Abstract

A method of creating rugate interference filters that have flat-topped reflectance across an extended spectral region is presented. The method applies known relations from the classical coupled wave theory to develop a set of equations that gives the spatial frequency distribution of rugate cycles to achieve constant reflectance across a given spectral region. Two examples of the application of this method are discussed: a highly reflective coating for eye protection against harmful laser radiation incident from normal to 45°, and a spectral beam splitter for efficient solar power conversion.

© 2006 Optical Society of America

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References

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  1. G. Minott, R. Sprague, and B. Shnapir, "Rugate notch filters find use in laser-based applications," Laser Focus World 40(9), 107-111 (2004).
  2. G. Tempea, F. Krausz, C. Spielmann, and K. Ferencz, "Dispersion control over 150 THz with chirped dielectric mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 193-196 (1998).
    [CrossRef]
  3. W. Southwell, "Spectral response calculations of rugate filters using coupled-wave theory," J. Opt. Soc. Am. A 5, 1558-1564 (1988).
    [CrossRef]
  4. B. Bovard, "Rugate filter theory: an overview," Appl. Opt. 32, 5427-5442 (1993).
    [CrossRef] [PubMed]
  5. D. Rats, D. Poitras, J. Soro, L. Martinu, and J. Stebut, "Mechanical properties of plasma-deposited silicon-based, inhomogeneous optical coatings," Surf. Coat. Technol. 111, 220-228 (1999).
    [CrossRef]
  6. R. Vernhes, O. Zabeida, J. Klemberg-Sapieha, and L. Martinu, "Single-material inhomogeneous optical filters based on microstructural gradients in plasma-deposited silicon nitride," Appl. Opt. 43, 97-103 (2004).
    [CrossRef] [PubMed]
  7. A. Imenes, D. Buie, and D. McKenzie, "The design of broadband, wide-angle interference filters for solar concentrating systems," Sol. Energy Mater. Sol. Cells 90, 1579-1606 (2006).
  8. W. Southwell, "Using apodization functions to reduce sidelobes in rugate filters," Appl. Opt. 28, 5091-5094 (1989).
    [CrossRef] [PubMed]
  9. H. Abu-Safia, A. Al-Sharif, and I. Abu Aljarayesh, "Rugate filter sidelobe suppression using half-apodization," Appl. Opt. 32, 4831-4835 (1993).
    [CrossRef] [PubMed]
  10. S. Kennedy and M. Brett, "Porous broadband antireflection coating by glancing angle deposition," Appl. Opt. 42, 4573-4579 (2003).
    [CrossRef] [PubMed]
  11. W. Southwell, "Extended-bandwidth reflector designs by using wavelets," Appl. Opt. 36, 314-318 (1997).
    [CrossRef] [PubMed]
  12. O. Heavens and H. Liddell, "Staggered broadband reflecting multilayers," Appl. Opt. 5, 373-376 (1966).
    [CrossRef] [PubMed]
  13. W. Southwell and R. Hall, "Rugate filter sidelobe suppression using quintic and rugated quintic matching layers," Appl. Opt. 28, 2949-2951 (1989).
    [CrossRef] [PubMed]
  14. W. Southwell, "Gradient-index antireflection coatings," Opt. Lett. 8, 584-586 (1983).
    [CrossRef] [PubMed]
  15. J. Dobrowolski and F. Ho, "High performance step down AR coatings for high refractive index IR materials," Appl. Opt. 21, 288-292 (1982).
    [CrossRef] [PubMed]
  16. W. Sainty, W. McFall, D. McKenzie, and Y. Yin, "Time-dependent phenomena in plasma-assisted chemical vapor deposition of rugate optical films," Appl. Opt. 34, 5659-5664 (1995).
    [CrossRef] [PubMed]
  17. P. Baumeister, "Simulation of a rugate filter via a stepped-index dielectric multilayer," Appl. Opt. 25, 2644-2645 (1986).
    [CrossRef] [PubMed]
  18. T. Rahmlow and J. Lazo-Wasem, "Rugate and discrete hybrid filter designs," in Optical Thin Films V: New Development,Proc. SPIE 3133, 25-35 (1997).
    [CrossRef]
  19. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1989), Chap. 10.
  20. H. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics Publications, 2001).
    [CrossRef]
  21. MatLab is distributed by The MathWorks, Inc., Massachusetts, USA. http://www.mathworks.com/products/matlab/.
  22. J. Dobrowolski and D. Lowe, "Optical thin film synthesis program based on the use of Fourier transforms," Appl. Opt. 17, 3039-3050 (1978).
    [CrossRef] [PubMed]
  23. W. Gunning, R. Hall, F. Woodberry, W. Southwell, and N. Gluck, "Codeposition of continuous composition rugate filters," Appl. Opt. 28, 2945-2948 (1989).
    [CrossRef] [PubMed]
  24. R. Harris, "Rockwell Scientific eyes big contract," (2002), http://www.rsc.rockwell.com/html/pr_alep_eyecontract.html.
  25. Spektronika, "Laser safety goggles," (2002), http://spectronika.com/Safety.html.
  26. A. Imenes and D. Mills, "Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review," Sol. Energy Mater. Sol. Cells 84, 19-69 (2004).
    [CrossRef]
  27. A. Imenes and D. Mills, "Effective electricity replacement of various receiver combinations in a multi tower solar array distributed combined heat and power plant," in Proceedings of the ISES Solar World Congress (International Solar Energy Society, 2003), paper P5-80.
  28. H. Fabricius, "Gradient index filters: conversion into a two-index solution by taking into account dispersion," Appl. Opt. 31, 5216-5220 (1992).
    [CrossRef] [PubMed]
  29. P. Verly, A. Tikhonravov, and M. Trubetskov, "Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization," in Optical Thin Films V: New Developments, Proc. SPIE 3133, 46-52 (1997).
  30. H. Bach and D. Krause, eds., Thin Films on Glass (Springer-Verlag, 1997), Chap 5.
  31. H. Bartzsch, J.-S. Liebig, S. Lange, K. Goedicke, P. Frach, W. Hentsch, and S. Roth, "New concepts for precision optical and antireflective coatings deposited by reactive pulse magnetron sputtering," presented at the 5th International Conference on Coatings on Glass (ICCG5), Saarbruecken, Germany, 4-8 July 2004.
  32. M. Elder, K. Jancaitis, and D. Milam, "Optical characterization of damage resistant 'kilolayer' rugate filters," in Laser-Induced Damage in Optical Materials, Proc. SPIE 1441,237-246 (1990).
  33. H. Bach and D. Krause, eds., Thin Films on Glass (Springer-Verlag, 1997), Chap. 6.

