Abstract

Single-mode fibers are advantageous over multi-mode fibers in many aspects, e.g., much smaller loss, much longer transmission distance, much greater bandwidth, and higher bit rates. We propose a kind of single-TM-mode Bragg fiber in which magnetic materials are introduced. The idea for designing this kind of Bragg fiber comes from the symmetry of TE modes and TM modes when permittivity and permeability are replaced by each other. Through the transfer matrix method, we demonstrated a special kind of single-TM-mode Bragg fiber in a wide frequency range. Guiding modes may be in the bandgaps, at the edges of bandgaps, and in some region in conduction bands, but much more strongly confined guiding TM modes are inside the bandgaps. In addition, the optimization of the structure is also discussed.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Yeh, A. Yariv, and E. Marom, "Theory of Bragg Fiber," J. Opt. Soc. Am. 68, 1196-1201 (1978).
    [CrossRef]
  2. E.  Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett.  58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  3. S.  John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett.  58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  4. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
    [CrossRef] [PubMed]
  5. J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).
    [CrossRef]
  6. Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all dielectric structure," J. Lightwave Technol. 17, 2039-2041 (1999).
    [CrossRef]
  7. M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, "An all-dielectric coaxial waveguide," Science 289, 415-419 (2000).
    [CrossRef] [PubMed]
  8. W. C. Chew, Waves and Fields in Inhomogeneous Media, Chap. 3 (Van Nostrand Reinhold, New York, 1990).
  9. Y. Xu, R. K. Lee, and A. Yariv, "Asymptotic analysis of Bragg fibers," Opt. Lett. 25, 1756-1758 (2000).
    [CrossRef]
  10. Y. Xu, G. X. Ouyang, R. K. Lee, and A. Yariv, "Asymptotic matrix theory of Bragg fibers," J. Lightwave Technol. 20, 428-440 (2002).
    [CrossRef]
  11. Y. Xu, R. K. Lee, and A. Yariv, "Asymptotic analysis of dielectric coaxial fibers," Opt. Lett. 27, 1019-1021 (2002).
    [CrossRef]
  12. Y. Xu, A. Yariv, J. Fleming, and S. -Y. Lin, "Asymptotic analysis of silicon based Bragg fibers," Opt. Express 11, 1039-1049 (2003).
    [CrossRef] [PubMed]
  13. S. Guo, S. Albin, and R. Rogowski, "Comparative analysis of Bragg fibers," Opt. Express 12, 198-207 (2004).
    [CrossRef] [PubMed]
  14. S. Guo, F. Wu, K. Ikram, and S. Albin, "Analysis of circular fibers with arbitrary index profiles by Galerkin method," Opt. Lett. 29, 32-34 (2004).
    [CrossRef] [PubMed]
  15. T. P. Horikis and W. L. Kath, "Modal analysis of circular Bragg fibers with arbitrary index profiles," Opt. Lett. 31, 3417-3419 (2006).
    [CrossRef] [PubMed]
  16. C. M. de Sterke, I. M. Bassett and A. G. Street, "Differential losses in Bragg fibres," J. Appl. Phys. 76, 680-688 (1994).
    [CrossRef]
  17. T. Kawanishi and M. Izutsu, "Coaxial periodic optical waveguide," Opt. Express 7, 10-22 (2000).
    [CrossRef] [PubMed]
  18. G. Ouyang, Y. Xu and A. Yariv, "Comparative study of air-core and coaxial Bragg fibers: single mode transmission and dispersion characteristics," Opt. Express 9, 733-747 (2001).
    [CrossRef] [PubMed]
  19. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large core omniguide fibers," Opt. Express 9, 748-779 (2001).
    [CrossRef] [PubMed]
  20. I. M. Bassett and A. Argyros, "Elimination of polarization degeneracy in round waveguides," Opt. Express 10, 1342-1346 (2002).
    [PubMed]
  21. A. Argyros, "Guided modes and loss in Bragg fibers," Opt. Express 10, 1411-1417 (2002).
    [PubMed]
  22. M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Jonnopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608-1-8 (2003).
    [CrossRef]
  23. N. Issa, A. Argyros, M. van Eijkelenborg, and J. Zagari, "Identifying hollow waveguide guidance in air-cored microstructured optical fibres," Opt. Express 11, 996-1001 (2003).
    [CrossRef] [PubMed]
  24. J. -I. Sakai, "Hybrid modes in a Bragg fiber: general properties and formulas under the quarter-wave stack condition," J. Opt. Soc. Am. B 22, 2319-2330 (2005).
    [CrossRef]
  25. J. -I. Sakai and J. Sasaki, "Hybrid modes in a Bragg fiber: dispersion relation and electromagnetic fields," J. Opt. Soc. Am. B 23, 1020-1028 (2006).
    [CrossRef]
  26. G. Ouyang, Y. Xu, and A. Yariv, "Theoretical study on dispersion compensation in air-core Bragg fibers," Opt. Express 10, 899-908 (2002).
    [PubMed]
  27. J. Monsoriu, E. Silvestre, A. Ferrando, P. Andrés, and J. Miret, "High-index-core Bragg fibers: dispersion properties," Opt. Express 11, 1400-1405 (2003).
    [CrossRef] [PubMed]
  28. Y. Ni, S. Jia, L. Zhang, and J. Peng, "A novel design for all-solid silica Bragg fiber with zero-dispersion wavelength at 1550 nm," Opt. Express 12, 4602-4607 (2004).
    [CrossRef] [PubMed]
  29. M. Born and E. Wolf, Principles of Optics, (Pergamon Press, Oxford, 1980) Chap. 1.6.

