Abstract

Fourier techniques and direct optimization are applied to the synthesis of complex rugate filters. A hybrid approach is presented. The design strategies are illustrated numerically for different spectral shapes.

© 2008 Optical Society of America

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  1. A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, M. A. Kokarev, N. Kaiser, O. Stenzel, S. Wilbrandt, and D. Gäbler, "New optimization algorithm for the synthesis of rugate optical coatings," Appl. Opt. 45, 1515-1524 (2006).
    [CrossRef] [PubMed]
  2. P. Ma, F. Lin, and P. G. Verly, "Reactively-sputtered silicon-oxynitride films and filters," in 49th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2006), pp. 725-727.
  3. A. G. Imenes and D. R. McKenzie, "Flat-topped broadband rugate filters," Appl. Opt. 45, 7841-7850 (2006).
    [CrossRef] [PubMed]
  4. S. Lange, H. Bartzsch, P. Frach, and K. Goedicke, "Pulse magnetron sputtering in a reactive gas mixture of variable composition to manufacture multilayer and gradient optical coatings," Thin Solid Films 502, 29-33 (2006).
    [CrossRef]
  5. M. Lappschies, B. Gortz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion-beam sputtering," Appl. Opt. 45, 1502-1506 (2006).
    [CrossRef] [PubMed]
  6. R. Leitel, O. Stenzel, S. Wilbrandt, D. Gabler, V. Janicki, and N. Kaiser, "Optical and non-optical characterization of Nb2O5-SiO2 compositional graded-index layers and rugate structures," Thin Solid Films 497, 135-141 (2006).
    [CrossRef]
  7. C. C. Lee, C. J. Tang, and J. Y. Wu, "Rugate filter made with composite thin films by ion-beam sputtering," Appl. Opt. 45, 1333-1337 (2006).
    [CrossRef] [PubMed]
  8. U. Ortabasi and B. Bovard, "Rugate technology for thermophotovoltaic (TPV) applications: a new approach to near perfect filter performance," AIP Conf. Proc. 653, 249-258 (2003).
    [CrossRef]
  9. 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]
  10. 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]
  11. R. W. Sprague, B. Shnapir, and G. L. Minott, "Rugate notch filters find use in laser-based applications," Laser Focus World 40, 107-108, 110-111 (2004).
  12. S. T. Allan, B. Herrington, C. Cole, K. Mackrodt, T. Slim, and D. Lingwood, "Rugate coatings for an avionics head-up display," Proc. SPIE 5443, 130-137 (2004).
    [CrossRef]
  13. 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]
  14. W. H. Southwell, "Using apodization functions to reduce sidelobes in rugate filters," Appl. Opt. 28, 5091-5094 (1989).
    [CrossRef] [PubMed]
  15. W. H. Southwell, "Gradient-index antireflection coatings," Opt. Lett. 8, 584-586 (1983).
    [CrossRef] [PubMed]
  16. D. Poitras and J. A. Dobrowolski, "Toward perfect antireflection coatings. 2. Theory," Appl. Opt. 43, 1286-1295 (2004).
    [CrossRef] [PubMed]
  17. W. E. Johnson and R. L. Crane, "Introduction to rugate filter technology," Proc. SPIE 2046, 88-108 (1993).
    [CrossRef]
  18. W. H. Southwell, "Extended-bandwidth reflector designs by using wavelets," Appl. Opt. 36, 314-318 (1997).
    [CrossRef] [PubMed]
  19. L. Sossi, "A method for the synthesis of multilayer dielectric interference coatings," Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229-237 (1974).
  20. J. A. Dobrowolski and D. Lowe, "Optical thin film synthesis program based on the use of Fourier transforms," Appl. Opt. 17, 3039-3050 (1978).
    [CrossRef] [PubMed]
  21. B. G. Bovard, "Rugate filter design: the modified Fourier transform technique," Appl. Opt. 29, 24-30 (1990).
    [CrossRef] [PubMed]
  22. P. G. Verly and J. A. Dobrowolski, "Iterative correction process for optical thin film synthesis with the Fourier transform method," Appl. Opt. 29, 3672-3684 (1990).
    [CrossRef] [PubMed]
  23. P. G. Verly, "Optical coating synthesis by simultaneous refractive-index and thickness refinement of inhomogeneous films," Appl. Opt. 37, 7327-7333 (1998).
    [CrossRef]
  24. P. G. Verly, "Design of inhomogeneous and quasi-inhomogeneous optical coatings at the NRC," Proc. SPIE 2046, 36-45 (1993).
    [CrossRef]
  25. P. G. Verly, "Fourier transform technique with frequency filtering for optical thin-film design," Appl. Opt. 34, 688-694 (1995).
    [CrossRef] [PubMed]
  26. H. Fabricius, "Gradient-index filters: conversion into a two-index solution by taking into account dispersion," Appl. Opt. 31, 5216-5220 (1992).
    [CrossRef] [PubMed]
  27. 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]
  28. B. G. Bovard, "Fourier transform technique applied to quarterwave optical coatings," Appl. Opt. 27, 3062-3063 (1988).
    [CrossRef] [PubMed]
  29. 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]
  30. P. G. Verly, "Fourier transform technique with frequency filtering for antireflection coating design," Proc. SPIE 2262, 161-167 (1994).
    [CrossRef]
  31. B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. II. Experimental results--sputtering system," Appl. Opt. 32, 2351-2360 (1993).
    [CrossRef] [PubMed]
  32. P. Baumeister, "Simulation of a rugate filter via a stepped-index dielectric multilayer," Appl. Opt. 25, 2644-2645 (1986).
    [CrossRef] [PubMed]
  33. P. G. Verly, "Design of complex rugate filters," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), paper WA5.

