Abstract

The supercell- based orthonormal basis method is proposed to investigate the modal properties of the Bragg fibers. A square lattice is constructed by the whole Bragg fiber which is considered as a supercell, and the periodical dielectric structure of the square lattice is decomposed using periodic functions (cosine). The modal electric field is expanded as the sum of the orthonormal set of Hermite-Gaussian basis functions based on the opposite parity of the transverse electric field. The propagation characteristics of Bragg fibers can be obtained after recasting the wave equation into an eigenvalue system. This method is implemented with very high efficiency and accuracy.

© 2003 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
  3. Y. Fink, D.J. Ripin, S. Fan, C. Chen, J.D. Joannopoulos, and E.L. Thomas, “Guiding optical light in air using an all-dielcetric structure,” J. Lightwave Technol. 17, 2039–2041 (1999).
    [Crossref]
  4. 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]
  5. S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513(2002).
    [Crossref] [PubMed]
  6. P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
    [Crossref] [PubMed]
  7. J.C. Knight and P. St. Russell, “New ways to guide light,” Science 296, 276–277 (2002).
    [Crossref] [PubMed]
  8. Jes Broeng, Stig E. B. Libori, T. Sondergaard, and Anders Bjarklev, “Analysis of air-guiding photonic bandgap fibers,” Opt. Lett. 25, 96–98 (2000).
    [Crossref]
  9. M. Ibanescu, S.G. Johnson, M. Soljacic, J.D. Joannopoulos, and Y. Fink, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608-1-8(2003).
    [Crossref]
  10. I.M. Bassett and A. Argyros, “Elimination of polarization degeneracy in round waveguides,” Opt. Express 10, 1342–1346 (2002), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-10-23-1342.
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  12. G. Ourang, Yong Xu, and A. Yariv, “Theoretical study on dispersion compensation in air-core Bragg fibers,” Opt. Express 10, 899–908 (2002), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-10-17-899.
    [Crossref]
  13. T.D. Engeness, M. Ibanescu, S.G. Johnson, O. Weisberg, M. Skorobogatiy, S. Jacobs, and Y. Fink, “Dispersion tailoring and compensation by modal interactions in omniguide fibers,” Opt. Express 11, 1175–1196 (2003), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-11-10-1175.
    [Crossref] [PubMed]
  14. J.A. Mosoriu, E. Silvestre, A. Ferrando, P. Andres, and J.J. Miret, “High-index-core Bragg fibers: dispersion properties,” Opt. Express 11, 1400–1405 (2003), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-11-12-1400.
    [Crossref]
  15. E. Silvestre, M.V. Andrés, and P. Andrés, “Biorthonormal-basis method for the vector description of optical-fiber mode,” J. Lightwave Technol. 16, 923–928 (1998).
    [Crossref]
  16. R. D. Meade, A.M. Rappe, K.D. Brommer, J.D. Joannopoulos, and O.L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
    [Crossref]
  17. Shangping Guo, Feng Wu, Khalid Ikram, and Sacharia Albin, “Analysis of circular fibers with arbitrary index profile by Galerkin method,” to be published by Opt. Lett..
  18. J.D. Joannopoulos, R.D. Meade, and J.N. Winn, “Photonic crystals: molding the flow of light,” (New York, Princeton university press, 1995).
  19. Shangping Guo and Sacharia Albin, “Simple plane wave implementation for photonic crystal calculations,” Opt. Express 11, 167–175 (2003), http://www. opticsexpress.org/ abstract. cfm? URI=OPEX-11-2-167.
    [Crossref] [PubMed]
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    [Crossref]
  22. Yu-Li Hsueh, E. S.T. Hu, M. E. Marhic, and G. Kazovsky, “Opposite-parity orthonormal function expansion for efficient full-vectorial modeling of holey optical fibers,” Opt. Lett. 28, 1188–1190(2003).
    [Crossref] [PubMed]
  23. W. Zhi, R.G. Bin, L.S. Qin, and J.S Sheng, “Supercell lattice method for photonic crystal fibers,” Opt. Express 11, 980–991 (2003), http:// www.opticsexpress.org/ abstract. cfm? URI=OPEX-11-9-980.
    [Crossref] [PubMed]
  24. R.G. Bin, W. Zhi, L.S. Qin, and J.S. Sheng, “Mode Classification and Degeneracy in Photonic Crystal Fiber,” Opt. Express 11, 1310–1321 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-1310.
    [Crossref]

