Abstract

A Rugate notch filter is fabricated by atomic layer deposition. By regulating the thickness ratio of TiO2 and Al2O3 in a nanoscale layer, the refractive index is tailored between the refractive indices of the two materials. With the method of equivalent refractive index, the continuously variable refractive index of the designed Rugate filter is dispersed into several discrete ones, so that it can be realized by the refractive index tailoring. To coincide with the thickness, the nanoscale layer is iteratively deposited in the equivalent layer. The experimental reflectance matches the designed one well, and the average reflectance is 86.7% (510–590 nm).

© 2014 Optical Society of America

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    [CrossRef]
  2. S. Zaitsu, S. Motokoshi, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Large-area optical coatings with uniform thickness grown by surface chemical reactions for high-power laser applications,” Jpn. J. Appl. Phys. 41, 160–165 (2002).
    [CrossRef]
  3. M. Ritala, M. Leskela, J. P. Dekker, C. Mutsaers, P. J. Soininen, and J. Skarp, “Perfectly conformal TiN and Al2O3 films deposited by atomic layer deposition,” Chem. Vapor. Depos. 5, 7–9 (1999).
    [CrossRef]
  4. N. T. Gabriel, S. S. Kim, and J. J. Talghader, “Control of thermal deformation in dielectric mirrors using mechanical design and atomic layer deposition,” Opt. Lett. 34, 1958–1960 (2009).
    [CrossRef]
  5. Y. H. Li, W. D. Shen, Y. G. Zhang, X. Hao, H. H. Fan, and X. Liu, “Precise broadband anti-refection coating fabricated by atomic layer deposition,” Opt. Commun. 292, 31–35 (2013).
    [CrossRef]
  6. D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
    [CrossRef]
  7. A. Szeghalmi, M. Helgert, R. Brunner, F. Heyroth, U. Gösele, and M. Knez, “Atomic layer deposition of Al2O3 and TiO2 multilayers for applications as bandpass filters and antireflection coatings,” Appl. Opt. 48, 1727–1732 (2009).
    [CrossRef]
  8. Y. W. Wei, H. Liu, O. Y. Sheng, Z. C. Liu, S. L. Chen, and L. M. Yang, “Laser damage properties of TiO2/Al2O3 thin films grown by atomic layer deposition,” Appl. Opt. 50, 4720–4727 (2011).
    [CrossRef]
  9. Z. C. Liu, S. L. Chen, P. Ma, Y. W. Wei, Y. Zheng, F. Pan, H. Liu, and G. Y. Tang, “Characterization of 1064 nm nanosecond laser-induced damage on antireflection coatings grown by atomic layer deposition,” Opt. Express 20, 854–863 (2012).
    [CrossRef]
  10. D. Riihela, M. Ritala, R. Matero, and M. Leskela, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
    [CrossRef]
  11. P. G. Verly, “Fourier-transform technique with frequency filtering for optical thin-film design,” Appl. Opt. 34, 688–694 (1995).
    [CrossRef]
  12. B. G. Bovard, “Rugate filter design—the modified Fourier-transform technique,” Appl. Opt. 29, 24–30 (1990).
    [CrossRef]
  13. H. Fabricius, “Gradient-index filters—designing filters with steep skirts, high reflection, and quintic matching layers,” Appl. Opt. 31, 5191–5196 (1992).
    [CrossRef]
  14. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Application of constrained optimization to the design of quasi-Rugate optical coatings,” Appl. Opt. 47, 5103–5109 (2008).
    [CrossRef]
  15. W. H. Southwell, “Using apodization functions to reduce sidelobes in Rugate filters,” Appl. Opt. 28, 5091–5094 (1989).
    [CrossRef]
  16. S. Lim, S. Shih, and J. F. Wager, “Design and fabrication of a double bandstop Rugate, filter grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 277, 144–146 (1996).
    [CrossRef]
  17. N. Perelman and I. Averbukh, “Rugate filter design: an analytical approach using uniform WKB solutions,” J. Appl. Phys. 79, 2839–2845 (1996).
    [CrossRef]
  18. S. Zaitsu, T. Jitsuno, M. Nakatsuka, T. Yamanaka, and S. Motokoshi, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
    [CrossRef]
  19. J. C. Zhang, M. Fang, Y. C. Shao, Y. X. Jin, and H. B. He, “Design and fabrication of broadband Rugate filter,” Chin. Phys. B 21, 054219 (2012).
  20. P. G. Verly, “Hybrid approach for Rugate filter design,” Appl. Opt. 47, C172–C178 (2008).
    [CrossRef]
  21. S. Larouche and L. Martinu, “OpenFilters: open-source software for the design, optimization, and synthesis of optical filters,” Appl. Opt. 47, C219–C230 (2008).
    [CrossRef]
  22. L. Zhao, Z. Sui, Q. H. Zhu, Y. Zhang, and Y. L. Zuo, “Design of Rugate filter for gain narrowing compensation,” Acta Phys. Sin. 58, 3977–3982 (2009).
  23. F. Aguayo-Rios, F. Villa-Villa, and J. A. Gaspar-Armenta, “One-dimensional photonic crystals of inhomogeneous thin films: band structure of Rugate filters,” Opt. Commun. 244, 259–267 (2005).
    [CrossRef]
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    [CrossRef]
  25. H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, and Y. Iimura, “Titanium oxide aluminum oxide multilayer reflectors for “water-window” wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
    [CrossRef]