2006 (2)

2005 (1)

2004 (3)

2003 (3)

2002 (5)

2001 (2)

2000 (3)

1999 (1)

1998 (2)

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

1994 (1)

C. M. de Sterke, I. M. Bassett and A. G. Street, "Differential losses in Bragg fibres," J. Appl. Phys. 76, 680-688 (1994).
[CrossRef]

1987 (2)

E.  Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett.  58, 2059-2062 (1987).
[CrossRef] [PubMed]

S.  John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett.  58, 2486-2489 (1987).
[CrossRef] [PubMed]

1978 (1)

Albin, S.

Andrés, P.

Argyros, A.

Bassett, I. M.

I. M. Bassett and A. Argyros, "Elimination of polarization degeneracy in round waveguides," Opt. Express 10, 1342-1346 (2002).
[PubMed]

C. M. de Sterke, I. M. Bassett and A. G. Street, "Differential losses in Bragg fibres," J. Appl. Phys. 76, 680-688 (1994).
[CrossRef]

Chen, C.

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all dielectric structure," J. Lightwave Technol. 17, 2039-2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

de Sterke, C. M.

C. M. de Sterke, I. M. Bassett and A. G. Street, "Differential losses in Bragg fibres," J. Appl. Phys. 76, 680-688 (1994).
[CrossRef]

Engeness, T. D.

Fan, S.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, "An all-dielectric coaxial waveguide," Science 289, 415-419 (2000).
[CrossRef] [PubMed]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all dielectric structure," J. Lightwave Technol. 17, 2039-2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).
[CrossRef]

Ferrando, A.

Fink, Y.

Fleming, J.

Guo, S.

Horikis, T. P.

Ibanescu, M.

Ikram, K.

Issa, N.

Izutsu, M.

Jacobs, S. A.

Jia, S.

Joannopoulos, J. D.

John, S.

S.  John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett.  58, 2486-2489 (1987).
[CrossRef] [PubMed]

Johnson, S. G.

Kath, W. L.

Kawanishi, T.

Lee, R. K.

Lin, S. -Y.

Marom, E.

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Miret, J.

Monsoriu, J.

Ni, Y.

Ouyang, G.

Ouyang, G. X.

Peng, J.

Ripin, D. J.

Rogowski, R.

Sakai, J. -I.

Sasaki, J.

Silvestre, E.

Skorobogatiy, M.

Soljacic, M.

Street, A. G.

C. M. de Sterke, I. M. Bassett and A. G. Street, "Differential losses in Bragg fibres," J. Appl. Phys. 76, 680-688 (1994).
[CrossRef]

Thomas, E. L.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, "An all-dielectric coaxial waveguide," Science 289, 415-419 (2000).
[CrossRef] [PubMed]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all dielectric structure," J. Lightwave Technol. 17, 2039-2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

van Eijkelenborg, M.

Weisberg, O.

Winn, J. N.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Wu, F.

Xu, Y.

Yablonovitch, E.

E.  Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett.  58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yariv, A.

Yeh, P.

Zagari, J.

Zhang, L.

