Abstract

A theoretical analysis of a design of multiple narrow bandpass filters based on one-dimensional (1D) rugate photonic structures with a period jump defect is presented. The optical properties, including transmittance and energy density distributions, are numerically calculated using the propagation matrix method. Our results show that multiple resonance transmission modes are produced when the period jump defect is introduced into the 1D rugate film. Both blueshift and redshift of the stop band of the rugate structure and wavelengths of resonant modes are observed, depending on the change of period jump. The number, the wavelengths, the band intervals, and the intensities of multiple resonance transmission modes are tunable by adjusting structure parameters of the rugate structure. Experimental feasibility of the proposed multiple narrow bandpass optical filters using the technique of glancing angle deposition is also discussed.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [Crossref] [PubMed]
  2. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
    [Crossref]
  3. J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
    [Crossref]
  4. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
    [Crossref] [PubMed]
  5. M. Deopura, C. K. Ullal, B. Temelkuran, and Y. Fink, Opt. Lett. 26, 1197 (2001).
    [Crossref]
  6. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  7. B. G. Bovard, Appl. Opt. 32, 5427 (1993).
    [Crossref] [PubMed]
  8. Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, Appl. Phys. Lett. 82, 4654 (2003).
    [Crossref]
  9. Z. Wang, L. Wang, Y. Wu, L. Chen, X. Chen, and W. Lu, Appl. Phys. Lett. 84, 1629 (2004).
    [Crossref]
  10. H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, J. Appl. Phys. 97, 103111 (2005).
    [Crossref]
  11. Y. H. Chen, J. W. Dong, and H. Z. Wang, Appl. Phys. Lett. 89, 141101 (2006).
    [Crossref]
  12. Y. H. Chen, Appl. Phys. Lett. 92, 011925 (2008).
    [Crossref]
  13. Y. H. Chen, J. Phys. D 42, 075106 (2009).
    [Crossref]
  14. A. C. van Popta, M. M. Hawkeye, J. C. Sit, and M. J. Brett, Opt. Lett. 29, 2545 (2004).
    [Crossref] [PubMed]
  15. M. M. Hawkeye and M. J. Brett, J. Appl. Phys. 100, 044322 (2006).
    [Crossref]
  16. M. M. Hawkeye and M. J. Brett, J. Vac. Sci. Technol. A 25, 1317 (2007).
    [Crossref]
  17. M. J. Brett and M. M. Hawkeye, Science 319, 1192 (2008).
    [Crossref] [PubMed]
  18. A. G. Imenes and D. R. McKenzie, Appl. Opt. 45, 7841 (2006).
    [Crossref] [PubMed]
  19. Z. Lu, PIER Letters 14, 1 (2010).
    [Crossref]
  20. Z. Lu, J. Opt. Soc. Am. A 24, 236 (2007).
    [Crossref]
  21. Z. Lu, Opt. Lett. 33, 1948 (2008).
    [Crossref] [PubMed]
  22. Y. Liu and Z. Lu, PIER 111, 213 (2011).
    [Crossref]
  23. J. M. Bendickson, J. P. Dowling, and M. Scalora, Phys. Rev. E 53, 4107 (1996).
    [Crossref]

2011 (1)

Y. Liu and Z. Lu, PIER 111, 213 (2011).
[Crossref]

2010 (1)

Z. Lu, PIER Letters 14, 1 (2010).
[Crossref]

2009 (1)

Y. H. Chen, J. Phys. D 42, 075106 (2009).
[Crossref]

2008 (3)

M. J. Brett and M. M. Hawkeye, Science 319, 1192 (2008).
[Crossref] [PubMed]

Y. H. Chen, Appl. Phys. Lett. 92, 011925 (2008).
[Crossref]

Z. Lu, Opt. Lett. 33, 1948 (2008).
[Crossref] [PubMed]

2007 (2)

Z. Lu, J. Opt. Soc. Am. A 24, 236 (2007).
[Crossref]

M. M. Hawkeye and M. J. Brett, J. Vac. Sci. Technol. A 25, 1317 (2007).
[Crossref]

2006 (3)

M. M. Hawkeye and M. J. Brett, J. Appl. Phys. 100, 044322 (2006).
[Crossref]

Y. H. Chen, J. W. Dong, and H. Z. Wang, Appl. Phys. Lett. 89, 141101 (2006).
[Crossref]

A. G. Imenes and D. R. McKenzie, Appl. Opt. 45, 7841 (2006).
[Crossref] [PubMed]

2005 (1)

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, J. Appl. Phys. 97, 103111 (2005).
[Crossref]

