Abstract

A model of a rugate coating that takes into account production potentialities of the Leybold Syrus Pro 1100 deposition system is presented. An efficient algorithm for the synthesis of rugate coatings is proposed. Numerical results are also presented.

© 2006 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. H. A. Abu-Safia, A. I. Al-Sharif, and I. O. Abu Aljarayesh, 'Rugate filter sidelobe suppression using half-apodization,' Appl. Opt. 32, 4831-4835 (1993).
    [CrossRef] [PubMed]
  4. H. Fabricius, 'Gradient-index filter: designing filters with step skirts, high reflection and quintic matching layers,' Appl. Opt. 31, 5191-5196 (1992).
    [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. B. G. Bovard, 'Rugate filter design: the modified Fourier transform technique,' Appl. Opt. 29, 24-30 (1990).
    [CrossRef] [PubMed]
  8. B. G. Bovard, 'Rugate filter theory: an overview,' Appl. Opt. 32, 5427-5442 (1993).
    [CrossRef] [PubMed]
  9. R. R. Willey, 'Rugate broadband antireflection coating design,' in Current Developments in Optical Engineering and Commercial Optics, R.E.Fischer, H.M.Pollicove, and W.J.Smith, eds. Proc. SPIE 1168, 224-228 (1989).
  10. R. R. Willey, P. G. Verly, and J. A. Dobrowolski, 'Design of wideband antireflection coating with the Fourier transform method,' in Optical Thin Films and Applications, R.Herrmann, ed., Proc. SPIE 1270, 36-44 (1990).
  11. 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]
  12. J. Allen and B. Harrington, 'Digitized rugate filters for laser application,' in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J.A.Dobrowolski and P.G.Verly, eds., Proc. SPIE 2046, 126-131 (1993).
  13. A. V. Tikhonravov, M. K. Trubetskov, and G. DeBell, 'Application of the needle optimization technique to the design of optical coatings,' Appl. Opt. 35, 5493-5508 (1996).
    [CrossRef] [PubMed]
  14. A. V. Tikhonravov, 'Synthesis of optical coatings using optimality conditions,' Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91-93 (1982).
  15. A. V. Tikhonravov and M. K. Trubetskov, 'Design of multilayers featuring inhomogeneous coating properties,' in Developments in Optical Component Coatings, I.Reid, ed., Proc. SPIE 2776, 48-57 (1996).
  16. E. P. Donovan, D. V. Vechten, A. D. F. Kahn, C. A. Carosella, and G. K. Hubler, 'Near infrared rugate filter fabrication by ion beam assisted deposition of Si1−xNx films,' Appl. Opt. 28, 2940-2944 (1989).
    [CrossRef] [PubMed]
  17. W. J. Gunning, R. L. Hall, F. J. Woodberry, W. H. Southwell, and N. S. Gluck, 'Codeposition of continuous composition rugate filters,' Appl. Opt. 28, 2945-2948 (1989).
    [CrossRef] [PubMed]
  18. J. P. Heuer, J. P. Elben, R. L. Hall, and W. J. Gunning, 'Scale-up considerations for codeposited gradient index optical thin film filters,' in Optical Interference Coatings, Vol. 15 of 1992 OSA Technical Digest Series (Optical Society of America, 1992), pp. 122-124.
  19. 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]
  20. A. G. Greenham, B. A. Nichols, R. M. Wood, N. Nourshargh, and K. L. Lewis, 'Optical interference filters with continuous refractive index modulations by microwave plasma-assisted chemical vapor deposition,' Opt. Eng. 32, 1018-1023 (1993).
    [CrossRef]
  21. P. G. Verly and J. A. Dobrowolski, 'Iterate correction procedure for optical thin film synthesis with the Fourier transform method,' Appl. Opt. 29, 3672-3684 (1990).
    [CrossRef] [PubMed]
  22. A. V. Tikhonravov, M. K. Trubetskov, I. V. Zuev, and P. G. Verly, 'Efficient refinement of inhomogeneous optical coatings,' in Optical Interference Coatings, Vol. 17 of 1995 OSA Technical Digest Series (Optical Society of America, 1995), pp. 22-24.
  23. P. G. Verly, A. V. Tikhonravov, and M. K. Trubetskov, 'Efficient refinement algorithm for the synthesis of inhomogeneous optical coatings,' Appl. Opt. 36, 1487-1495 (1997).
    [CrossRef] [PubMed]
  24. S. Furman and A. V. Tikhnravov, Optics of Multilayer Systems (Editions Frontieres, 1992).
  25. A. V. Tikhonravov, 'Some theoretical aspects of thin film optics and their applications,' Appl. Opt. 32, 5417-5426 (1993).
    [CrossRef] [PubMed]
  26. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems (Wiley, 1977).
  27. D. Himmelblau, Applied Nonlinar Programming (McGraw-Hill, 1972).
  28. A. V. Tikhonravov and M. K. Trubetskov, OptiLayer Software, version 4.76, http://www.optilayer.com (2003).
  29. R. L. Hall and W. H. Southwell, 'Graded reflector/absorber coating,' in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J.A.Dobrowolski and P.G.Verly, eds., Proc. SPIE 2046, 78-85 (1993).
  30. J. C. M. Garnett, 'Colors in metal glasses and metal films,' Trans. R. Soc. London 53, 385-420 (1904).
    [CrossRef]
  31. D. A. G. Bruggeman, 'Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen, insbesondere Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen,' Ann. Phys 24, 636-664 (1935).
    [CrossRef]
  32. D. J. Bergman, 'The dielectric constant of a composite material--a problem in classical physics,' Phys. Lett. 43C, 377-407 (1978).
  33. A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov, 'Second-order optimization methods in the synthesis of multilayer coatings,' J. Comput. Math. Math. Phys. 33, 1518-1535 (1993).