2013

Y. H. Li, W. D. Shen, Y. G. Zhang, X. Hao, H. H. Fan, and X. Liu, “Precise broadband anti-refection coating fabricated by atomic layer deposition,” Opt. Commun. 292, 31–35 (2013).
[CrossRef]

2012

2011

2009

2008

2005

F. Aguayo-Rios, F. Villa-Villa, and J. A. Gaspar-Armenta, “One-dimensional photonic crystals of inhomogeneous thin films: band structure of Rugate filters,” Opt. Commun. 244, 259–267 (2005).
[CrossRef]

2002

S. Zaitsu, S. Motokoshi, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Large-area optical coatings with uniform thickness grown by surface chemical reactions for high-power laser applications,” Jpn. J. Appl. Phys. 41, 160–165 (2002).
[CrossRef]

S. Zaitsu, T. Jitsuno, M. Nakatsuka, T. Yamanaka, and S. Motokoshi, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[CrossRef]

1999

M. Ritala, M. Leskela, J. P. Dekker, C. Mutsaers, P. J. Soininen, and J. Skarp, “Perfectly conformal TiN and Al2O3 films deposited by atomic layer deposition,” Chem. Vapor. Depos. 5, 7–9 (1999).
[CrossRef]

1997

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, and Y. Iimura, “Titanium oxide aluminum oxide multilayer reflectors for “water-window” wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

1996

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

D. Riihela, M. Ritala, R. Matero, and M. Leskela, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

S. Lim, S. Shih, and J. F. Wager, “Design and fabrication of a double bandstop Rugate, filter grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 277, 144–146 (1996).
[CrossRef]

N. Perelman and I. Averbukh, “Rugate filter design: an analytical approach using uniform WKB solutions,” J. Appl. Phys. 79, 2839–2845 (1996).
[CrossRef]

1995

1992

1990

1989

1952

Aguayo-Rios, F.

F. Aguayo-Rios, F. Villa-Villa, and J. A. Gaspar-Armenta, “One-dimensional photonic crystals of inhomogeneous thin films: band structure of Rugate filters,” Opt. Commun. 244, 259–267 (2005).
[CrossRef]

Amotchkina, T. V.

Averbukh, I.

N. Perelman and I. Averbukh, “Rugate filter design: an analytical approach using uniform WKB solutions,” J. Appl. Phys. 79, 2839–2845 (1996).
[CrossRef]

Bovard, B. G.

Brunner, R.

Chen, S. L.

Dekker, J. P.

M. Ritala, M. Leskela, J. P. Dekker, C. Mutsaers, P. J. Soininen, and J. Skarp, “Perfectly conformal TiN and Al2O3 films deposited by atomic layer deposition,” Chem. Vapor. Depos. 5, 7–9 (1999).
[CrossRef]

Epstein, L. I.