2004

G. Minott, R. Sprague, and B. Shnapir, "Rugate notch filters find use in laser-based applications," Laser Focus World 40(9), 107-111 (2004).

A. Imenes and D. Mills, "Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review," Sol. Energy Mater. Sol. Cells 84, 19-69 (2004).
[CrossRef]

R. Vernhes, O. Zabeida, J. Klemberg-Sapieha, and L. Martinu, "Single-material inhomogeneous optical filters based on microstructural gradients in plasma-deposited silicon nitride," Appl. Opt. 43, 97-103 (2004).
[CrossRef] [PubMed]

2003

2002

R. Harris, "Rockwell Scientific eyes big contract," (2002), http://www.rsc.rockwell.com/html/pr_alep_eyecontract.html.

2001

H. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics Publications, 2001).
[CrossRef]

1999

D. Rats, D. Poitras, J. Soro, L. Martinu, and J. Stebut, "Mechanical properties of plasma-deposited silicon-based, inhomogeneous optical coatings," Surf. Coat. Technol. 111, 220-228 (1999).
[CrossRef]

1998

G. Tempea, F. Krausz, C. Spielmann, and K. Ferencz, "Dispersion control over 150 THz with chirped dielectric mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 193-196 (1998).
[CrossRef]

1997

T. Rahmlow and J. Lazo-Wasem, "Rugate and discrete hybrid filter designs," in Optical Thin Films V: New Development,Proc. SPIE 3133, 25-35 (1997).
[CrossRef]

P. Verly, A. Tikhonravov, and M. Trubetskov, "Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization," in Optical Thin Films V: New Developments, Proc. SPIE 3133, 46-52 (1997).