J. Appl. Phys. (1)

C. M. de Sterke, I. M. Bassett and A. G. Street, "Differential losses in Bragg fibres," J. Appl. Phys. 76, 680-688 (1994).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Opt. Express (11)

S. Guo, S. Albin, and R. Rogowski, "Comparative analysis of Bragg fibers," Opt. Express 12, 198-207 (2004).
[CrossRef] [PubMed]

Y. Ni, S. Jia, L. Zhang, and J. Peng, "A novel design for all-solid silica Bragg fiber with zero-dispersion wavelength at 1550 nm," Opt. Express 12, 4602-4607 (2004).
[CrossRef] [PubMed]

G. Ouyang, Y. Xu and A. Yariv, "Comparative study of air-core and coaxial Bragg fibers: single mode transmission and dispersion characteristics," Opt. Express 9, 733-747 (2001).
[CrossRef] [PubMed]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large core omniguide fibers," Opt. Express 9, 748-779 (2001).
[CrossRef] [PubMed]

T. Kawanishi and M. Izutsu, "Coaxial periodic optical waveguide," Opt. Express 7, 10-22 (2000).
[CrossRef] [PubMed]

G. Ouyang, Y. Xu, and A. Yariv, "Theoretical study on dispersion compensation in air-core Bragg fibers," Opt. Express 10, 899-908 (2002).
[PubMed]

I. M. Bassett and A. Argyros, "Elimination of polarization degeneracy in round waveguides," Opt. Express 10, 1342-1346 (2002).
[PubMed]

A. Argyros, "Guided modes and loss in Bragg fibers," Opt. Express 10, 1411-1417 (2002).
[PubMed]

Y. Xu, A. Yariv, J. Fleming, and S. -Y. Lin, "Asymptotic analysis of silicon based Bragg fibers," Opt. Express 11, 1039-1049 (2003).
[CrossRef] [PubMed]

N. Issa, A. Argyros, M. van Eijkelenborg, and J. Zagari, "Identifying hollow waveguide guidance in air-cored microstructured optical fibres," Opt. Express 11, 996-1001 (2003).
[CrossRef] [PubMed]

J. Monsoriu, E. Silvestre, A. Ferrando, P. Andrés, and J. Miret, "High-index-core Bragg fibers: dispersion properties," Opt. Express 11, 1400-1405 (2003).
[CrossRef] [PubMed]

Opt. Lett. (5)

Phys. Rev. Lett. (2)

E.  Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett.  58, 2059-2062 (1987).
[CrossRef] [PubMed]

S.  John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett.  58, 2486-2489 (1987).
[CrossRef] [PubMed]

Science (2)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, "An all-dielectric coaxial waveguide," Science 289, 415-419 (2000).
[CrossRef] [PubMed]

Other (3)

W. C. Chew, Waves and Fields in Inhomogeneous Media, Chap. 3 (Van Nostrand Reinhold, New York, 1990).

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Jonnopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608-1-8 (2003).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, (Pergamon Press, Oxford, 1980) Chap. 1.6.

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.

The structure and the profiles of refractive index, relative permittivity, relative permeability of the Bragg fiber proposed

Fig. 2.
Fig. 2.

The TE (a, c, e) and TM (b, d, f) transmissivity spectrum of the 1-D PC corresponding to the Bragg fiber in Fig.1 for incident angle being 0° (a, b), 40° (c,d), and 80° (e, f)

Fig. 3.
Fig. 3.

The dispersion relation (a) and loss coefficient (c) of TE modes and the dispersion relation (b) and loss coefficient (d) of TM modes. The transmissivities for the region marked with green, olive, orange, and chocolate are 0.1~0.3, 0.1~0.01, 0.01~0.001, and <0.001, respectively. The modes in the 1st, 2nd, and 3rd bandgap are in purple, cyan, and brown respectively, while all other modes are in blue.

Fig. 4.
Fig. 4.

Dispersion relation (a) and loss coefficient (b) of hybrid modes (m=1) in the Bragg fiber

Fig. 5.
Fig. 5.

Field distribution of the TM mode at ωa/2πc=0.4575, neff =0.848178 in the Bragg fiber

Equations (6)

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

× E TE = μ 0 μ H TE t , × H TM = ε 0 ε E TM t ,
r TE = ε 1 μ 1 cos θ 1 ε 2 μ 2 cos θ 2 ε 1 μ 1 cos θ 1 + ε 2 μ 2 cos θ 2 , r TM = ε 2 μ 2 cos θ 1 ε 1 μ 1 cos θ 2 ε 2 μ 2 cos θ 1 + ε 1 μ 1 cos θ 2 ,
( r TE ) Before exchange = ( r TM ) After exchange ,
( r TM ) Before   exchange = ( r TE ) After exchange ,
( r TE r TM ) Before   exchange = ( r TM r TE ) After exchange .
γ = 40 π Im ( n eff ) ( λ l n 10 ) .

Metrics