2004 (2)

Z. Wang, L. Wang, Y. Wu, L. Chen, X. Chen, and W. Lu, Appl. Phys. Lett. 84, 1629 (2004).
[Crossref]

A. C. van Popta, M. M. Hawkeye, J. C. Sit, and M. J. Brett, Opt. Lett. 29, 2545 (2004).
[Crossref] [PubMed]

2003 (1)

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, Appl. Phys. Lett. 82, 4654 (2003).
[Crossref]

2001 (1)

1998 (2)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[Crossref] [PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[Crossref]

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[Crossref]

1996 (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, Phys. Rev. E 53, 4107 (1996).
[Crossref]

1993 (1)

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[Crossref] [PubMed]

Baba, T.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, J. Appl. Phys. 97, 103111 (2005).
[Crossref]

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, Phys. Rev. E 53, 4107 (1996).
[Crossref]

Bovard, B. G.

Brett, M. J.

M. J. Brett and M. M. Hawkeye, Science 319, 1192 (2008).
[Crossref] [PubMed]

M. M. Hawkeye and M. J. Brett, J. Vac. Sci. Technol. A 25, 1317 (2007).
[Crossref]

M. M. Hawkeye and M. J. Brett, J. Appl. Phys. 100, 044322 (2006).
[Crossref]

A. C. van Popta, M. M. Hawkeye, J. C. Sit, and M. J. Brett, Opt. Lett. 29, 2545 (2004).
[Crossref] [PubMed]

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[Crossref] [PubMed]

Chen, L.

Z. Wang, L. Wang, Y. Wu, L. Chen, X. Chen, and W. Lu, Appl. Phys. Lett. 84, 1629 (2004).
[Crossref]

Chen, X.

Z. Wang, L. Wang, Y. Wu, L. Chen, X. Chen, and W. Lu, Appl. Phys. Lett. 84, 1629 (2004).
[Crossref]

Chen, Y. H.

Y. H. Chen, J. Phys. D 42, 075106 (2009).
[Crossref]

Y. H. Chen, Appl. Phys. Lett. 92, 011925 (2008).
[Crossref]

Y. H. Chen, J. W. Dong, and H. Z. Wang, Appl. Phys. Lett. 89, 141101 (2006).
[Crossref]

Cho, M. W.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, J. Appl. Phys. 97, 103111 (2005).
[Crossref]

Cho, S. J.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, J. Appl. Phys. 97, 103111 (2005).
[Crossref]

Deopura, M.

Dong, J. W.

Y. H. Chen, J. W. Dong, and H. Z. Wang, Appl. Phys. Lett. 89, 141101 (2006).
[Crossref]

Dowling, J. P.

J. M. Bendickson, J. P. Dowling, and M. Scalora, Phys. Rev. E 53, 4107 (1996).
[Crossref]

Fan, S.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[Crossref]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[Crossref] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[Crossref]

Fink, Y.

Hawkeye, M. M.

M. J. Brett and M. M. Hawkeye, Science 319, 1192 (2008).
[Crossref] [PubMed]

M. M. Hawkeye and M. J. Brett, J. Vac. Sci. Technol. A 25, 1317 (2007).
[Crossref]

M. M. Hawkeye and M. J. Brett, J. Appl. Phys. 100, 044322 (2006).
[Crossref]

A. C. van Popta, M. M. Hawkeye, J. C. Sit, and M. J. Brett, Opt. Lett. 29, 2545 (2004).
[Crossref] [PubMed]

Imenes, A. G.

Joannopoulos, J. D.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[Crossref]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[Crossref] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[Crossref]

Lee, H. Y.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, J. Appl. Phys. 97, 103111 (2005).
[Crossref]

Lee, W. H.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, J. Appl. Phys. 97, 103111 (2005).
[Crossref]

Liu, Y.

Y. Liu and Z. Lu, PIER 111, 213 (2011).
[Crossref]

Lu, H.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, Appl. Phys. Lett. 82, 4654 (2003).
[Crossref]

Lu, W.

Z. Wang, L. Wang, Y. Wu, L. Chen, X. Chen, and W. Lu, Appl. Phys. Lett. 84, 1629 (2004).
[Crossref]

Lu, Z.

Makino, H.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, J. Appl. Phys. 97, 103111 (2005).
[Crossref]

McKenzie, D. R.