H. Bach and D. Krause, eds., Thin Films on Glass (Springer-Verlag, 1997), Chap 5.

H. Bach and D. Krause, eds., Thin Films on Glass (Springer-Verlag, 1997), Chap. 6.

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

1995

1993

1992

1990

M. Elder, K. Jancaitis, and D. Milam, "Optical characterization of damage resistant 'kilolayer' rugate filters," in Laser-Induced Damage in Optical Materials, Proc. SPIE 1441,237-246 (1990).

1989

1988

1986

1983

1982

1978

1966

Abu Aljarayesh, I.

Abu-Safia, H.

Al-Sharif, A.

Bach, H.

H. Bach and D. Krause, eds., Thin Films on Glass (Springer-Verlag, 1997), Chap 5.

H. Bach and D. Krause, eds., Thin Films on Glass (Springer-Verlag, 1997), Chap. 6.

Bartzsch, H.

H. Bartzsch, J.-S. Liebig, S. Lange, K. Goedicke, P. Frach, W. Hentsch, and S. Roth, "New concepts for precision optical and antireflective coatings deposited by reactive pulse magnetron sputtering," presented at the 5th International Conference on Coatings on Glass (ICCG5), Saarbruecken, Germany, 4-8 July 2004.

Baumeister, P.

Bovard, B.

Brett, M.

Buie, D.

A. Imenes, D. Buie, and D. McKenzie, "The design of broadband, wide-angle interference filters for solar concentrating systems," Sol. Energy Mater. Sol. Cells 90, 1579-1606 (2006).

Dobrowolski, J.

Elder, M.

M. Elder, K. Jancaitis, and D. Milam, "Optical characterization of damage resistant 'kilolayer' rugate filters," in Laser-Induced Damage in Optical Materials, Proc. SPIE 1441,237-246 (1990).

Fabricius, H.

Ferencz, K.

G. Tempea, F. Krausz, C. Spielmann, and K. Ferencz, "Dispersion control over 150 THz with chirped dielectric mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 193-196 (1998).
[CrossRef]

Frach, P.

H. Bartzsch, J.-S. Liebig, S. Lange, K. Goedicke, P. Frach, W. Hentsch, and S. Roth, "New concepts for precision optical and antireflective coatings deposited by reactive pulse magnetron sputtering," presented at the 5th International Conference on Coatings on Glass (ICCG5), Saarbruecken, Germany, 4-8 July 2004.

Gluck, N.

Goedicke, K.

H. Bartzsch, J.-S. Liebig, S. Lange, K. Goedicke, P. Frach, W. Hentsch, and S. Roth, "New concepts for precision optical and antireflective coatings deposited by reactive pulse magnetron sputtering," presented at the 5th International Conference on Coatings on Glass (ICCG5), Saarbruecken, Germany, 4-8 July 2004.

Gunning, W.

Hall, R.

Harris, R.

R. Harris, "Rockwell Scientific eyes big contract," (2002), http://www.rsc.rockwell.com/html/pr_alep_eyecontract.html.

Heavens, O.

Hentsch, W.

H. Bartzsch, J.-S. Liebig, S. Lange, K. Goedicke, P. Frach, W. Hentsch, and S. Roth, "New concepts for precision optical and antireflective coatings deposited by reactive pulse magnetron sputtering," presented at the 5th International Conference on Coatings on Glass (ICCG5), Saarbruecken, Germany, 4-8 July 2004.

Ho, F.

Imenes, A.

A. Imenes and D. Mills, "Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review," Sol. Energy Mater. Sol. Cells 84, 19-69 (2004).
[CrossRef]

A. Imenes, D. Buie, and D. McKenzie, "The design of broadband, wide-angle interference filters for solar concentrating systems," Sol. Energy Mater. Sol. Cells 90, 1579-1606 (2006).

A. Imenes and D. Mills, "Effective electricity replacement of various receiver combinations in a multi tower solar array distributed combined heat and power plant," in Proceedings of the ISES Solar World Congress (International Solar Energy Society, 2003), paper P5-80.

Jancaitis, K.