Fabricius, H.

Fan, H. H.

Y. H. Li, W. D. Shen, Y. G. Zhang, X. Hao, H. H. Fan, and X. Liu, “Precise broadband anti-refection coating fabricated by atomic layer deposition,” Opt. Commun. 292, 31–35 (2013).
[CrossRef]

Fang, M.

J. C. Zhang, M. Fang, Y. C. Shao, Y. X. Jin, and H. B. He, “Design and fabrication of broadband Rugate filter,” Chin. Phys. B 21, 054219 (2012).

Gabriel, N. T.

Gaspar-Armenta, J. A.

F. Aguayo-Rios, F. Villa-Villa, and J. A. Gaspar-Armenta, “One-dimensional photonic crystals of inhomogeneous thin films: band structure of Rugate filters,” Opt. Commun. 244, 259–267 (2005).
[CrossRef]

Gösele, U.

Hao, X.

Y. H. Li, W. D. Shen, Y. G. Zhang, X. Hao, H. H. Fan, and X. Liu, “Precise broadband anti-refection coating fabricated by atomic layer deposition,” Opt. Commun. 292, 31–35 (2013).
[CrossRef]

He, H. B.

J. C. Zhang, M. Fang, Y. C. Shao, Y. X. Jin, and H. B. He, “Design and fabrication of broadband Rugate filter,” Chin. Phys. B 21, 054219 (2012).

Helgert, M.

Heyroth, F.

Iimura, Y.

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, and Y. Iimura, “Titanium oxide aluminum oxide multilayer reflectors for “water-window” wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

Jin, Y. X.

J. C. Zhang, M. Fang, Y. C. Shao, Y. X. Jin, and H. B. He, “Design and fabrication of broadband Rugate filter,” Chin. Phys. B 21, 054219 (2012).

Jitsuno, T.

S. Zaitsu, S. Motokoshi, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Large-area optical coatings with uniform thickness grown by surface chemical reactions for high-power laser applications,” Jpn. J. Appl. Phys. 41, 160–165 (2002).
[CrossRef]

S. Zaitsu, T. Jitsuno, M. Nakatsuka, T. Yamanaka, and S. Motokoshi, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[CrossRef]

Kim, S. S.

Knez, M.

Kobayashi, K.

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, and Y. Iimura, “Titanium oxide aluminum oxide multilayer reflectors for “water-window” wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

Kumagai, H.

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, and Y. Iimura, “Titanium oxide aluminum oxide multilayer reflectors for “water-window” wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

Larouche, S.

Leskela, M.

M. Ritala, M. Leskela, J. P. Dekker, C. Mutsaers, P. J. Soininen, and J. Skarp, “Perfectly conformal TiN and Al2O3 films deposited by atomic layer deposition,” Chem. Vapor. Depos. 5, 7–9 (1999).
[CrossRef]

D. Riihela, M. Ritala, R. Matero, and M. Leskela, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

Leskelä, M.

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

Li, Y. H.

Y. H. Li, W. D. Shen, Y. G. Zhang, X. Hao, H. H. Fan, and X. Liu, “Precise broadband anti-refection coating fabricated by atomic layer deposition,” Opt. Commun. 292, 31–35 (2013).
[CrossRef]

Lim, S.

S. Lim, S. Shih, and J. F. Wager, “Design and fabrication of a double bandstop Rugate, filter grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 277, 144–146 (1996).
[CrossRef]

Liu, H.

Liu, X.

Y. H. Li, W. D. Shen, Y. G. Zhang, X. Hao, H. H. Fan, and X. Liu, “Precise broadband anti-refection coating fabricated by atomic layer deposition,” Opt. Commun. 292, 31–35 (2013).
[CrossRef]

Liu, Z. C.

Ma, P.

Martinu, L.

Matero, R.

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

D. Riihela, M. Ritala, R. Matero, and M. Leskela, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

Motokoshi, S.

