Abstract

The constrained optimization approach is applied to the design of quasi-rugate optical coatings. These coatings are defined as multilayers with no thin layers where refractive index profiles resemble rugate-type refractive index profiles and where spectral properties are typical for rugate filters. It is shown that all design problems that are usually solved using rugate filters can be solved successfully in the frame of quasi-rugate optical coatings. Comparison between quasi-rugate and two-component multilayer designs is provided.

© 2008 Optical Society of America

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  1. W. H. Southwell and R. L. Hall, “Rugate filter sidelobe suppression using quintic and rugated quintic matching layers,” Appl. Opt. 28, 2949-2951 (1989).
    [CrossRef] [PubMed]
  2. W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091-5094 (1989).
    [CrossRef] [PubMed]
  3. B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427-5442 (1993).
    [CrossRef] [PubMed]
  4. J. A. Dobrowolski and D. Lowe, “Optical thin film synthesis program based on the use of Fourier transform,” Appl. Opt. 17, 3039-3050 (1978).
    [CrossRef] [PubMed]
  5. P. G. Verly, J. A. Dobrowolski, W. J. Wild, and R. L. Burton, “Synthesis of high rejection filters with the Fourier transform method,” Appl. Opt. 28, 2864-2875 (1989).
    [CrossRef] [PubMed]
  6. B. G. Bovard, “Rugate filter design: the modified Fourier transform technique,” Appl. Opt. 29, 24-30 (1990).
    [CrossRef] [PubMed]
  7. R. R. Willey, P. G. Verly, and J. A. Dobrowolski, “Design of wideband antireflection coating with the Fourier transform method,” Proc. SPIE 1270, 36-44 (1990).
    [CrossRef]
  8. P. G. Verly, J. A. Dobrowolski, and R. R. Willey, “Fourier-transform method for the design of wideband antireflection coatings,” Appl. Opt. 31, 3836-3846 (1992).
    [CrossRef] [PubMed]
  9. A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, M. A. Kokarev, N. Kaiser, O. Stenzel, S. Willbrandt, and D. Gäbler, “New optimization algorithm for the synthesis of rugate optical coatings,” Appl. Opt. 45, 1515-1524 (2006).
    [CrossRef] [PubMed]
  10. P. G. Verly, “Hybrid approach for rugate filter design,” Appl. Opt. 47, C172-C178 (2008).
    [CrossRef] [PubMed]
  11. P. V. Bulkin, P. L. Swart, and B. M. Lacquet, “Fourier-transform design and electron cyclotron resonance plasma-enhanced deposition of lossy graded-index optical coatings,” Appl. Opt. 35, 4413-4419 (1996).
    [CrossRef] [PubMed]
  12. D. Poitras, S. Larouche, and L. Martinu, “Design and plasma deposition of dispersion-corrected multiband rugate filters,” Appl. Opt. 41, 5249-5255 (2002).
    [CrossRef] [PubMed]
  13. M. Lappschies, B. Görtz, and D. Ristau, “Application of optical broadband monitoring to quasi-rugate filters by ion-beam sputtering”, Appl. Opt. 45, 1502-1506 (2006).
    [CrossRef] [PubMed]
  14. A. V. Tikhonravov and M. K. Trubetskov, “Design of multilayers featuring inhomogeneous coating properties,” Proc. SPIE 2776, 48-57 (1996).
    [CrossRef]
  15. V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, J. Pistner, F. Krausz, and A. Apolonski, “Band filters: two-material technology versus rugate,” Appl. Opt. 46, 1190-1193 (2007).
    [CrossRef] [PubMed]
  16. W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457-460 (1985).
    [CrossRef] [PubMed]
  17. J. Allen and B. Herrington, “Digitized rugate filters for laser rejection,” Proc. SPIE 2046, 126-131 (1993).
    [CrossRef]
  18. Y. Wada, N. Toyohara, Y. Shinta, Sh. Iura, K. Takahashi, and K. Kawamata, “Design of minus filters using arbitrary refractive index films,” in Proceedings of Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), paper TuB5.
  19. J. A. Dobrowolski, “Numerical methods for optical thin films,” Opt. Photonics News 8, 24-33 (1997).
    [CrossRef]
  20. P. G. Verly, A. V. Tikhonravov, and M. K. Trubeskov, “Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization,” Proc. SPIE 3133, 46-52 (1997).
    [CrossRef]
  21. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).
  22. A. V. Tikhonravov, “Some theoretical aspects of thin film optics and their applications,” Appl. Opt. 32, 5417-5426 (1993).
    [CrossRef] [PubMed]
  23. A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov. “Second order optimization methods in the synthesis of multilayer coatings.,” Comp. Maths. Math. Phys. 33, 1339-1352 (1993).
  24. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1988).
  25. A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312-321 (2004).
    [CrossRef]