M. Elder, K. Jancaitis, and D. Milam, "Optical characterization of damage resistant 'kilolayer' rugate filters," in Laser-Induced Damage in Optical Materials, Proc. SPIE 1441,237-246 (1990).

Kennedy, S.

Klemberg-Sapieha, J.

Krause, D.

H. Bach and D. Krause, eds., Thin Films on Glass (Springer-Verlag, 1997), Chap. 6.

H. Bach and D. Krause, eds., Thin Films on Glass (Springer-Verlag, 1997), Chap 5.

Krausz, F.

G. Tempea, F. Krausz, C. Spielmann, and K. Ferencz, "Dispersion control over 150 THz with chirped dielectric mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 193-196 (1998).
[CrossRef]

Lange, S.

H. Bartzsch, J.-S. Liebig, S. Lange, K. Goedicke, P. Frach, W. Hentsch, and S. Roth, "New concepts for precision optical and antireflective coatings deposited by reactive pulse magnetron sputtering," presented at the 5th International Conference on Coatings on Glass (ICCG5), Saarbruecken, Germany, 4-8 July 2004.

Lazo-Wasem, J.

T. Rahmlow and J. Lazo-Wasem, "Rugate and discrete hybrid filter designs," in Optical Thin Films V: New Development,Proc. SPIE 3133, 25-35 (1997).
[CrossRef]

Liddell, H.

Liebig, J.-S.

H. Bartzsch, J.-S. Liebig, S. Lange, K. Goedicke, P. Frach, W. Hentsch, and S. Roth, "New concepts for precision optical and antireflective coatings deposited by reactive pulse magnetron sputtering," presented at the 5th International Conference on Coatings on Glass (ICCG5), Saarbruecken, Germany, 4-8 July 2004.

Lowe, D.

Macleod, H.

H. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics Publications, 2001).
[CrossRef]

Martinu, L.

R. Vernhes, O. Zabeida, J. Klemberg-Sapieha, and L. Martinu, "Single-material inhomogeneous optical filters based on microstructural gradients in plasma-deposited silicon nitride," Appl. Opt. 43, 97-103 (2004).
[CrossRef] [PubMed]

D. Rats, D. Poitras, J. Soro, L. Martinu, and J. Stebut, "Mechanical properties of plasma-deposited silicon-based, inhomogeneous optical coatings," Surf. Coat. Technol. 111, 220-228 (1999).
[CrossRef]

McFall, W.

McKenzie, D.

W. Sainty, W. McFall, D. McKenzie, and Y. Yin, "Time-dependent phenomena in plasma-assisted chemical vapor deposition of rugate optical films," Appl. Opt. 34, 5659-5664 (1995).
[CrossRef] [PubMed]

A. Imenes, D. Buie, and D. McKenzie, "The design of broadband, wide-angle interference filters for solar concentrating systems," Sol. Energy Mater. Sol. Cells 90, 1579-1606 (2006).

Milam, D.

M. Elder, K. Jancaitis, and D. Milam, "Optical characterization of damage resistant 'kilolayer' rugate filters," in Laser-Induced Damage in Optical Materials, Proc. SPIE 1441,237-246 (1990).

Mills, D.

A. Imenes and D. Mills, "Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review," Sol. Energy Mater. Sol. Cells 84, 19-69 (2004).
[CrossRef]

A. Imenes and D. Mills, "Effective electricity replacement of various receiver combinations in a multi tower solar array distributed combined heat and power plant," in Proceedings of the ISES Solar World Congress (International Solar Energy Society, 2003), paper P5-80.

Minott, G.

G. Minott, R. Sprague, and B. Shnapir, "Rugate notch filters find use in laser-based applications," Laser Focus World 40(9), 107-111 (2004).

Poitras, D.

D. Rats, D. Poitras, J. Soro, L. Martinu, and J. Stebut, "Mechanical properties of plasma-deposited silicon-based, inhomogeneous optical coatings," Surf. Coat. Technol. 111, 220-228 (1999).
[CrossRef]

Rahmlow, T.

T. Rahmlow and J. Lazo-Wasem, "Rugate and discrete hybrid filter designs," in Optical Thin Films V: New Development,Proc. SPIE 3133, 25-35 (1997).
[CrossRef]

Rats, D.