2007 (2)

P. G. Verly, "Design of complex rugate filters," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), paper WA5.

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]

2006 (7)

C. C. Lee, C. J. Tang, and J. Y. Wu, "Rugate filter made with composite thin films by ion-beam sputtering," Appl. Opt. 45, 1333-1337 (2006).
[CrossRef] [PubMed]

M. Lappschies, B. Gortz, 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. G. Imenes and D. R. McKenzie, "Flat-topped broadband rugate filters," Appl. Opt. 45, 7841-7850 (2006).
[CrossRef] [PubMed]

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

P. Ma, F. Lin, and P. G. Verly, "Reactively-sputtered silicon-oxynitride films and filters," in 49th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2006), pp. 725-727.

S. Lange, H. Bartzsch, P. Frach, and K. Goedicke, "Pulse magnetron sputtering in a reactive gas mixture of variable composition to manufacture multilayer and gradient optical coatings," Thin Solid Films 502, 29-33 (2006).
[CrossRef]

R. Leitel, O. Stenzel, S. Wilbrandt, D. Gabler, V. Janicki, and N. Kaiser, "Optical and non-optical characterization of Nb2O5-SiO2 compositional graded-index layers and rugate structures," Thin Solid Films 497, 135-141 (2006).
[CrossRef]

2004 (3)

R. W. Sprague, B. Shnapir, and G. L. Minott, "Rugate notch filters find use in laser-based applications," Laser Focus World 40, 107-108, 110-111 (2004).

S. T. Allan, B. Herrington, C. Cole, K. Mackrodt, T. Slim, and D. Lingwood, "Rugate coatings for an avionics head-up display," Proc. SPIE 5443, 130-137 (2004).
[CrossRef]

D. Poitras and J. A. Dobrowolski, "Toward perfect antireflection coatings. 2. Theory," Appl. Opt. 43, 1286-1295 (2004).
[CrossRef] [PubMed]

2003 (1)

U. Ortabasi and B. Bovard, "Rugate technology for thermophotovoltaic (TPV) applications: a new approach to near perfect filter performance," AIP Conf. Proc. 653, 249-258 (2003).
[CrossRef]

2002 (1)

1998 (1)

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

1997 (1)

W. H. Southwell, "Extended-bandwidth reflector designs by using wavelets," Appl. Opt. 36, 314-318 (1997).
[CrossRef] [PubMed]

1996 (1)

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]

1995 (1)

1994 (1)

P. G. Verly, "Fourier transform technique with frequency filtering for antireflection coating design," Proc. SPIE 2262, 161-167 (1994).
[CrossRef]

