovard, “Rugate filter theory, an overview,” Appl. Opt. 33, 5427–5442 (1993).
    [CrossRef]
  4. A. V. Tikhonravov, “Some theoretical aspects of thin film optics and their applications,” Appl. Opt. 32, 5417–5426 (1993).
    [CrossRef] [PubMed]
  5. A. V. Tikhonravov, M. K. Trubetskov, “Development of the needle optimization method and new features of the ‘Optilayer’ software,” Proc. SPIE 2253, 10–20 (1993).
    [CrossRef]
  6. A. V. Tikhonravov, J. A. Dobrowolski, “Quasi-optimal synthesis for antireflection coatings: a new method,” Appl. Opt. 32, 4265–4275 (1993).
    [CrossRef] [PubMed]
  7. T. Eisenhammer, M. Lazarov, M. Leutbecher, U. Stöffel, R. Sizmann, “Optimization of interference filters with genetic algorithms applied to silver-based heat mirrors,” Appl. Opt. 32, 6310–6315 (1993).
    [CrossRef] [PubMed]
  8. B. T. Sullivan, J. A. Dobrowolski, “Implementation of a numerical needle method for thin film design,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 72–74.
  9. W. H. Southwell, “Extended bandwidth reflector designs using wavelets,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 11–13.
  10. A. V. Tikhonravov, M. K. Trubetskov, I. V. Zuev, P. G. Verly, “Efficient refinement of inhomogeneous optical coatings,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 22–24.
  11. J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, P. G. Verly, “Optimal single-band normal-incidence antireflection coatings,” Appl. Opt. 35, 644–658 (1996).
    [CrossRef] [PubMed]
  12. B. G. Bovard, “Rugate filter design: the modified Fourier transform technique,” Appl. Opt. 29, 24–30 (1990).
    [CrossRef] [PubMed]
  13. 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).
  14. H. Fabricius, “Gradient index filters: designing filters with steep skirts, high reflection and quintic matching layers,” Appl. Opt. 31, 5191–5196 (1992).
    [CrossRef] [PubMed]
  15. A. V. Tikhonravov, B. T. Sullivan, M. V. Borisova, “Discrete Fourier transform approach to inhomogeneous layer synthesis,” Appl. Opt. 33, 5142–5150 (1994).
    [CrossRef] [PubMed]
  16. 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]
  17. T. R. Cuthbert, Optimization Using Personal Computers (Wiley, New York, 1987), Chap. 5, p. 300.
  18. P. G. Verly, “Fourier transform technique with frequency filtering for optical thin film design,” Appl. Opt. 34, 688–694 (1995).
    [CrossRef] [PubMed]
  19. P. G. Verly, “Fourier transform method with refinement in the frequency domain for optical thin film design,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 22–24.

1996 (1)

1995 (1)

1994 (1)

1993 (5)

1992 (2)

1990 (2)

1985 (1)

Borisova, M. V.

Bovard, B. G.

Cuthbert, T. R.

T. R. Cuthbert, Optimization Using Personal Computers (Wiley, New York, 1987), Chap. 5, p. 300.

Dobrowolski, J. A.

Eisenhammer, T.

Fabricius, H.

Kemp, R. A.

Lazarov, M.

Leutbecher, M.

Sizmann, R.

Southwell, W. H.

W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
[CrossRef] [PubMed]

W. H. Southwell, “Extended bandwidth reflector designs using wavelets,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 11–13.

Stöffel, U.

Sullivan, B. T.

Tikhonravov, A. V.

Trubetskov, M. K.

J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, P. G. Verly, “Optimal single-band normal-incidence antireflection coatings,” Appl. Opt. 35, 644–658 (1996).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, “Development of the needle optimization method and new features of the ‘Optilayer’ software,” Proc. SPIE 2253, 10–20 (1993).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, I. V. Zuev, P. G. Verly, “Efficient refinement of inhomogeneous optical coatings,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 22–24.

Verly, P. G.

J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, P. G. Verly, “Optimal single-band normal-incidence antireflection coatings,” Appl. Opt. 35, 644–658 (1996).
[CrossRef] [PubMed]

P. G. Verly, “Fourier transform technique with frequency filtering for optical thin film design,” Appl. Opt. 34, 688–694 (1995).
[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]

P. G. Verly, “Fourier transform method with refinement in the frequency domain for optical thin film design,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 22–24.

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).

A. V. Tikhonravov, M. K. Trubetskov, I. V. Zuev, P. G. Verly, “Efficient refinement of inhomogeneous optical coatings,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 22–24.

Zuev, I. V.

A. V. Tikhonravov, M. K. Trubetskov, I. V. Zuev, P. G. Verly, “Efficient refinement of inhomogeneous optical coatings,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 22–24.