1997 (1)

1996 (2)

1993 (5)

A. G. Greenham, B. A. Nichols, R. M. Wood, N. Nourshargh, and K. L. Lewis, 'Optical interference filters with continuous refractive index modulations by microwave plasma-assisted chemical vapor deposition,' Opt. Eng. 32, 1018-1023 (1993).
[CrossRef]

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

H. A. Abu-Safia, A. I. Al-Sharif, and I. O. Abu Aljarayesh, 'Rugate filter sidelobe suppression using half-apodization,' Appl. Opt. 32, 4831-4835 (1993).
[CrossRef] [PubMed]

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

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov, 'Second-order optimization methods in the synthesis of multilayer coatings,' J. Comput. Math. Math. Phys. 33, 1518-1535 (1993).

1992 (2)

1990 (2)

1989 (5)

1982 (1)

A. V. Tikhonravov, 'Synthesis of optical coatings using optimality conditions,' Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91-93 (1982).

1978 (2)

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]

D. J. Bergman, 'The dielectric constant of a composite material--a problem in classical physics,' Phys. Lett. 43C, 377-407 (1978).

1935 (1)

D. A. G. Bruggeman, 'Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen, insbesondere Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen,' Ann. Phys 24, 636-664 (1935).
[CrossRef]

1904 (1)

J. C. M. Garnett, 'Colors in metal glasses and metal films,' Trans. R. Soc. London 53, 385-420 (1904).
[CrossRef]

Abu Aljarayesh, I. O.

Abu-Safia, H. A.

Allen, J.

J. Allen and B. Harrington, 'Digitized rugate filters for laser application,' in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J.A.Dobrowolski and P.G.Verly, eds., Proc. SPIE 2046, 126-131 (1993).

Al-Sharif, A. I.

Arsenin, V. Y.

A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems (Wiley, 1977).

Bergman, D. J.

D. J. Bergman, 'The dielectric constant of a composite material--a problem in classical physics,' Phys. Lett. 43C, 377-407 (1978).

Bovard, B. G.

Bruggeman, D. A. G.

D. A. G. Bruggeman, 'Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen, insbesondere Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen,' Ann. Phys 24, 636-664 (1935).
[CrossRef]

Bulkin, P. V.

Burton, R. L.

Carosella, C. A.

DeBell, G.

Dobrowolski, J. A.

Donovan, E. P.

Elben, J. P.

J. P. Heuer, J. P. Elben, R. L. Hall, and W. J. Gunning, 'Scale-up considerations for codeposited gradient index optical thin film filters,' in Optical Interference Coatings, Vol. 15 of 1992 OSA Technical Digest Series (Optical Society of America, 1992), pp. 122-124.

Fabricius, H.

Furman, S.

S. Furman and A. V. Tikhnravov, Optics of Multilayer Systems (Editions Frontieres, 1992).

Garnett, J. C. M.

J. C. M. Garnett, 'Colors in metal glasses and metal films,' Trans. R. Soc. London 53, 385-420 (1904).
[CrossRef]

Gluck, N. S.

Greenham, A. G.