S. Zaitsu, T. Jitsuno, M. Nakatsuka, T. Yamanaka, and S. Motokoshi, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[CrossRef]

S. Zaitsu, S. Motokoshi, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Large-area optical coatings with uniform thickness grown by surface chemical reactions for high-power laser applications,” Jpn. J. Appl. Phys. 41, 160–165 (2002).
[CrossRef]

Mutsaers, C.

M. Ritala, M. Leskela, J. P. Dekker, C. Mutsaers, P. J. Soininen, and J. Skarp, “Perfectly conformal TiN and Al2O3 films deposited by atomic layer deposition,” Chem. Vapor. Depos. 5, 7–9 (1999).
[CrossRef]

Nakatsuka, M.

S. Zaitsu, T. Jitsuno, M. Nakatsuka, T. Yamanaka, and S. Motokoshi, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[CrossRef]

S. Zaitsu, S. Motokoshi, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Large-area optical coatings with uniform thickness grown by surface chemical reactions for high-power laser applications,” Jpn. J. Appl. Phys. 41, 160–165 (2002).
[CrossRef]

Obara, M.

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, and Y. Iimura, “Titanium oxide aluminum oxide multilayer reflectors for “water-window” wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

Pan, F.

Perelman, N.

N. Perelman and I. Averbukh, “Rugate filter design: an analytical approach using uniform WKB solutions,” J. Appl. Phys. 79, 2839–2845 (1996).
[CrossRef]

Riihela, D.

D. Riihela, M. Ritala, R. Matero, and M. Leskela, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

Riihelä, D.

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

Ritala, M.

M. Ritala, M. Leskela, J. P. Dekker, C. Mutsaers, P. J. Soininen, and J. Skarp, “Perfectly conformal TiN and Al2O3 films deposited by atomic layer deposition,” Chem. Vapor. Depos. 5, 7–9 (1999).
[CrossRef]

D. Riihela, M. Ritala, R. Matero, and M. Leskela, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

Shao, Y. C.

J. C. Zhang, M. Fang, Y. C. Shao, Y. X. Jin, and H. B. He, “Design and fabrication of broadband Rugate filter,” Chin. Phys. B 21, 054219 (2012).

Shen, W. D.

Y. H. Li, W. D. Shen, Y. G. Zhang, X. Hao, H. H. Fan, and X. Liu, “Precise broadband anti-refection coating fabricated by atomic layer deposition,” Opt. Commun. 292, 31–35 (2013).
[CrossRef]

Sheng, O. Y.

Shih, S.

S. Lim, S. Shih, and J. F. Wager, “Design and fabrication of a double bandstop Rugate, filter grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 277, 144–146 (1996).
[CrossRef]

Skarp, J.

M. Ritala, M. Leskela, J. P. Dekker, C. Mutsaers, P. J. Soininen, and J. Skarp, “Perfectly conformal TiN and Al2O3 films deposited by atomic layer deposition,” Chem. Vapor. Depos. 5, 7–9 (1999).
[CrossRef]

Soininen, P. J.

M. Ritala, M. Leskela, J. P. Dekker, C. Mutsaers, P. J. Soininen, and J. Skarp, “Perfectly conformal TiN and Al2O3 films deposited by atomic layer deposition,” Chem. Vapor. Depos. 5, 7–9 (1999).
[CrossRef]

Southwell, W. H.

Sui, Z.

L. Zhao, Z. Sui, Q. H. Zhu, Y. Zhang, and Y. L. Zuo, “Design of Rugate filter for gain narrowing compensation,” Acta Phys. Sin. 58, 3977–3982 (2009).

Suntola, T.

T. Suntola, “Atomic layer epitaxy,” Thin Solid Films 216, 84–89 (1992).
[CrossRef]

Szeghalmi, A.

Talghader, J. J.

Tang, G. Y.

Tikhonravov, A. V.

Toyoda, K.

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, and Y. Iimura, “Titanium oxide aluminum oxide multilayer reflectors for “water-window” wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

Trubetskov, M. K.

Verly, P. G.

Villa-Villa, F.