1993 (3)

P. G. Verly, "Design of inhomogeneous and quasi-inhomogeneous optical coatings at the NRC," Proc. SPIE 2046, 36-45 (1993).
[CrossRef]

W. E. Johnson and R. L. Crane, "Introduction to rugate filter technology," Proc. SPIE 2046, 88-108 (1993).
[CrossRef]

B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. II. Experimental results--sputtering system," Appl. Opt. 32, 2351-2360 (1993).
[CrossRef] [PubMed]

1992 (2)

1990 (2)

1989 (2)

1988 (1)

B. G. Bovard, "Fourier transform technique applied to quarterwave optical coatings," Appl. Opt. 27, 3062-3063 (1988).
[CrossRef] [PubMed]

1986 (1)

1983 (1)

W. H. Southwell, "Gradient-index antireflection coatings," Opt. Lett. 8, 584-586 (1983).
[CrossRef] [PubMed]

1978 (1)

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

1974 (1)

L. Sossi, "A method for the synthesis of multilayer dielectric interference coatings," Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229-237 (1974).

Allan, S. T.

S. T. Allan, B. Herrington, C. Cole, K. Mackrodt, T. Slim, and D. Lingwood, "Rugate coatings for an avionics head-up display," Proc. SPIE 5443, 130-137 (2004).
[CrossRef]

Amotchkina, T. V.

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

Apolonski, A.

Bartzsch, H.

S. Lange, H. Bartzsch, P. Frach, and K. Goedicke, "Pulse magnetron sputtering in a reactive gas mixture of variable composition to manufacture multilayer and gradient optical coatings," Thin Solid Films 502, 29-33 (2006).
[CrossRef]

Baumeister, P.

Bovard, B.

U. Ortabasi and B. Bovard, "Rugate technology for thermophotovoltaic (TPV) applications: a new approach to near perfect filter performance," AIP Conf. Proc. 653, 249-258 (2003).
[CrossRef]

Bovard, B. G.

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

B. G. Bovard, "Fourier transform technique applied to quarterwave optical coatings," Appl. Opt. 27, 3062-3063 (1988).
[CrossRef] [PubMed]

Bulkin, P. V.

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]

Burton, R. L.

Cole, C.

S. T. Allan, B. Herrington, C. Cole, K. Mackrodt, T. Slim, and D. Lingwood, "Rugate coatings for an avionics head-up display," Proc. SPIE 5443, 130-137 (2004).
[CrossRef]

Crane, R. L.

W. E. Johnson and R. L. Crane, "Introduction to rugate filter technology," Proc. SPIE 2046, 88-108 (1993).
[CrossRef]

Dobrowolski, J. A.

Fabricius, H.

Frach, P.

S. Lange, H. Bartzsch, P. Frach, and K. Goedicke, "Pulse magnetron sputtering in a reactive gas mixture of variable composition to manufacture multilayer and gradient optical coatings," Thin Solid Films 502, 29-33 (2006).
[CrossRef]

Gabler, D.

R. Leitel, O. Stenzel, S. Wilbrandt, D. Gabler, V. Janicki, and N. Kaiser, "Optical and non-optical characterization of Nb2O5-SiO2 compositional graded-index layers and rugate structures," Thin Solid Films 497, 135-141 (2006).
[CrossRef]

Gäbler, D.

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

Goedicke, K.

S. Lange, H. Bartzsch, P. Frach, and K. Goedicke, "Pulse magnetron sputtering in a reactive gas mixture of variable composition to manufacture multilayer and gradient optical coatings," Thin Solid Films 502, 29-33 (2006).
[CrossRef]

Gortz, B.

Herrington, B.

S. T. Allan, B. Herrington, C. Cole, K. Mackrodt, T. Slim, and D. Lingwood, "Rugate coatings for an avionics head-up display," Proc. SPIE 5443, 130-137 (2004).
[CrossRef]

Imenes, A. G.

Janicki, V.

R. Leitel, O. Stenzel, S. Wilbrandt, D. Gabler, V. Janicki, and N. Kaiser, "Optical and non-optical characterization of Nb2O5-SiO2 compositional graded-index layers and rugate structures," Thin Solid Films 497, 135-141 (2006).
[CrossRef]

Johnson, W. E.