A. G. Greenham, B. A. Nichols, R. M. Wood, N. Nourshargh, and K. L. Lewis, 'Optical interference filters with continuous refractive index modulations by microwave plasma-assisted chemical vapor deposition,' Opt. Eng. 32, 1018-1023 (1993).
[CrossRef]

Gunning, W. J.

W. J. Gunning, R. L. Hall, F. J. Woodberry, W. H. Southwell, and N. S. Gluck, 'Codeposition of continuous composition rugate filters,' Appl. Opt. 28, 2945-2948 (1989).
[CrossRef] [PubMed]

J. P. Heuer, J. P. Elben, R. L. Hall, and W. J. Gunning, 'Scale-up considerations for codeposited gradient index optical thin film filters,' in Optical Interference Coatings, Vol. 15 of 1992 OSA Technical Digest Series (Optical Society of America, 1992), pp. 122-124.

Hall, R. L.

W. J. Gunning, R. L. Hall, F. J. Woodberry, W. H. Southwell, and N. S. Gluck, 'Codeposition of continuous composition rugate filters,' Appl. Opt. 28, 2945-2948 (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]

J. P. Heuer, J. P. Elben, R. L. Hall, and W. J. Gunning, 'Scale-up considerations for codeposited gradient index optical thin film filters,' in Optical Interference Coatings, Vol. 15 of 1992 OSA Technical Digest Series (Optical Society of America, 1992), pp. 122-124.

R. L. Hall and W. H. Southwell, 'Graded reflector/absorber coating,' in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J.A.Dobrowolski and P.G.Verly, eds., Proc. SPIE 2046, 78-85 (1993).

Harrington, B.

J. Allen and B. Harrington, 'Digitized rugate filters for laser application,' in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J.A.Dobrowolski and P.G.Verly, eds., Proc. SPIE 2046, 126-131 (1993).

Heuer, J. P.

J. P. Heuer, J. P. Elben, R. L. Hall, and W. J. Gunning, 'Scale-up considerations for codeposited gradient index optical thin film filters,' in Optical Interference Coatings, Vol. 15 of 1992 OSA Technical Digest Series (Optical Society of America, 1992), pp. 122-124.

Himmelblau, D.

D. Himmelblau, Applied Nonlinar Programming (McGraw-Hill, 1972).

Hubler, G. K.

Kahn, A. D. F.

Lacquet, B. M.

Lewis, K. L.

A. G. Greenham, B. A. Nichols, R. M. Wood, N. Nourshargh, and K. L. Lewis, 'Optical interference filters with continuous refractive index modulations by microwave plasma-assisted chemical vapor deposition,' Opt. Eng. 32, 1018-1023 (1993).
[CrossRef]

Lowe, D.

Nichols, B. A.

A. G. Greenham, B. A. Nichols, R. M. Wood, N. Nourshargh, and K. L. Lewis, 'Optical interference filters with continuous refractive index modulations by microwave plasma-assisted chemical vapor deposition,' Opt. Eng. 32, 1018-1023 (1993).
[CrossRef]

Nourshargh, N.

A. G. Greenham, B. A. Nichols, R. M. Wood, N. Nourshargh, and K. L. Lewis, 'Optical interference filters with continuous refractive index modulations by microwave plasma-assisted chemical vapor deposition,' Opt. Eng. 32, 1018-1023 (1993).
[CrossRef]

Southwell, W. H.

Swart, P. L.

Tikhnravov, A. V.

S. Furman and A. V. Tikhnravov, Optics of Multilayer Systems (Editions Frontieres, 1992).

Tikhonov, A. N.

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov, 'Second-order optimization methods in the synthesis of multilayer coatings,' J. Comput. Math. Math. Phys. 33, 1518-1535 (1993).

A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems (Wiley, 1977).

Tikhonravov, A. V.

P. G. Verly, A. V. Tikhonravov, and 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, and G. DeBell, 'Application of the needle optimization technique to the design of optical coatings,' Appl. Opt. 35, 5493-5508 (1996).
[CrossRef] [PubMed]

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

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov, 'Second-order optimization methods in the synthesis of multilayer coatings,' J. Comput. Math. Math. Phys. 33, 1518-1535 (1993).

A. V. Tikhonravov, 'Synthesis of optical coatings using optimality conditions,' Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91-93 (1982).

A. V. Tikhonravov and M. K. Trubetskov, 'Design of multilayers featuring inhomogeneous coating properties,' in Developments in Optical Component Coatings, I.Reid, ed., Proc. SPIE 2776, 48-57 (1996).