F. Aguayo-Rios, F. Villa-Villa, and J. A. Gaspar-Armenta, “One-dimensional photonic crystals of inhomogeneous thin films: band structure of Rugate filters,” Opt. Commun. 244, 259–267 (2005).
[CrossRef]

Wager, J. F.

S. Lim, S. Shih, and J. F. Wager, “Design and fabrication of a double bandstop Rugate, filter grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 277, 144–146 (1996).
[CrossRef]

Wei, Y. W.

Yamanaka, T.

S. Zaitsu, T. Jitsuno, M. Nakatsuka, T. Yamanaka, and S. Motokoshi, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[CrossRef]

S. Zaitsu, S. Motokoshi, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Large-area optical coatings with uniform thickness grown by surface chemical reactions for high-power laser applications,” Jpn. J. Appl. Phys. 41, 160–165 (2002).
[CrossRef]

Yang, L. M.

Zaitsu, S.

S. Zaitsu, T. Jitsuno, M. Nakatsuka, T. Yamanaka, and S. Motokoshi, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[CrossRef]

S. Zaitsu, S. Motokoshi, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Large-area optical coatings with uniform thickness grown by surface chemical reactions for high-power laser applications,” Jpn. J. Appl. Phys. 41, 160–165 (2002).
[CrossRef]

Zhang, J. C.

J. C. Zhang, M. Fang, Y. C. Shao, Y. X. Jin, and H. B. He, “Design and fabrication of broadband Rugate filter,” Chin. Phys. B 21, 054219 (2012).

Zhang, Y.

L. Zhao, Z. Sui, Q. H. Zhu, Y. Zhang, and Y. L. Zuo, “Design of Rugate filter for gain narrowing compensation,” Acta Phys. Sin. 58, 3977–3982 (2009).

Zhang, Y. G.

Y. H. Li, W. D. Shen, Y. G. Zhang, X. Hao, H. H. Fan, and X. Liu, “Precise broadband anti-refection coating fabricated by atomic layer deposition,” Opt. Commun. 292, 31–35 (2013).
[CrossRef]

Zhao, L.

L. Zhao, Z. Sui, Q. H. Zhu, Y. Zhang, and Y. L. Zuo, “Design of Rugate filter for gain narrowing compensation,” Acta Phys. Sin. 58, 3977–3982 (2009).

Zheng, Y.

Zhu, Q. H.

L. Zhao, Z. Sui, Q. H. Zhu, Y. Zhang, and Y. L. Zuo, “Design of Rugate filter for gain narrowing compensation,” Acta Phys. Sin. 58, 3977–3982 (2009).

Zuo, Y. L.

L. Zhao, Z. Sui, Q. H. Zhu, Y. Zhang, and Y. L. Zuo, “Design of Rugate filter for gain narrowing compensation,” Acta Phys. Sin. 58, 3977–3982 (2009).

Acta Phys. Sin.

L. Zhao, Z. Sui, Q. H. Zhu, Y. Zhang, and Y. L. Zuo, “Design of Rugate filter for gain narrowing compensation,” Acta Phys. Sin. 58, 3977–3982 (2009).

Appl. Opt.

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

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

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

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

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

S. Larouche and L. Martinu, “OpenFilters: open-source software for the design, optimization, and synthesis of optical filters,” Appl. Opt. 47, C219–C230 (2008).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Application of constrained optimization to the design of quasi-Rugate optical coatings,” Appl. Opt. 47, 5103–5109 (2008).
[CrossRef]

A. Szeghalmi, M. Helgert, R. Brunner, F. Heyroth, U. Gösele, and M. Knez, “Atomic layer deposition of Al2O3 and TiO2 multilayers for applications as bandpass filters and antireflection coatings,” Appl. Opt. 48, 1727–1732 (2009).
[CrossRef]

Y. W. Wei, H. Liu, O. Y. Sheng, Z. C. Liu, S. L. Chen, and L. M. Yang, “Laser damage properties of TiO2/Al2O3 thin films grown by atomic layer deposition,” Appl. Opt. 50, 4720–4727 (2011).
[CrossRef]

Appl. Phys. Lett.