Appl. Opt. (12)

W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
[CrossRef] [PubMed]

J. A. Dobrowolski, R. A. Kemp, “Flip-flop thin film design program with enhanced capabilities,” Appl. Opt. 31, 3807–3812 (1992).
[CrossRef] [PubMed]

B. G. Bovard, “Rugate filter theory, an overview,” Appl. Opt. 33, 5427–5442 (1993).
[CrossRef]

A. V. Tikhonravov, “Some theoretical aspects of thin film optics and their applications,” Appl. Opt. 32, 5417–5426 (1993).
[CrossRef] [PubMed]

A. V. Tikhonravov, J. A. Dobrowolski, “Quasi-optimal synthesis for antireflection coatings: a new method,” Appl. Opt. 32, 4265–4275 (1993).
[CrossRef] [PubMed]

T. Eisenhammer, M. Lazarov, M. Leutbecher, U. Stöffel, R. Sizmann, “Optimization of interference filters with genetic algorithms applied to silver-based heat mirrors,” Appl. Opt. 32, 6310–6315 (1993).
[CrossRef] [PubMed]

H. Fabricius, “Gradient index filters: designing filters with steep skirts, high reflection and quintic matching layers,” Appl. Opt. 31, 5191–5196 (1992).
[CrossRef] [PubMed]

A. V. Tikhonravov, B. T. Sullivan, M. V. Borisova, “Discrete Fourier transform approach to inhomogeneous layer synthesis,” Appl. Opt. 33, 5142–5150 (1994).
[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]

J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, P. G. Verly, “Optimal single-band normal-incidence antireflection coatings,” Appl. Opt. 35, 644–658 (1996).
[CrossRef] [PubMed]

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

P. G. Verly, “Fourier transform technique with frequency filtering for optical thin film design,” Appl. Opt. 34, 688–694 (1995).
[CrossRef] [PubMed]

Proc. SPIE (1)

A. V. Tikhonravov, M. K. Trubetskov, “Development of the needle optimization method and new features of the ‘Optilayer’ software,” Proc. SPIE 2253, 10–20 (1993).
[CrossRef]

Other (6)

B. T. Sullivan, J. A. Dobrowolski, “Implementation of a numerical needle method for thin film design,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 72–74.

W. H. Southwell, “Extended bandwidth reflector designs using wavelets,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 11–13.

A. V. Tikhonravov, M. K. Trubetskov, I. V. Zuev, P. G. Verly, “Efficient refinement of inhomogeneous optical coatings,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 22–24.

P. G. Verly, “Fourier transform method with refinement in the frequency domain for optical thin film design,” in Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1995), pp. 22–24.

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).

T. R. Cuthbert, Optimization Using Personal Computers (Wiley, New York, 1987), Chap. 5, p. 300.

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Figures (4)

Fig. 1
Fig. 1

Filter acting as a beam splitter and reflector. A, Design by the established FT method with iterative corrections.13,16 B, Proposed method. C, Refined multilayer obtained from system B. The points represent the target transmittance.

Fig. 2
Fig. 2

Convergence of the merit function in Fig. 1. Curves 1 and 2 correspond to Figs. 1A and 1B.

Fig. 3
Fig. 3

Double-cavity filter. A, Original multilayer (known solution). B, Design by the established FT method.13,16 C, Proposed method after 10 s of computation time. D, Proposed method after 50 s of computation time.

Fig. 4
Fig. 4

Convergence of the merit function in Fig. 3. Curve 1 corresponds to Fig. 3B, and curve 2 to Figs. 3C and 3D. Curve 3 corresponds to the synthesis of the same inhomogeneous refractive-index profile by the method described in Ref. 10.

Equations (12)

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ln [ n ( x ) n 0 ] FT i π Q ˜ ( T , σ ) σ .
ln [ n ( x ) Δ n ( x ) n 0 ] FT i π Q ˜ ( σ ) + Δ Q ˜ ( σ ) σ .
Δ Q ˜ ( σ ) = { Q [ T D ( σ ) ] - Q [ T C ( σ ) ] } exp [ i ϕ ( σ ) ] ,
ϕ ( σ ) = arg [ r ( σ ) t ( σ ) ] C
ln [ Δ n ( x ) ] = i π k Δ Q k exp [ - i ( 2 π σ k x - ϕ k ) ] σ k d σ + c . c . ,
Δ n ( x ) = Δ n ( x ) π σ k sin ( 2 π σ k - ϕ k ) d σ Δ Q k ,             k = 1 , 2 , 3 ,
Δ n ( x ) = Δ n ( x ) π σ k Δ Q k [ sin ( 2 π σ k - ϕ k - ϕ k ) - sin ( 2 π σ k - ϕ k ) ] d σ .
F = { 1 K k = 1 K [ T C ( σ k ) - T D ( σ k ) δ T k ] 2 } 1 / 2 ,
T = 0.50 ± 0.01 for 0.75 σ 0.99 μ m - 1 , T 0.01 ± 0.01 for 1.01 σ 1.25 μ m - 1 .
T 0.965 ± 0.01 for 1.99375 σ 2.00625 μ m - 1 ,
T 0.001 ± 0.0005 for 1.833 σ 1.9375 μ m - 1 , 2.0625 σ 2.166 μ m - 1 .
Δ n ( x ) = Δ n A ( x ) Δ n B ( x ) Δ n C ( x ) .

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