A. V. Tikhonravov and M. K. Trubetskov, OptiLayer Software, version 4.76, http://www.optilayer.com (2003).

A. V. Tikhonravov, M. K. Trubetskov, I. V. Zuev, and P. G. Verly, 'Efficient refinement of inhomogeneous optical coatings,' in Optical Interference Coatings, Vol. 17 of 1995 OSA Technical Digest Series (Optical Society of America, 1995), pp. 22-24.

Trubetskov, M. K.

P. G. Verly, A. V. Tikhonravov, and 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, and G. DeBell, 'Application of the needle optimization technique to the design of optical coatings,' Appl. Opt. 35, 5493-5508 (1996).
[CrossRef] [PubMed]

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov, 'Second-order optimization methods in the synthesis of multilayer coatings,' J. Comput. Math. Math. Phys. 33, 1518-1535 (1993).

A. V. Tikhonravov and M. K. Trubetskov, 'Design of multilayers featuring inhomogeneous coating properties,' in Developments in Optical Component Coatings, I.Reid, ed., Proc. SPIE 2776, 48-57 (1996).

A. V. Tikhonravov, M. K. Trubetskov, I. V. Zuev, and P. G. Verly, 'Efficient refinement of inhomogeneous optical coatings,' in Optical Interference Coatings, Vol. 17 of 1995 OSA Technical Digest Series (Optical Society of America, 1995), pp. 22-24.

A. V. Tikhonravov and M. K. Trubetskov, OptiLayer Software, version 4.76, http://www.optilayer.com (2003).

Vechten, D. V.

Verly, P. G.

Wild, W. J.

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, 'Rugate broadband antireflection coating design,' in Current Developments in Optical Engineering and Commercial Optics, R.E.Fischer, H.M.Pollicove, and W.J.Smith, eds. Proc. SPIE 1168, 224-228 (1989).

R. R. Willey, P. G. Verly, and J. A. Dobrowolski, 'Design of wideband antireflection coating with the Fourier transform method,' in Optical Thin Films and Applications, R.Herrmann, ed., Proc. SPIE 1270, 36-44 (1990).

Wood, R. M.

A. G. Greenham, B. A. Nichols, R. M. Wood, N. Nourshargh, and K. L. Lewis, 'Optical interference filters with continuous refractive index modulations by microwave plasma-assisted chemical vapor deposition,' Opt. Eng. 32, 1018-1023 (1993).
[CrossRef]

Woodberry, F. J.

Zuev, I. V.

A. V. Tikhonravov, M. K. Trubetskov, I. V. Zuev, and P. G. Verly, 'Efficient refinement of inhomogeneous optical coatings,' in Optical Interference Coatings, Vol. 17 of 1995 OSA Technical Digest Series (Optical Society of America, 1995), pp. 22-24.

Ann. Phys (1)

D. A. G. Bruggeman, 'Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen, insbesondere Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen,' Ann. Phys 24, 636-664 (1935).
[CrossRef]

Appl. Opt. (16)

P. G. Verly and J. A. Dobrowolski, 'Iterate correction procedure for optical thin film synthesis with the Fourier transform method,' Appl. Opt. 29, 3672-3684 (1990).
[CrossRef] [PubMed]

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

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

H. A. Abu-Safia, A. I. Al-Sharif, and I. O. Abu Aljarayesh, 'Rugate filter sidelobe suppression using half-apodization,' Appl. Opt. 32, 4831-4835 (1993).
[CrossRef] [PubMed]

H. Fabricius, 'Gradient-index filter: designing filters with step skirts, high reflection and quintic matching layers,' Appl. Opt. 31, 5191-5196 (1992).
[CrossRef] [PubMed]

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]

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]

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

B. G. Bovard, 'Rugate filter theory: an overview,' Appl. Opt. 32, 5427-5442 (1993).
[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, M. K. Trubetskov, and G. DeBell, 'Application of the needle optimization technique to the design of optical coatings,' Appl. Opt. 35, 5493-5508 (1996).
[CrossRef] [PubMed]

E. P. Donovan, D. V. Vechten, A. D. F. Kahn, C. A. Carosella, and G. K. Hubler, 'Near infrared rugate filter fabrication by ion beam assisted deposition of Si1−xNx films,' Appl. Opt. 28, 2940-2944 (1989).
[CrossRef] [PubMed]

W. J. Gunning, R. L. Hall, F. J. Woodberry, W. H. Southwell, and N. S. Gluck, 'Codeposition of continuous composition rugate filters,' Appl. Opt. 28, 2945-2948 (1989).
[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]

J. Comput. Math. Math. Phys. (1)

A. N. Tikhonov, A. V. Tikhonravov, and M. K. Trubetskov, 'Second-order optimization methods in the synthesis of multilayer coatings,' J. Comput. Math. Math. Phys. 33, 1518-1535 (1993).