2008 (1)

2007 (1)

2006 (2)

2004 (1)

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312-321 (2004).
[CrossRef]

2002 (1)

1997 (2)

J. A. Dobrowolski, “Numerical methods for optical thin films,” Opt. Photonics News 8, 24-33 (1997).
[CrossRef]

P. G. Verly, A. V. Tikhonravov, and M. K. Trubeskov, “Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization,” Proc. SPIE 3133, 46-52 (1997).
[CrossRef]

1996 (2)

1993 (4)

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

B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427-5442 (1993).
[CrossRef] [PubMed]

J. Allen and B. Herrington, “Digitized rugate filters for laser rejection,” Proc. SPIE 2046, 126-131 (1993).
[CrossRef]

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov. “Second order optimization methods in the synthesis of multilayer coatings.,” Comp. Maths. Math. Phys. 33, 1339-1352 (1993).

1992 (1)

1990 (2)

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

R. R. Willey, P. G. Verly, and J. A. Dobrowolski, “Design of wideband antireflection coating with the Fourier transform method,” Proc. SPIE 1270, 36-44 (1990).
[CrossRef]

1989 (3)

1985 (1)

1978 (1)

Allen, J.

J. Allen and B. Herrington, “Digitized rugate filters for laser rejection,” Proc. SPIE 2046, 126-131 (1993).
[CrossRef]

Amotchkina, T. V.

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, M. A. Kokarev, N. Kaiser, O. Stenzel, S. Willbrandt, and D. Gäbler, “New optimization algorithm for the synthesis of rugate optical coatings,” Appl. Opt. 45, 1515-1524 (2006).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312-321 (2004).
[CrossRef]

Apolonski, A.

Bovard, B. G.

Bulkin, P. V.

Burton, R. L.

Dobrowolski, J. A.

Gäbler, D.

Gill, P. E.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).

Görtz, B.

Hall, R. L.

Herrington, B.

J. Allen and B. Herrington, “Digitized rugate filters for laser rejection,” Proc. SPIE 2046, 126-131 (1993).
[CrossRef]

Iura, Sh.

Y. Wada, N. Toyohara, Y. Shinta, Sh. Iura, K. Takahashi, and K. Kawamata, “Design of minus filters using arbitrary refractive index films,” in Proceedings of Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), paper TuB5.

Kaiser, N.

Kawamata, K.

Y. Wada, N. Toyohara, Y. Shinta, Sh. Iura, K. Takahashi, and K. Kawamata, “Design of minus filters using arbitrary refractive index films,” in Proceedings of Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), paper TuB5.

Kokarev, M. A.

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, M. A. Kokarev, N. Kaiser, O. Stenzel, S. Willbrandt, and D. Gäbler, “New optimization algorithm for the synthesis of rugate optical coatings,” Appl. Opt. 45, 1515-1524 (2006).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312-321 (2004).
[CrossRef]

Krausz, F.

Lacquet, B. M.

Lappschies, M.

Larouche, S.

Lowe, D.

Martinu, L.

Murray, W.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).

Pervak, V.

Pistner, J.

Poitras, D.

Ristau, D.

Shinta, Y.

Y. Wada, N. Toyohara, Y. Shinta, Sh. Iura, K. Takahashi, and K. Kawamata, “Design of minus filters using arbitrary refractive index films,” in Proceedings of Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), paper TuB5.

Southwell, W. H.

Stenzel, O.

Swart, P. L.

Takahashi, K.

Y. Wada, N. Toyohara, Y. Shinta, Sh. Iura, K. Takahashi, and K. Kawamata, “Design of minus filters using arbitrary refractive index films,” in Proceedings of Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), paper TuB5.

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1988).

Tikhonov, A. N.

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov. “Second order optimization methods in the synthesis of multilayer coatings.,” Comp. Maths. Math. Phys. 33, 1339-1352 (1993).

Tikhonravov, A. V.