2003 (8)

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

M. Ibanescu, S.G. Johnson, M. Soljacic, J.D. Joannopoulos, and Y. Fink, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608-1-8(2003).
[Crossref]

T.D. Engeness, M. Ibanescu, S.G. Johnson, O. Weisberg, M. Skorobogatiy, S. Jacobs, and Y. Fink, “Dispersion tailoring and compensation by modal interactions in omniguide fibers,” Opt. Express 11, 1175–1196 (2003), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-11-10-1175.
[Crossref] [PubMed]

J.A. Mosoriu, E. Silvestre, A. Ferrando, P. Andres, and J.J. Miret, “High-index-core Bragg fibers: dispersion properties,” Opt. Express 11, 1400–1405 (2003), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-11-12-1400.
[Crossref]

Shangping Guo and Sacharia Albin, “Simple plane wave implementation for photonic crystal calculations,” Opt. Express 11, 167–175 (2003), http://www. opticsexpress.org/ abstract. cfm? URI=OPEX-11-2-167.
[Crossref] [PubMed]

Yu-Li Hsueh, E. S.T. Hu, M. E. Marhic, and G. Kazovsky, “Opposite-parity orthonormal function expansion for efficient full-vectorial modeling of holey optical fibers,” Opt. Lett. 28, 1188–1190(2003).
[Crossref] [PubMed]

W. Zhi, R.G. Bin, L.S. Qin, and J.S Sheng, “Supercell lattice method for photonic crystal fibers,” Opt. Express 11, 980–991 (2003), http:// www.opticsexpress.org/ abstract. cfm? URI=OPEX-11-9-980.
[Crossref] [PubMed]

R.G. Bin, W. Zhi, L.S. Qin, and J.S. Sheng, “Mode Classification and Degeneracy in Photonic Crystal Fiber,” Opt. Express 11, 1310–1321 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-1310.
[Crossref]

2002 (4)

2001 (1)

2000 (2)

Jes Broeng, Stig E. B. Libori, T. Sondergaard, and Anders Bjarklev, “Analysis of air-guiding photonic bandgap fibers,” Opt. Lett. 25, 96–98 (2000).
[Crossref]

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]

1999 (2)

1998 (2)

E. Silvestre, M.V. Andrés, and P. Andrés, “Biorthonormal-basis method for the vector description of optical-fiber mode,” J. Lightwave Technol. 16, 923–928 (1998).
[Crossref]

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

1993 (1)

R. D. Meade, A.M. Rappe, K.D. Brommer, J.D. Joannopoulos, and O.L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[Crossref]

1978 (1)

Albin, Sacharia

Shangping Guo and Sacharia Albin, “Simple plane wave implementation for photonic crystal calculations,” Opt. Express 11, 167–175 (2003), http://www. opticsexpress.org/ abstract. cfm? URI=OPEX-11-2-167.
[Crossref] [PubMed]

Shangping Guo, Feng Wu, Khalid Ikram, and Sacharia Albin, “Analysis of circular fibers with arbitrary index profile by Galerkin method,” to be published by Opt. Lett..

Alerhand, O.L.

R. D. Meade, A.M. Rappe, K.D. Brommer, J.D. Joannopoulos, and O.L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[Crossref]

Andres, P.

Andrés, M.V.

Andrés, P.

Argyros, A.

Bassett, I.M.

Bennett, P.J.

Bin, R.G.

Bjarklev, Anders

Broderick, N.G.R.

Broeng, Jes

Brommer, K.D.

R. D. Meade, A.M. Rappe, K.D. Brommer, J.D. Joannopoulos, and O.L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[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-dielcetric structure,” J. Lightwave Technol. 17, 2039–2041 (1999).
[Crossref]

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

Engeness, T.D.

Fan, S.

Fan, S.H.

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

Ferrando, A.

Fink, Y.

T.D. Engeness, M. Ibanescu, S.G. Johnson, O. Weisberg, M. Skorobogatiy, S. Jacobs, and Y. Fink, “Dispersion tailoring and compensation by modal interactions in omniguide fibers,” Opt. Express 11, 1175–1196 (2003), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-11-10-1175.
[Crossref] [PubMed]

M. Ibanescu, S.G. Johnson, M. Soljacic, J.D. Joannopoulos, and Y. Fink, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608-1-8(2003).
[Crossref]

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513(2002).
[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), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-9-13-748.
[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]

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

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

Guo, Shangping

Shangping Guo and Sacharia Albin, “Simple plane wave implementation for photonic crystal calculations,” Opt. Express 11, 167–175 (2003), http://www. opticsexpress.org/ abstract. cfm? URI=OPEX-11-2-167.
[Crossref] [PubMed]

Shangping Guo, Feng Wu, Khalid Ikram, and Sacharia Albin, “Analysis of circular fibers with arbitrary index profile by Galerkin method,” to be published by Opt. Lett..