Opt. Eng. (1)

A. G. Greenham, B. A. Nichols, R. M. Wood, N. Nourshargh, and K. L. Lewis, 'Optical interference filters with continuous refractive index modulations by microwave plasma-assisted chemical vapor deposition,' Opt. Eng. 32, 1018-1023 (1993).
[CrossRef]

Phys. Lett. (1)

D. J. Bergman, 'The dielectric constant of a composite material--a problem in classical physics,' Phys. Lett. 43C, 377-407 (1978).

Trans. R. Soc. London (1)

J. C. M. Garnett, 'Colors in metal glasses and metal films,' Trans. R. Soc. London 53, 385-420 (1904).
[CrossRef]

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

A. V. Tikhonravov, 'Synthesis of optical coatings using optimality conditions,' Vestn. Mosk. Univ. Fiz. Astronomiya 23, 91-93 (1982).

Other (11)

A. V. Tikhonravov and M. K. Trubetskov, 'Design of multilayers featuring inhomogeneous coating properties,' in Developments in Optical Component Coatings, I.Reid, ed., Proc. SPIE 2776, 48-57 (1996).

J. Allen and B. Harrington, 'Digitized rugate filters for laser application,' in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J.A.Dobrowolski and P.G.Verly, eds., Proc. SPIE 2046, 126-131 (1993).

J. P. Heuer, J. P. Elben, R. L. Hall, and W. J. Gunning, 'Scale-up considerations for codeposited gradient index optical thin film filters,' in Optical Interference Coatings, Vol. 15 of 1992 OSA Technical Digest Series (Optical Society of America, 1992), pp. 122-124.

R. R. Willey, 'Rugate broadband antireflection coating design,' in Current Developments in Optical Engineering and Commercial Optics, R.E.Fischer, H.M.Pollicove, and W.J.Smith, eds. Proc. SPIE 1168, 224-228 (1989).

R. R. Willey, P. G. Verly, and J. A. Dobrowolski, 'Design of wideband antireflection coating with the Fourier transform method,' in Optical Thin Films and Applications, R.Herrmann, ed., Proc. SPIE 1270, 36-44 (1990).

A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems (Wiley, 1977).

D. Himmelblau, Applied Nonlinar Programming (McGraw-Hill, 1972).

A. V. Tikhonravov and M. K. Trubetskov, OptiLayer Software, version 4.76, http://www.optilayer.com (2003).

R. L. Hall and W. H. Southwell, 'Graded reflector/absorber coating,' in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J.A.Dobrowolski and P.G.Verly, eds., Proc. SPIE 2046, 78-85 (1993).

S. Furman and A. V. Tikhnravov, Optics of Multilayer Systems (Editions Frontieres, 1992).

A. V. Tikhonravov, M. K. Trubetskov, I. V. Zuev, and P. G. Verly, 'Efficient refinement of inhomogeneous optical coatings,' in Optical Interference Coatings, Vol. 17 of 1995 OSA Technical Digest Series (Optical Society of America, 1995), pp. 22-24.

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Figures (14)

Fig. 1
Fig. 1

Modeling of a rugate refractive-index profile: an arbitrary continuous profile (left-hand side) and an approximating polyline (right-hand side).

Fig. 2
Fig. 2

Dispersion of mixture refractive indices: solid curves, refractive indices of the pure high- and low-index materials nH  (λ) and nL  (λ), dashed lines, refractive indices of mixtures. A one-to-one correspondence between design parameters ni and mixture refractive-index wavelength dependencies is established at the reference wavelength λ0.

Fig. 3
Fig. 3

Subdivision of a polyline segment into subsegments for calculating model spectral characteristics.

Fig. 4
Fig. 4

Refractive-index profiles of the starting design of the first design problem (triangles) and of the final design (circles). The final design is obtained by the synthesis algorithm without regularization.

Fig. 5
Fig. 5

Reflectances of the starting design (solid curve), of the final design obtained by the synthesis procedure without regularization (dashed curve), and of the target reflectance of the first design problem (crosses).