D. Rats, D. Poitras, J. Soro, L. Martinu, and J. Stebut, "Mechanical properties of plasma-deposited silicon-based, inhomogeneous optical coatings," Surf. Coat. Technol. 111, 220-228 (1999).
[CrossRef]

Roth, S.

H. Bartzsch, J.-S. Liebig, S. Lange, K. Goedicke, P. Frach, W. Hentsch, and S. Roth, "New concepts for precision optical and antireflective coatings deposited by reactive pulse magnetron sputtering," presented at the 5th International Conference on Coatings on Glass (ICCG5), Saarbruecken, Germany, 4-8 July 2004.

Sainty, W.

Shnapir, B.

G. Minott, R. Sprague, and B. Shnapir, "Rugate notch filters find use in laser-based applications," Laser Focus World 40(9), 107-111 (2004).

Soro, J.

D. Rats, D. Poitras, J. Soro, L. Martinu, and J. Stebut, "Mechanical properties of plasma-deposited silicon-based, inhomogeneous optical coatings," Surf. Coat. Technol. 111, 220-228 (1999).
[CrossRef]

Southwell, W.

Spielmann, C.

G. Tempea, F. Krausz, C. Spielmann, and K. Ferencz, "Dispersion control over 150 THz with chirped dielectric mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 193-196 (1998).
[CrossRef]

Sprague, R.

G. Minott, R. Sprague, and B. Shnapir, "Rugate notch filters find use in laser-based applications," Laser Focus World 40(9), 107-111 (2004).

Stebut, J.

D. Rats, D. Poitras, J. Soro, L. Martinu, and J. Stebut, "Mechanical properties of plasma-deposited silicon-based, inhomogeneous optical coatings," Surf. Coat. Technol. 111, 220-228 (1999).
[CrossRef]

Tempea, G.

G. Tempea, F. Krausz, C. Spielmann, and K. Ferencz, "Dispersion control over 150 THz with chirped dielectric mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 193-196 (1998).
[CrossRef]

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1989), Chap. 10.

Tikhonravov, A.

P. Verly, A. Tikhonravov, and M. Trubetskov, "Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization," in Optical Thin Films V: New Developments, Proc. SPIE 3133, 46-52 (1997).

Trubetskov, M.

P. Verly, A. Tikhonravov, and M. Trubetskov, "Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization," in Optical Thin Films V: New Developments, Proc. SPIE 3133, 46-52 (1997).

Verly, P.

P. Verly, A. Tikhonravov, and M. Trubetskov, "Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization," in Optical Thin Films V: New Developments, Proc. SPIE 3133, 46-52 (1997).

Vernhes, R.

Woodberry, F.

Yin, Y.

Zabeida, O.

Appl. Opt.

O. Heavens and H. Liddell, "Staggered broadband reflecting multilayers," Appl. Opt. 5, 373-376 (1966).
[CrossRef] [PubMed]

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

J. Dobrowolski and F. Ho, "High performance step down AR coatings for high refractive index IR materials," Appl. Opt. 21, 288-292 (1982).
[CrossRef] [PubMed]

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

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

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

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

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

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

W. Sainty, W. McFall, D. McKenzie, and Y. Yin, "Time-dependent phenomena in plasma-assisted chemical vapor deposition of rugate optical films," Appl. Opt. 34, 5659-5664 (1995).
[CrossRef] [PubMed]

H. Fabricius, "Gradient index filters: conversion into a two-index solution by taking into account dispersion," Appl. Opt. 31, 5216-5220 (1992).
[CrossRef] [PubMed]

S. Kennedy and M. Brett, "Porous broadband antireflection coating by glancing angle deposition," Appl. Opt. 42, 4573-4579 (2003).
[CrossRef] [PubMed]

R. Vernhes, O. Zabeida, J. Klemberg-Sapieha, and L. Martinu, "Single-material inhomogeneous optical filters based on microstructural gradients in plasma-deposited silicon nitride," Appl. Opt. 43, 97-103 (2004).
[CrossRef] [PubMed]

P. Baumeister, "Simulation of a rugate filter via a stepped-index dielectric multilayer," Appl. Opt. 25, 2644-2645 (1986).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron.