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, J. Pistner, F. Krausz, and A. Apolonski, “Band filters: two-material technology versus rugate,” Appl. Opt. 46, 1190-1193 (2007).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, M. A. Kokarev, N. Kaiser, O. Stenzel, S. Willbrandt, and D. Gäbler, “New optimization algorithm for the synthesis of rugate optical coatings,” Appl. Opt. 45, 1515-1524 (2006).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312-321 (2004).
[CrossRef]

P. G. Verly, A. V. Tikhonravov, and M. K. Trubeskov, “Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization,” Proc. SPIE 3133, 46-52 (1997).
[CrossRef]

A. V. Tikhonravov and M. K. Trubetskov, “Design of multilayers featuring inhomogeneous coating properties,” Proc. SPIE 2776, 48-57 (1996).
[CrossRef]

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov. “Second order optimization methods in the synthesis of multilayer coatings.,” Comp. Maths. Math. Phys. 33, 1339-1352 (1993).

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

Toyohara, N.

Y. Wada, N. Toyohara, Y. Shinta, Sh. Iura, K. Takahashi, and K. Kawamata, “Design of minus filters using arbitrary refractive index films,” in Proceedings of Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), paper TuB5.

Trubeskov, M. K.

P. G. Verly, A. V. Tikhonravov, and M. K. Trubeskov, “Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization,” Proc. SPIE 3133, 46-52 (1997).
[CrossRef]

Trubetskov, M. K.

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, J. Pistner, F. Krausz, and A. Apolonski, “Band filters: two-material technology versus rugate,” Appl. Opt. 46, 1190-1193 (2007).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, M. A. Kokarev, N. Kaiser, O. Stenzel, S. Willbrandt, and D. Gäbler, “New optimization algorithm for the synthesis of rugate optical coatings,” Appl. Opt. 45, 1515-1524 (2006).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312-321 (2004).
[CrossRef]

A. V. Tikhonravov and M. K. Trubetskov, “Design of multilayers featuring inhomogeneous coating properties,” Proc. SPIE 2776, 48-57 (1996).
[CrossRef]

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov. “Second order optimization methods in the synthesis of multilayer coatings.,” Comp. Maths. Math. Phys. 33, 1339-1352 (1993).

Verly, P. G.

P. G. Verly, “Hybrid approach for rugate filter design,” Appl. Opt. 47, C172-C178 (2008).
[CrossRef] [PubMed]

P. G. Verly, A. V. Tikhonravov, and M. K. Trubeskov, “Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization,” Proc. SPIE 3133, 46-52 (1997).
[CrossRef]

P. G. Verly, J. A. Dobrowolski, and R. R. Willey, “Fourier-transform method for the design of wideband antireflection coatings,” Appl. Opt. 31, 3836-3846 (1992).
[CrossRef] [PubMed]

R. R. Willey, P. G. Verly, and J. A. Dobrowolski, “Design of wideband antireflection coating with the Fourier transform method,” Proc. SPIE 1270, 36-44 (1990).
[CrossRef]

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

Wada, Y.

Y. Wada, N. Toyohara, Y. Shinta, Sh. Iura, K. Takahashi, and K. Kawamata, “Design of minus filters using arbitrary refractive index films,” in Proceedings of Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), paper TuB5.

Wild, W. J.

Willbrandt, S.

Willey, R. R.

P. G. Verly, J. A. Dobrowolski, and R. R. Willey, “Fourier-transform method for the design of wideband antireflection coatings,” Appl. Opt. 31, 3836-3846 (1992).
[CrossRef] [PubMed]

R. R. Willey, P. G. Verly, and J. A. Dobrowolski, “Design of wideband antireflection coating with the Fourier transform method,” Proc. SPIE 1270, 36-44 (1990).
[CrossRef]

Wright, M. H.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).

Appl. Opt. (15)

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

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

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

W. H. Southwell and R. L. Hall, “Rugate filter sidelobe suppression using quintic and rugated quintic matching layers,” Appl. Opt. 28, 2949-2951 (1989).
[CrossRef] [PubMed]

W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091-5094 (1989).
[CrossRef] [PubMed]

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

P. G. Verly, J. A. Dobrowolski, and R. R. Willey, “Fourier-transform method for the design of wideband antireflection coatings,” Appl. Opt. 31, 3836-3846 (1992).
[CrossRef] [PubMed]

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

B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427-5442 (1993).
[CrossRef] [PubMed]

P. V. Bulkin, P. L. Swart, and B. M. Lacquet, “Fourier-transform design and electron cyclotron resonance plasma-enhanced deposition of lossy graded-index optical coatings,” Appl. Opt. 35, 4413-4419 (1996).
[CrossRef] [PubMed]

D. Poitras, S. Larouche, and L. Martinu, “Design and plasma deposition of dispersion-corrected multiband rugate filters,” Appl. Opt. 41, 5249-5255 (2002).
[CrossRef] [PubMed]