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, and Y. Iimura, “Titanium oxide aluminum oxide multilayer reflectors for “water-window” wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

S. Zaitsu, T. Jitsuno, M. Nakatsuka, T. Yamanaka, and S. Motokoshi, “Optical thin films consisting of nanoscale laminated layers,” Appl. Phys. Lett. 80, 2442–2444 (2002).
[CrossRef]

Chem. Vapor. Depos.

M. Ritala, M. Leskela, J. P. Dekker, C. Mutsaers, P. J. Soininen, and J. Skarp, “Perfectly conformal TiN and Al2O3 films deposited by atomic layer deposition,” Chem. Vapor. Depos. 5, 7–9 (1999).
[CrossRef]

Chin. Phys. B

J. C. Zhang, M. Fang, Y. C. Shao, Y. X. Jin, and H. B. He, “Design and fabrication of broadband Rugate filter,” Chin. Phys. B 21, 054219 (2012).

J. Appl. Phys.

N. Perelman and I. Averbukh, “Rugate filter design: an analytical approach using uniform WKB solutions,” J. Appl. Phys. 79, 2839–2845 (1996).
[CrossRef]

J. Opt. Soc. Am.

Jpn. J. Appl. Phys.

S. Zaitsu, S. Motokoshi, T. Jitsuno, M. Nakatsuka, and T. Yamanaka, “Large-area optical coatings with uniform thickness grown by surface chemical reactions for high-power laser applications,” Jpn. J. Appl. Phys. 41, 160–165 (2002).
[CrossRef]

Opt. Commun.

Y. H. Li, W. D. Shen, Y. G. Zhang, X. Hao, H. H. Fan, and X. Liu, “Precise broadband anti-refection coating fabricated by atomic layer deposition,” Opt. Commun. 292, 31–35 (2013).
[CrossRef]

F. Aguayo-Rios, F. Villa-Villa, and J. A. Gaspar-Armenta, “One-dimensional photonic crystals of inhomogeneous thin films: band structure of Rugate filters,” Opt. Commun. 244, 259–267 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Thin Solid Films

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

D. Riihela, M. Ritala, R. Matero, and M. Leskela, “Introducing atomic layer epitaxy for the deposition of optical thin films,” Thin Solid Films 289, 250–255 (1996).
[CrossRef]

S. Lim, S. Shih, and J. F. Wager, “Design and fabrication of a double bandstop Rugate, filter grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 277, 144–146 (1996).
[CrossRef]

T. Suntola, “Atomic layer epitaxy,” Thin Solid Films 216, 84–89 (1992).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Refractive indices with different thickness ratios. NT and NA separately represent the number of cycles for TiO2 and Al2O3 in the nanoscale layer. Solid curves correspond to experimental data and dashed curves to calculated data according to the linear interpolation.

Fig. 2.
Fig. 2.

Refractive index profile of the Rugate notch filter.

Fig. 3.
Fig. 3.

Theoretical reflectance, equivalent reflectance, and experimental reflectance of the Rugate notch filter.

Fig. 4.
Fig. 4.

Equivalent method of symmetrical film system.

Fig. 5.
Fig. 5.

Equivalent refractive indices.

Tables (1)

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Table 1. Deposited Parameters for Equivalent Refractive Index of the Rugate Notch Filter

Equations (11)

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n(x)=exp[2π0Q(k)ksin[ϕ(k)kx]·dk].
Q(k)={1/2[1T(k)T(k)]}1/2.
n=(nH×dH+nL×dL)/(dH+dL).
M11=M22=cosγ,
N=(isinγ)/M12=iM21/sinγ.
M11=M22=cos2φpcosφq12(nq/np+np/nq)sin2φpsinφq,
M12=(i/np){sin2φpcosφq+12(np/nq+nq/np)cos2φpsinφq+12(np/nqnq/np)sinφq},
M21=inp{sin2φpcosφq+12(np/nq+nq/np)cos2φpsinφq12(np/nqnq/np)sinφq}.
dTiO2=RTiO2×NTiO2,
dAl2O3=RAl2O3×NAl2O3.
T=d/(dTiO2+dAl2O3).

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