Hart, S.D.

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513(2002).
[Crossref] [PubMed]

Hsueh, Yu-Li

Hu, E. S.T.

Ibanescu, M.

Ikram, Khalid

Shangping Guo, Feng Wu, Khalid Ikram, and Sacharia Albin, “Analysis of circular fibers with arbitrary index profile by Galerkin method,” to be published by Opt. Lett..

Jacobs, S.

Jacobs, S.A.

Joannopoulos, J.D.

M. Ibanescu, S.G. Johnson, M. Soljacic, J.D. Joannopoulos, and Y. Fink, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608-1-8(2003).
[Crossref]

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513(2002).
[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), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-9-13-748.
[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]

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

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

R. D. Meade, A.M. Rappe, K.D. Brommer, J.D. Joannopoulos, and O.L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[Crossref]

J.D. Joannopoulos, R.D. Meade, and J.N. Winn, “Photonic crystals: molding the flow of light,” (New York, Princeton university press, 1995).

Johnson, S.G.

Kazovsky, G.

Knight, J.C.

J.C. Knight and P. St. Russell, “New ways to guide light,” Science 296, 276–277 (2002).
[Crossref] [PubMed]

Libori, Stig E. B.

Love, J.D.

A.W. Snyder and J.D. Love, Optical waveguide theory, (New York: Chapman and Hall, 1983).

Marhic, M. E.

Marom, E.

Maskaly, G.R.

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513(2002).
[Crossref] [PubMed]

Meade, R. D.

R. D. Meade, A.M. Rappe, K.D. Brommer, J.D. Joannopoulos, and O.L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[Crossref]

Meade, R.D.

J.D. Joannopoulos, R.D. Meade, and J.N. Winn, “Photonic crystals: molding the flow of light,” (New York, Princeton university press, 1995).

Michel, J.

Y. Fink, J.N. Winn, S.H. 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.J.

Monro, T.M.

Mosoriu, J.A.

Ourang, G.

Prideaux, P.H.

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513(2002).
[Crossref] [PubMed]

Qin, L.S.

Rappe, A.M.

R. D. Meade, A.M. Rappe, K.D. Brommer, J.D. Joannopoulos, and O.L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[Crossref]

Richardson, D.J.

Ripin, D.J.

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

Russell, P. St.

J.C. Knight and P. St. Russell, “New ways to guide light,” Science 296, 276–277 (2002).
[Crossref] [PubMed]

Sheng, J.S

Sheng, J.S.

Silvestre, E.

Skorobogatiy, M.

Snyder, A.W.

A.W. Snyder and J.D. Love, Optical waveguide theory, (New York: Chapman and Hall, 1983).

Soljacic, M.

Sondergaard, T.

Temelkuran, B.

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513(2002).
[Crossref] [PubMed]

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-dielcetric structure,” J. Lightwave Technol. 17, 2039–2041 (1999).
[Crossref]

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

Weisberg, O.

Winn, J.N.

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

J.D. Joannopoulos, R.D. Meade, and J.N. Winn, “Photonic crystals: molding the flow of light,” (New York, Princeton university press, 1995).

Wu, Feng

Shangping Guo, Feng Wu, Khalid Ikram, and Sacharia Albin, “Analysis of circular fibers with arbitrary index profile by Galerkin method,” to be published by Opt. Lett..

Xu, Yong

Yariv, A.

Yeh, P.

Zhi, W.

