Abstract

A finite-difference approach based upon the immersed interface method is used to analyze the mode structure of Bragg fibers with arbitrary index profiles. The method allows general propagation constants and eigenmodes to be calculated to a high degree of accuracy, while computation times are kept to a minimum by exploiting sparse matrix algebra. The method is well suited to handle complicated structures comprised of a large number of thin layers with high-index contrast and simultaneously determines multiple eigenmodes without modification.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Yeh, A. Yariv, and E. Marom, J. Opt. Soc. Am. 68, 1196 (1978).
    [CrossRef]
  2. Y. Fink, J. Winn, F. Shanhui, J. M. C. Chiping, J. Joannopoulos, and E. Thomas, Science 282, 1679 (1998).
    [CrossRef] [PubMed]
  3. B. Temelkuran, S. D. Hart, G. Benolt, J. D. Joannopoulos, and Y. Fink, Nature 420, 650 (2002).
    [CrossRef] [PubMed]
  4. M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
    [CrossRef] [PubMed]
  5. S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopolos, and Y. Fink, Opt. Express 9, 748 (2001).
    [CrossRef] [PubMed]
  6. Y. Xu, R. K. Lee, and A. Yariv, Opt. Lett. 25, 1756 (2000).
    [CrossRef]
  7. S. Guo and S. Albin, Opt. Express 12, 198 (2004).
    [CrossRef] [PubMed]
  8. T. Kawanishi and M. Izutsu, Opt. Express 7, 10 (2000).
    [CrossRef] [PubMed]
  9. S. Guo, F. Wu, K. Ikram, and S. Albin, Opt. Lett. 29, 32 (2004).
    [CrossRef] [PubMed]
  10. R. J. Leveque and Z. Li, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 31, 1019 (1994).
  11. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).
  12. K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, Opt. Express 12, 1510 (2004).
    [CrossRef] [PubMed]
  13. N. Issa, A. Argyros, M. van Eijkelenborg, and J. Zagari, Opt. Express 11, 996 (2003).
    [CrossRef] [PubMed]
  14. Y. C. Zhou, S. Zhao, M. Feig, and G. W. Wei, J. Comput. Phys. 213, 1 (2006).
    [CrossRef]

2006 (1)

Y. C. Zhou, S. Zhao, M. Feig, and G. W. Wei, J. Comput. Phys. 213, 1 (2006).
[CrossRef]

2004 (3)

2003 (1)

2002 (1)

B. Temelkuran, S. D. Hart, G. Benolt, J. D. Joannopoulos, and Y. Fink, Nature 420, 650 (2002).
[CrossRef] [PubMed]

2001 (1)

2000 (3)

1998 (1)

Y. Fink, J. Winn, F. Shanhui, J. M. C. Chiping, J. Joannopoulos, and E. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

1994 (1)

R. J. Leveque and Z. Li, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 31, 1019 (1994).

1978 (1)

Albin, S.

Argyros, A.

Bayindir, M.

Benoit, G.

Benolt, G.

B. Temelkuran, S. D. Hart, G. Benolt, J. D. Joannopoulos, and Y. Fink, Nature 420, 650 (2002).
[CrossRef] [PubMed]

Chiping, J. M. C.

Y. Fink, J. Winn, F. Shanhui, J. M. C. Chiping, J. Joannopoulos, and E. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Engeness, T.

Fan, S.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
[CrossRef] [PubMed]

Feig, M.

Y. C. Zhou, S. Zhao, M. Feig, and G. W. Wei, J. Comput. Phys. 213, 1 (2006).
[CrossRef]

Fink, Y.

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, Opt. Express 12, 1510 (2004).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benolt, J. D. Joannopoulos, and Y. Fink, Nature 420, 650 (2002).
[CrossRef] [PubMed]

S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopolos, and Y. Fink, Opt. Express 9, 748 (2001).
[CrossRef] [PubMed]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
[CrossRef] [PubMed]

Y. Fink, J. Winn, F. Shanhui, J. M. C. Chiping, J. Joannopoulos, and E. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Guo, S.

Hart, S. D.

Ibanescu, M.

Ikram, K.

Issa, N.

Izutsu, M.

Jacobs, S.

Joannopolos, J.

Joannopoulos, J.

Y. Fink, J. Winn, F. Shanhui, J. M. C. Chiping, J. Joannopoulos, and E. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Joannopoulos, J. D.

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, Opt. Express 12, 1510 (2004).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benolt, J. D. Joannopoulos, and Y. Fink, Nature 420, 650 (2002).
[CrossRef] [PubMed]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
[CrossRef] [PubMed]

Johnson, S.

Kawanishi, T.

Kuriki, K.

Kuriki, Y.

Lee, R. K.

Leveque, R. J.

R. J. Leveque and Z. Li, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 31, 1019 (1994).

Li, Z.

R. J. Leveque and Z. Li, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 31, 1019 (1994).

Love, J. D.

W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

Marom, E.

Shanhui, F.

Y. Fink, J. Winn, F. Shanhui, J. M. C. Chiping, J. Joannopoulos, and E. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Shapira, O.

Skorobogatiy, M.

Snyder, W.

W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

Soljacic, M.