W. E. Johnson and R. L. Crane, "Introduction to rugate filter technology," Proc. SPIE 2046, 88-108 (1993).
[CrossRef]

Kaiser, N.

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

R. Leitel, O. Stenzel, S. Wilbrandt, D. Gabler, V. Janicki, and N. Kaiser, "Optical and non-optical characterization of Nb2O5-SiO2 compositional graded-index layers and rugate structures," Thin Solid Films 497, 135-141 (2006).
[CrossRef]

Kokarev, M. A.

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

Krausz, F.

Lacquet, B. M.

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]

Lange, S.

S. Lange, H. Bartzsch, P. Frach, and K. Goedicke, "Pulse magnetron sputtering in a reactive gas mixture of variable composition to manufacture multilayer and gradient optical coatings," Thin Solid Films 502, 29-33 (2006).
[CrossRef]

Lappschies, M.

Larouche, S.

Lee, C. C.

Leitel, R.

R. Leitel, O. Stenzel, S. Wilbrandt, D. Gabler, V. Janicki, and N. Kaiser, "Optical and non-optical characterization of Nb2O5-SiO2 compositional graded-index layers and rugate structures," Thin Solid Films 497, 135-141 (2006).
[CrossRef]

Lin, F.

P. Ma, F. Lin, and P. G. Verly, "Reactively-sputtered silicon-oxynitride films and filters," in 49th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2006), pp. 725-727.

Lingwood, D.

S. T. Allan, B. Herrington, C. Cole, K. Mackrodt, T. Slim, and D. Lingwood, "Rugate coatings for an avionics head-up display," Proc. SPIE 5443, 130-137 (2004).
[CrossRef]

Lowe, D.

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

Ma, P.

P. Ma, F. Lin, and P. G. Verly, "Reactively-sputtered silicon-oxynitride films and filters," in 49th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2006), pp. 725-727.

Mackrodt, K.

S. T. Allan, B. Herrington, C. Cole, K. Mackrodt, T. Slim, and D. Lingwood, "Rugate coatings for an avionics head-up display," Proc. SPIE 5443, 130-137 (2004).
[CrossRef]

Martinu, L.

McKenzie, D. R.

Minott, G. L.

R. W. Sprague, B. Shnapir, and G. L. Minott, "Rugate notch filters find use in laser-based applications," Laser Focus World 40, 107-108, 110-111 (2004).

Ortabasi, U.

U. Ortabasi and B. Bovard, "Rugate technology for thermophotovoltaic (TPV) applications: a new approach to near perfect filter performance," AIP Conf. Proc. 653, 249-258 (2003).
[CrossRef]

Pervak, V.

Pistner, J.

Poitras, D.

Ristau, D.

Shnapir, B.

R. W. Sprague, B. Shnapir, and G. L. Minott, "Rugate notch filters find use in laser-based applications," Laser Focus World 40, 107-108, 110-111 (2004).

Slim, T.

S. T. Allan, B. Herrington, C. Cole, K. Mackrodt, T. Slim, and D. Lingwood, "Rugate coatings for an avionics head-up display," Proc. SPIE 5443, 130-137 (2004).
[CrossRef]

Sossi, L.

L. Sossi, "A method for the synthesis of multilayer dielectric interference coatings," Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229-237 (1974).

Southwell, W. H.

W. H. Southwell, "Extended-bandwidth reflector designs by using wavelets," Appl. Opt. 36, 314-318 (1997).
[CrossRef] [PubMed]

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

W. H. Southwell, "Gradient-index antireflection coatings," Opt. Lett. 8, 584-586 (1983).
[CrossRef] [PubMed]

Sprague, R. W.

R. W. Sprague, B. Shnapir, and G. L. Minott, "Rugate notch filters find use in laser-based applications," Laser Focus World 40, 107-108, 110-111 (2004).

Stenzel, O.

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

R. Leitel, O. Stenzel, S. Wilbrandt, D. Gabler, V. Janicki, and N. Kaiser, "Optical and non-optical characterization of Nb2O5-SiO2 compositional graded-index layers and rugate structures," Thin Solid Films 497, 135-141 (2006).
[CrossRef]

Sullivan, B. T.