G. Tempea, F. Krausz, C. Spielmann, and K. Ferencz, "Dispersion control over 150 THz with chirped dielectric mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 193-196 (1998).
[CrossRef]

J. Opt. Soc. Am. A

Laser Focus World

G. Minott, R. Sprague, and B. Shnapir, "Rugate notch filters find use in laser-based applications," Laser Focus World 40(9), 107-111 (2004).

Opt. Lett.

Optical Thin Films V: New Developments, Proc. SPIE

P. Verly, A. Tikhonravov, and M. Trubetskov, "Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization," in Optical Thin Films V: New Developments, Proc. SPIE 3133, 46-52 (1997).

Proc. SPIE

T. Rahmlow and J. Lazo-Wasem, "Rugate and discrete hybrid filter designs," in Optical Thin Films V: New Development,Proc. SPIE 3133, 25-35 (1997).
[CrossRef]

Sol. Energy Mater. Sol. Cells

A. Imenes and D. Mills, "Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review," Sol. Energy Mater. Sol. Cells 84, 19-69 (2004).
[CrossRef]

Surf. Coat. Technol.

D. Rats, D. Poitras, J. Soro, L. Martinu, and J. Stebut, "Mechanical properties of plasma-deposited silicon-based, inhomogeneous optical coatings," Surf. Coat. Technol. 111, 220-228 (1999).
[CrossRef]

Other

A. Imenes, D. Buie, and D. McKenzie, "The design of broadband, wide-angle interference filters for solar concentrating systems," Sol. Energy Mater. Sol. Cells 90, 1579-1606 (2006).

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1989), Chap. 10.

H. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics Publications, 2001).
[CrossRef]

MatLab is distributed by The MathWorks, Inc., Massachusetts, USA. http://www.mathworks.com/products/matlab/.

R. Harris, "Rockwell Scientific eyes big contract," (2002), http://www.rsc.rockwell.com/html/pr_alep_eyecontract.html.

Spektronika, "Laser safety goggles," (2002), http://spectronika.com/Safety.html.

A. Imenes and D. Mills, "Effective electricity replacement of various receiver combinations in a multi tower solar array distributed combined heat and power plant," in Proceedings of the ISES Solar World Congress (International Solar Energy Society, 2003), paper P5-80.

H. Bach and D. Krause, eds., Thin Films on Glass (Springer-Verlag, 1997), Chap 5.

H. Bartzsch, J.-S. Liebig, S. Lange, K. Goedicke, P. Frach, W. Hentsch, and S. Roth, "New concepts for precision optical and antireflective coatings deposited by reactive pulse magnetron sputtering," presented at the 5th International Conference on Coatings on Glass (ICCG5), Saarbruecken, Germany, 4-8 July 2004.

M. Elder, K. Jancaitis, and D. Milam, "Optical characterization of damage resistant 'kilolayer' rugate filters," in Laser-Induced Damage in Optical Materials, Proc. SPIE 1441,237-246 (1990).

H. Bach and D. Krause, eds., Thin Films on Glass (Springer-Verlag, 1997), Chap. 6.

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Figures (7)

Fig. 1
Fig. 1

Partial linear apodization and quintic matching of the sinusoidal refractive index profile reduces the undesired reflectance sidelobes of the simple rugate structure [compare (a) and (b)]. Linear chirping of the refractive index profile results in a broader stopband, and partial apodization and matching is still effective in reducing the unwanted sidelobes [compare (c) and (d)].

Fig. 2
Fig. 2

(a) Six different frequency modulation functions K, (b) chirped K ( z ) functions versus depth z, (c) corresponding K ( z ) z values versus depth z.

Fig. 3
Fig. 3

Semilogarithmic plot of the resulting transmittance characteristics corresponding to the six different K ( z ) functions displayed in Fig. 2.

Fig. 4
Fig. 4

Illustration of the serial method used in the design of broadband, flat-topped rugate filters. (a) Simple rugate structures of fixed K values, (b) reflectance bands centered at different wavelengths, according to the fixed K values, (c) reducing the spacing between the individual rugate structures creates a contiguous, broad spectral region of high reflectance.