Temelkuran, B.

B. Temelkuran, S. D. Hart, G. Benolt, J. D. Joannopoulos, and Y. Fink, Nature 420, 650 (2002).
[CrossRef] [PubMed]

Thomas, E.

Y. Fink, J. Winn, F. Shanhui, J. M. C. Chiping, J. Joannopoulos, and E. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Thomas, E. L.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
[CrossRef] [PubMed]

van Eijkelenborg, M.

Viens, J. F.

Wei, G. W.

Y. C. Zhou, S. Zhao, M. Feig, and G. W. Wei, J. Comput. Phys. 213, 1 (2006).
[CrossRef]

Weisberg, O.

Winn, J.

Y. Fink, J. Winn, F. Shanhui, J. M. C. Chiping, J. Joannopoulos, and E. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Wu, F.

Xu, Y.

Yariv, A.

Yeh, P.

Zagari, J.

Zhao, S.

Y. C. Zhou, S. Zhao, M. Feig, and G. W. Wei, J. Comput. Phys. 213, 1 (2006).
[CrossRef]

Zhou, Y. C.

Y. C. Zhou, S. Zhao, M. Feig, and G. W. Wei, J. Comput. Phys. 213, 1 (2006).
[CrossRef]

J. Comput. Phys. (1)

Y. C. Zhou, S. Zhao, M. Feig, and G. W. Wei, J. Comput. Phys. 213, 1 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (1)

B. Temelkuran, S. D. Hart, G. Benolt, J. D. Joannopoulos, and Y. Fink, Nature 420, 650 (2002).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (2)

Science (2)

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
[CrossRef] [PubMed]

Y. Fink, J. Winn, F. Shanhui, J. M. C. Chiping, J. Joannopoulos, and E. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. (1)

R. J. Leveque and Z. Li, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 31, 1019 (1994).

Other (1)

W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

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 (2)

Fig. 1
Fig. 1

Fields associated with the first four entries in Table 1. Layer positions are as described in the text.

Fig. 2
Fig. 2

Normalized magnetic fields for the TE mode of the second example Bragg fiber. Layer positions are as described in the text. In the top figure only the positions of the first and last layers are displayed.

Tables (1)

Tables Icon

Table 1 The Effective Index for the First Bragg Fiber Described in the Text

Equations (15)

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

1 r d d r ( r d H r m d r ) 1 r 2 [ ( 1 + m 2 ) H r m + 2 m H θ m ] + k 2 n 2 H r m = β 2 H r m ,
n 2 r d d r [ 1 n 2 ( r d H θ m d r + H θ m + m H r m ) ] 1 r 2 [ 2 m H r m + ( 1 + m 2 ) H θ m ] 1 r d d r ( m H r m + H θ m ) + k 2 n 2 H θ m = β 2 H θ m .
d H d r 2 + 1 r d H d r + B H = β 2 H ,
B = ( k 2 n 2 m 2 + 1 r 2 2 m r 2 2 m r 2 k 2 n 2 m 2 + 1 r 2 ) .
( 1 h 2 1 2 h r i ) H i 1 + ( k 2 n i 2 m 2 + 1 r i 2 2 h 2 ) H i + ( 1 h 2 + 1 2 h r i ) H i + 1 = β 2 H i ,
Γ 1 H i 1 + Γ 2 H i + Γ 3 H i + 1 = β 2 H i ,
Γ 1 + Γ 2 + Γ 3 [ I 2 + ( r j + 1 r * ) D + 1 2 ( r j + 1 r * ) 2 F 1 ] = B ,
( r j 1 r * ) Γ 1 + ( r j r * ) Γ 2 + Γ 3 [ ( r j + 1 r * ) C + 1 2 ( r j + 1 r * ) 2 E 1 ] = 1 r * I 2 ,
1 2 ( r j 1 r * ) 2 Γ 1 + 1 2 ( r j r * ) 2 Γ 2 + 1 2 ( r j + 1 r * ) 2 Γ 3 = I 2 ,
Γ 1 [ I 2 ( r j r * ) C 1 D + 1 2 ( r j r * ) F 2 ] + Γ 2 + Γ 3 = B + ,
Γ 1 [ ( r j r * ) C 1 + 1 2 ( r j r * ) 2 E 2 ] + ( r j + 1 r * ) Γ 2 + ( r j + 2 r * ) Γ 3 = 1 r * I 2 ,
1 2 ( r j r * ) 2 Γ 1 + 1 2 ( r j + 1 r * ) 2 Γ 2 + 1 2 ( r j + 2 r * ) 2 Γ 3 = I 2 .
D = ( 0 0 m r * ( n + 2 n 2 1 ) 1 r * ( n + 2 n 2 1 ) ) ,
F 1 = ( k 2 ( n + 2 n 2 ) 0 m r * 2 ( n + 2 n 2 1 ) 1 r * 2 ( n + 2 n 2 1 ) k 2 ( n + 2 n 2 ) ) ,
F 2 = ( k 2 ( n + 2 n 2 ) 0 m r * 2 ( n 2 n + 2 1 ) 1 r * 2 ( n 2 n + 2 1 ) + k 2 ( n + 2 n 2 ) ) .

Metrics