Swart, P. L.

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]

Tang, C. J.

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. Wilbrandt, and D. Gäbler, "New optimization algorithm for the synthesis of rugate optical coatings," Appl. Opt. 45, 1515-1524 (2006).
[CrossRef] [PubMed]

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. Wilbrandt, and D. Gäbler, "New optimization algorithm for the synthesis of rugate optical coatings," Appl. Opt. 45, 1515-1524 (2006).
[CrossRef] [PubMed]

Verly, P. G.

P. G. Verly, "Design of complex rugate filters," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), paper WA5.

P. Ma, F. Lin, and P. G. Verly, "Reactively-sputtered silicon-oxynitride films and filters," in 49th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2006), pp. 725-727.

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, "Fourier transform technique with frequency filtering for optical thin-film design," Appl. Opt. 34, 688-694 (1995).
[CrossRef] [PubMed]

P. G. Verly, "Fourier transform technique with frequency filtering for antireflection coating design," Proc. SPIE 2262, 161-167 (1994).
[CrossRef]

P. G. Verly, "Design of inhomogeneous and quasi-inhomogeneous optical coatings at the NRC," Proc. SPIE 2046, 36-45 (1993).
[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]

P. G. Verly and 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, 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]

Wilbrandt, S.

R. Leitel, O. Stenzel, S. Wilbrandt, D. Gabler, V. Janicki, and N. Kaiser, "Optical and non-optical characterization of Nb2O5-SiO2 compositional graded-index layers and rugate structures," Thin Solid Films 497, 135-141 (2006).
[CrossRef]

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

Wild, W. J.

Willey, R. R.

Wu, J. Y.

AIP Conf. Proc. (1)

U. Ortabasi and B. Bovard, "Rugate technology for thermophotovoltaic (TPV) applications: a new approach to near perfect filter performance," AIP Conf. Proc. 653, 249-258 (2003).
[CrossRef]

Appl. Opt. (8)

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

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

W. H. Southwell, "Extended-bandwidth reflector designs by using wavelets," Appl. Opt. 36, 314-318 (1997).
[CrossRef] [PubMed]

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

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

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Figures (9)

Fig. 1
Fig. 1

Basic FT design obtained from Eq. (1). Thick gray curve, spectral target. Black curves, calculated data. Dotted curve, support layer for the refractive index modulation. Material dispersion is not included.

Fig. 2
Fig. 2

Rugate solution obtained by the iterative FT correction process. The dotted curve in the bottom part of the figure is the starting design. Material dispersion is included. The refractive-index profile is plotted at the reference wavelength of 1.2 μ m .

Fig. 3
Fig. 3

Material dispersion. The top and bottom curves correspond to N b 2 O 5 and S i O 2 , respectively. The middle curve is a linear mixture of the outer refractive indices.

Fig. 4
Fig. 4

Design obtained by refractive-index optimization without active smoothing. The dotted line in the bottom part of the figure is the starting design. Material dispersion is included in the reflectance calculation.

Fig. 5
Fig. 5

Smoothing by spatial frequency filtering of the Refinh design illustrated in Fig. 4. The wavelengths < 0.65 μ m are suppressed from the Fourier spectrum of the index profile. Material dispersion is included.

Fig. 6
Fig. 6

Reoptimization of the smoothed rugate design shown in Fig. 5.

Fig. 7
Fig. 7

FT design of a rugate filter corresponding to the silhouette of the Taj Mahal. The refractive-index profile is calculated at the middle inverse wavelength of 1.6 μ m 1 without taking dispersion into account. The plotted reflectance includes dispersion. The nondispersive reflectance is a good fit of the target (not plotted for clarity).

Fig. 8
Fig. 8

Semirugate solution obtained when dispersion is taken into account in the FT correction process.

Fig. 9
Fig. 9

Rugate solution obtained by the Refinh approach and spatial frequency filtering. Material dispersion is included.

Equations (3)

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ln [ n ( x ) n 0 ] FT i π Q ˜ ( T , σ ) σ ,
Q 2 ( T ) = R = 1 T ,
Q 7 ( T ) = ln ( 1 T ) .

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