M. Lappschies, B. Görtz, and D. Ristau, “Application of optical broadband monitoring to quasi-rugate filters by ion-beam sputtering”, Appl. Opt. 45, 1502-1506 (2006).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, M. A. Kokarev, N. Kaiser, O. Stenzel, S. Willbrandt, and D. Gäbler, “New optimization algorithm for the synthesis of rugate optical coatings,” Appl. Opt. 45, 1515-1524 (2006).
[CrossRef] [PubMed]

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, J. Pistner, F. Krausz, and A. Apolonski, “Band filters: two-material technology versus rugate,” Appl. Opt. 46, 1190-1193 (2007).
[CrossRef] [PubMed]

P. G. Verly, “Hybrid approach for rugate filter design,” Appl. Opt. 47, C172-C178 (2008).
[CrossRef] [PubMed]

Comp. Maths. Math. Phys. (1)

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov. “Second order optimization methods in the synthesis of multilayer coatings.,” Comp. Maths. Math. Phys. 33, 1339-1352 (1993).

Opt. Photonics News (1)

J. A. Dobrowolski, “Numerical methods for optical thin films,” Opt. Photonics News 8, 24-33 (1997).
[CrossRef]

Proc. SPIE (5)

P. G. Verly, A. V. Tikhonravov, and M. K. Trubeskov, “Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization,” Proc. SPIE 3133, 46-52 (1997).
[CrossRef]

R. R. Willey, P. G. Verly, and J. A. Dobrowolski, “Design of wideband antireflection coating with the Fourier transform method,” Proc. SPIE 1270, 36-44 (1990).
[CrossRef]

A. V. Tikhonravov and M. K. Trubetskov, “Design of multilayers featuring inhomogeneous coating properties,” Proc. SPIE 2776, 48-57 (1996).
[CrossRef]

J. Allen and B. Herrington, “Digitized rugate filters for laser rejection,” Proc. SPIE 2046, 126-131 (1993).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312-321 (2004).
[CrossRef]

Other (3)

Y. Wada, N. Toyohara, Y. Shinta, Sh. Iura, K. Takahashi, and K. Kawamata, “Design of minus filters using arbitrary refractive index films,” in Proceedings of Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), paper TuB5.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1988).

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Figures (12)

Fig. 1
Fig. 1

Target reflectance of the high reflector with an extended high transmission zone (thick lines) and reflectance of the starting design used to design a quasi-rugate filter (solid curve).

Fig. 2
Fig. 2

Refractive index profile of the quasi-rugate coating with the spectral reflectance shown in Fig. 3.

Fig. 3
Fig. 3

Reflectance of the quasi-rugate reflector (solid curve) and target reflectance (thick lines).

Fig. 4
Fig. 4

Reflectance of the 47-layer minus filter with the refractive index profile shown in Fig. 5. Target reflectance is shown by thick lines.

Fig. 5
Fig. 5

Refractive index profile of the 47-layer minus filter with reflectance shown in Fig. 4.

Fig. 6
Fig. 6

Reflectance of the minus filter with extremely narrow high reflection zone (solid curve). Target reflectance is shown by thick lines.

Fig. 7
Fig. 7

Refractive index profile of the 160-layer minus filter with the reflectance shown in Fig. 6.

Fig. 8
Fig. 8

Target reflectance of the same high reflector as in Fig. 2 (thick lines) and reflectance of the designed two-component multilayer.

Fig. 9
Fig. 9

Refractive index profile of the two-component multilayer with the spectral reflectance depicted in Fig. 8.

Fig. 10
Fig. 10

Reflectance of the 120-layer two-component design with layer refractive indices 1.47 and 2.4 (solid curve). Target reflectance is shown by thick lines.

Fig. 11
Fig. 11

Reflectances of two filters with three high reflection zones: dashed curve corresponds to the quasi-rugate filter with the refractive index profile (a) in Fig. 12 and solid curve corresponds to the two-component filter with the refractive index profile (b) in Fig. 12. Target reflectance is shown by thick lines.

Fig. 12
Fig. 12

Refractive index profiles of the quasi-rugate (a) and two-component (b) filters with the reflectances shown in Fig. 11.

Equations (5)

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n j , L n j n j , H , d j , L d j d j , H , j = 1 , , m .
n ( λ ) = μ n L ( λ ) + ( 1 μ ) n H ( λ ) ,
MF ( X ) = 1 2 { { λ j } 1 [ R ( X , λ j ) Δ R j ] 2 + { λ j } 2 [ R ( X , λ j ) 100 % Δ R j ] 2 } ,
n j d j = λ 0 / 4 , j = 1 , , m .
d MF d n j = MF n j λ 0 4 n j 2 MF d j .

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