Fig. 6
Fig. 6

Refractive-index profiles of the starting design for solving the first design problem with regularization (triangles) and of the final rugate design (circles). The final design is obtained by the synthesis algorithm with regularization.

Fig. 7
Fig. 7

Reflectances of the starting design (solid curve), of the final design obtained by the synthesis procedure with regularization (dashed curve), and of the target reflectance of the first design problem (crosses).

Fig. 8
Fig. 8

Refractive-index profiles of a constant starting design for solving the antireflection design problem (triangles) and of the final rugate design (circles).

Fig. 9
Fig. 9

Reflectances of the starting design for solving the antireflection design problem (solid curves) of the final rugate design (dashed curves) at different incidence angles: normal incidence, gray curves, 30° incidence, thin black curves, 50° incidence, thick black curves.

Fig. 10
Fig. 10

Refractive-index profiles of a constant starting design for solving the narrowband reflector design problem (triangles) and of the final rugate design (circles).

Fig. 11
Fig. 11

Reflectance of the constant polyline taken as a starting design for the narrowband reflector design problem (solid curve), of the final rugate design (dashed curve), and of the target reflectance (crosses).

Fig. 12
Fig. 12

Fitting of the measured transmittance data for the first test sample (crosses) by the model transmittance (solid curve). The refractive index of this sample is depicted in Fig. 14.

Fig. 13
Fig. 13

Fitting of the measured reflectance data for the first test sample (crosses) by the model reflectance (solid curve). The refractive index of this sample is depicted in Fig. 14.

Fig. 14
Fig. 14

Refractive indices of pure SiO2 and Nb2O5 films (lower and upper curves, respectively) and five test mixture films (samples 1–5) with different SiO2 and Nb2O5 ratios.

Equations (26)

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z i z i + 1 , i = 1 , , N 1 ,
n L n i n H , i = 1 , , N ,
Φ ( X ) = 1 L j = 1 L [ R ( X , λ j ) R ˜ ( λ j ) Δ j ] 2 ,
P ( X ) = i = 1 N 1 [ max ( g i , 0 ) ] 2 + i = 1 N [ max ( g H i , 0 ) ] 2 + i = 1 N [ max ( g L i , 0 ) ] 2 ,
g i = z i z i + 1 0 , i = 1 , , N 1 ,
g H i = n i n H 0 ,
g L i = n L n i 0 , i = 1 , , N .
[ Φ ( X ) + P ( X ) ] min .
Ω ( X ) = j = 1 N 1 ( n j + 1 n j z j + 1 z j ) 2 .
[ Φ ( X ) + P ( X ) + α Ω ( X ) ] inf ,
n i ( λ ) = μ n H ( λ ) + ( 1 μ ) n L ( λ ) ,
n i = μ n H ( λ 0 ) + ( 1 μ ) n L ( λ 0 )
n i ( λ ) = [ n i n L ( λ 0 ) ] n H ( λ ) + [ n H ( λ 0 ) n i ] n L ( λ ) n H ( λ 0 ) n L ( λ 0 ) .
d i , k = z i + 1 z i l .
n i , k = n i + ( n i + 1 n i ) k 0.5 l .
n ( λ ) = μ n Nb 2 O 5 ( λ ) + ( 1 μ ) n SiO 2 ( λ ) ,
Φ z i = 2 L j = 1 L [ R ( X , λ j ) R ˜ ( λ j ) Δ j ] R ( X , λ j ) z i ,
Φ n i = 2 L j = 1 L [ R ( X , λ j ) R ˜ ( λ j ) Δ j ] R ( X , λ j ) n i ,
i = 1 , , N .
R z i = 1 l k = 1 l ( R d i 1 , k R d i , k ) ,     i = 2 , , N 1 ,
R z N = 1 l k = 1 l R d N 1 , k ,
R n i = 1 l k = 1 l [ ( R n i 1 , k R n i , k ) ( k 1 2 ) ] + k = 1 l R n i , k , i = 2 , , N 1 ,
R n 1 = k = 1 l [ R n 1 , k ( 1 k 1 / 2 l ) ] ,
R n N = k = 1 l [ R n N 1 , k k 0.5 l ] ,
R ( X , λ j ) n i = R n i ( λ j ) d n i ( λ j ) d n i ,
d n i ( λ j ) d n i = n H ( λ j ) n L ( λ j ) n H ( λ 0 ) n L ( λ 0 ) , R ( X , λ j ) n i

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