Fig. 5
Fig. 5

Comparing the effect of different spacing parameter W on the performance of a flat-topped broadband rugate filter consisting of approximately 400 periods. (a) W = 1 , (b) W = 0.5 , (c) W = 0.1 .

Fig. 6
Fig. 6

Examples of flat-topped broadband rugate filters, designed for protection against harmful radiation from the copper-vapor laser, for angles of incidence from normal to 45°. (a) K ( z ) z product as a function of depth z, (b) semilogarithmic plot of the resulting transmittance profiles, (c) corresponding reflectance profiles.

Fig. 7
Fig. 7

Broadband spectral beam splitter for a photovoltaic–thermal hybrid receiver solar concentrating system. This passband filter was designed by placing two different flat-topped rugate coatings in series.

Equations (128)

Equations on this page are rendered with MathJax. Learn more.

n a = 0.5 ( n H + n L )
n p = ( n H n L )
n ( z ) = n a + 0.5 n p sin [ K ( z ) z + ϕ ] ,
K ( z )
n p 10 1
OD = - log 10 T = log 10 1 1 R ,
λ 0
λ 0 = 2 n a P
λ θ = λ 0 cos θ a = λ 0 ( 1 sin 2 θ 0 n a     2 ) 0.5 .
θ 0
θ a
n a
( n a )
( n s )
n ( z ) = n s + ( n a n s ) ( 10 t 3 15 t 4 + 6 t 5 ) ,
t = z / T m
T m
1 / e 2
n a
n s = 1.51
n L = 1.6
n H = 2.0
( n s = 1.51 )
n min = 1.45
K ( z )
K ( z ) z
K ( z )
n L = 1.4
n H = 2.0
n p
500 1000   nm
K ( z )
( n p n a )
BW c = Δ λ λ 0 = n p 2 n a ,
Δ λ
λ 0
λ 0
λ i
Δ λ i
K i
Δ z i
K i
ϵ [ 1 , , N ]
G = S × N
λ i
λ i
n p
n a
BW c
Δ λ 1 = BW c × λ 1 .
BW c
λ 2 = λ 1 + ( 0.5 Δ λ 1 + 0.5 Δ λ 2 ) λ 1 + Δ λ 1 ,
C = ( 1 + BW c )
λ 2 = λ 1 + BW c × λ 1 = C λ 1 .
λ i = C i 1 λ 1 .
K i
K i = 4 π n a λ i = 4 π n a λ 1 C 1 i .
K i
Δ z i = λ i 2 n a S .
Z N = i = 1 N Δ z i = S 2 n a i = 1 N λ i .
Z N = S 2 n a ( λ 1 + C λ 1 + C 2 λ 1 + + C N 1 λ 1 )
= S λ 1 2 n a ( 1 + C + C 2 + + C N 1 ) .
Z N = S λ 1 2 n a ( 1 C N 1 C ) = S λ 1 n p ( C N 1 ) .
λ 1
λ 1
λ N
( λ N λ 1 )
Δ λ i
i = [ 1 , , N ]
λ N λ 1 = i = 1 N Δ λ i = λ 1 ( C N 1 ) .
N = ln λ N ln λ 1 ln C .
n ( z )
0 < W 1
BW w = W × BW c ,
C = 1 + BW w ,
1000   nm
K ( z ) z
W = 1
λ 1 = 500   nm
K ( z ) z
K ( z ) z
578   nm
n a = 1.9
474   nm
536   nm
470 580   nm
45 °
C = 1051
W = 0.005
S = 1
C = 584 ( W = 0.009 , S = 1 )
n L = 1.8
n H = 2.0
80.5 μm
600   nm
n p
C = 214 ( W = 0.017 , S = 1 )
n L = 1.7
n H = 2.1
29.5 μ m
630   nm
590   nm
1090 2 5 0 0   nm
n L = 1.9
n H = 2.0
W = 0.01
1.7   mm
n p n a
n p / n a
n p
λ 1
λ 2
n p / n a
z = 0
Δ λ
n p / n a
λ 0
λ 1 , λ N
λ i
θ 0
θ a
K ( z )
K ( z ) z
K ( z )
W = 1
W = 0.5
W = 0.1
K ( z ) z

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