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[Crossref] [PubMed]

Ming, N. B.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, Appl. Phys. Lett. 82, 4654 (2003).
[Crossref]

Nam, G. Y.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, J. Appl. Phys. 97, 103111 (2005).
[Crossref]

Qin, Q.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, Appl. Phys. Lett. 82, 4654 (2003).
[Crossref]

Scalora, M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, Phys. Rev. E 53, 4107 (1996).
[Crossref]

Sit, J. C.

Temelkuran, B.

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[Crossref] [PubMed]

Ullal, C. K.

van Popta, A. C.

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[Crossref]

Wang, H. Z.

Y. H. Chen, J. W. Dong, and H. Z. Wang, Appl. Phys. Lett. 89, 141101 (2006).
[Crossref]

Wang, L.

Z. Wang, L. Wang, Y. Wu, L. Chen, X. Chen, and W. Lu, Appl. Phys. Lett. 84, 1629 (2004).
[Crossref]

Wang, Z.

Z. Wang, L. Wang, Y. Wu, L. Chen, X. Chen, and W. Lu, Appl. Phys. Lett. 84, 1629 (2004).
[Crossref]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[Crossref] [PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[Crossref]

Wu, Y.

Z. Wang, L. Wang, Y. Wu, L. Chen, X. Chen, and W. Lu, Appl. Phys. Lett. 84, 1629 (2004).
[Crossref]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[Crossref] [PubMed]

Yao, T.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, J. Appl. Phys. 97, 103111 (2005).
[Crossref]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Yuan, C. S.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, Appl. Phys. Lett. 82, 4654 (2003).
[Crossref]

Zhu, S. N.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, Appl. Phys. Lett. 82, 4654 (2003).
[Crossref]

Zhu, Y. Y.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, Appl. Phys. Lett. 82, 4654 (2003).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

Y. H. Chen, J. W. Dong, and H. Z. Wang, Appl. Phys. Lett. 89, 141101 (2006).
[Crossref]

Y. H. Chen, Appl. Phys. Lett. 92, 011925 (2008).
[Crossref]

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, Appl. Phys. Lett. 82, 4654 (2003).
[Crossref]

Z. Wang, L. Wang, Y. Wu, L. Chen, X. Chen, and W. Lu, Appl. Phys. Lett. 84, 1629 (2004).
[Crossref]

J. Appl. Phys. (2)

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, J. Appl. Phys. 97, 103111 (2005).
[Crossref]

M. M. Hawkeye and M. J. Brett, J. Appl. Phys. 100, 044322 (2006).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Phys. D (1)

Y. H. Chen, J. Phys. D 42, 075106 (2009).
[Crossref]

J. Vac. Sci. Technol. A (1)

M. M. Hawkeye and M. J. Brett, J. Vac. Sci. Technol. A 25, 1317 (2007).
[Crossref]

Nature (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[Crossref]

Opt. Lett. (4)

Phys. Rev. E (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, Phys. Rev. E 53, 4107 (1996).
[Crossref]

Phys. Rev. Lett. (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[Crossref] [PubMed]

PIER (1)

Y. Liu and Z. Lu, PIER 111, 213 (2011).
[Crossref]

PIER Letters (1)

Z. Lu, PIER Letters 14, 1 (2010).
[Crossref]

Science (2)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[Crossref] [PubMed]

M. J. Brett and M. M. Hawkeye, Science 319, 1192 (2008).
[Crossref] [PubMed]

Other (1)

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Refraction index profile of a 1D rugate structure with a period jump defect in the center; (a) Δ p = 0.5 p A , (b) Δ p = + 0.5 p A .

Fig. 2
Fig. 2

Transmittance of five different changes of the modified period, δ = 0.2 , 0.1 , 0, 0.1, 0.2. The equal number of cycles of the end and defect segments is assumed, N A = N B = 10 .

Fig. 3
Fig. 3

Transmittance for (a) δ = 0.5 and (b)  δ = + 0.5 , with fixed N A = 10 .

Fig. 4
Fig. 4

Energy density distributions with respect to the physical thickness of the rugate structure at three resonance transmission modes labeled as I, II, and III in Fig. 3b for N A = 10 . The energy density distributions for N A = 20 at the same three resonant modes are denoted by I′, II′, and III′.

Fig. 5
Fig. 5

Group velocities of the three middle panels shown in Fig. 3b.

Equations (1)

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

n ( z ) = { n a + n p 2 sin ( 2 π p A z + α 0 ) , z [ z 0 , z 1 ] n a + n p 2 sin ( 2 π p B ( z z 1 ) + α 0 ) , z [ z 1 , z 2 ] n a + n p 2 sin ( 2 π p A ( z z 2 ) + α 0 ) , z [ z 2 , z 3 ] .

Metrics