J. Lightwave Technol. (3)

J. Opt. Soc. Am. (1)

Opt. Express (8)

I.M. Bassett and A. Argyros, “Elimination of polarization degeneracy in round waveguides,” Opt. Express 10, 1342–1346 (2002), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-10-23-1342.
[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), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-9-13-748.
[Crossref] [PubMed]

G. Ourang, Yong Xu, and A. Yariv, “Theoretical study on dispersion compensation in air-core Bragg fibers,” Opt. Express 10, 899–908 (2002), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-10-17-899.
[Crossref]

T.D. Engeness, M. Ibanescu, S.G. Johnson, O. Weisberg, M. Skorobogatiy, S. Jacobs, and Y. Fink, “Dispersion tailoring and compensation by modal interactions in omniguide fibers,” Opt. Express 11, 1175–1196 (2003), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-11-10-1175.
[Crossref] [PubMed]

J.A. Mosoriu, E. Silvestre, A. Ferrando, P. Andres, and J.J. Miret, “High-index-core Bragg fibers: dispersion properties,” Opt. Express 11, 1400–1405 (2003), http://www.opticsexpress.org/ abstract. cfm? URI =OPEX-11-12-1400.
[Crossref]

Shangping Guo and Sacharia Albin, “Simple plane wave implementation for photonic crystal calculations,” Opt. Express 11, 167–175 (2003), http://www. opticsexpress.org/ abstract. cfm? URI=OPEX-11-2-167.
[Crossref] [PubMed]

W. Zhi, R.G. Bin, L.S. Qin, and J.S Sheng, “Supercell lattice method for photonic crystal fibers,” Opt. Express 11, 980–991 (2003), http:// www.opticsexpress.org/ abstract. cfm? URI=OPEX-11-9-980.
[Crossref] [PubMed]

R.G. Bin, W. Zhi, L.S. Qin, and J.S. Sheng, “Mode Classification and Degeneracy in Photonic Crystal Fiber,” Opt. Express 11, 1310–1321 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-1310.
[Crossref]

Opt. Lett. (2)

Phys. Rev. B (1)

R. D. Meade, A.M. Rappe, K.D. Brommer, J.D. Joannopoulos, and O.L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[Crossref]

Phys. Rev. E (1)

M. Ibanescu, S.G. Johnson, M. Soljacic, J.D. Joannopoulos, and Y. Fink, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E 67, 046608-1-8(2003).
[Crossref]

Science (5)

Y. Fink, J.N. Winn, S.H. 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]

S.D. Hart, G.R. Maskaly, B. Temelkuran, P.H. Prideaux, J.D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513(2002).
[Crossref] [PubMed]

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

J.C. Knight and P. St. Russell, “New ways to guide light,” Science 296, 276–277 (2002).
[Crossref] [PubMed]

Other (3)

Shangping Guo, Feng Wu, Khalid Ikram, and Sacharia Albin, “Analysis of circular fibers with arbitrary index profile by Galerkin method,” to be published by Opt. Lett..

J.D. Joannopoulos, R.D. Meade, and J.N. Winn, “Photonic crystals: molding the flow of light,” (New York, Princeton university press, 1995).

A.W. Snyder and J.D. Love, Optical waveguide theory, (New York: Chapman and Hall, 1983).

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Figures (4)

Fig. 1.
Fig. 1.

scheme of the construction of the supercell square lattice of the Bragg fiber, (a) is the radial distribution of the dielectric constant and (b) is the supercell square lattice.

Fig. 2.
Fig. 2.

The simulation result of the dielectric constant of the Bragg fiber, with the parameters ε 1=4.62, ε 2=1.62, ε 3=1.0, Λ=0.434µm, R=30Λ, a=0.78Λ, and m=17, supercell lattice constant D=1.2(2R+18Λ), P=1200.

Fig. 3.
Fig. 3.

The electric field of the modes HE11, TE01, TM01 and HE21 of the Bragg fiber with the structure parameters same as in Fig. 2, the annular dielectric constant is superimposed.

Fig. 4. (a)
Fig. 4. (a)

The propagation constant of TE01 mode, and (b) the difference between two different approaches

Equations (20)

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ε F ( k ) = 1 A A ε ( r ) e i k · r d s ,
ε ( r ) = { ε i , r i 1 < r < r i ε b , r > r m = ε b + { ε i ε b , r i 1 < r < r i 0 , r > r m ,
ε F ( k ) = 1 A A ε b e i k · r d s + 1 A i = 1 m A ( ε i ε b ) e i k · r d s
= ε b δ ( k ) + i = 1 m ( ε i ε b ) [ 2 f i J 1 ( k r i ) k r i 2 f i 1 J 1 ( k r i 1 ) k r i 1 ] ,
ε ( r ) = ε ( x , y ) = a , b = 0 P P ab cos 2 π a x D cos 2 π b y D
ln ε ( r ) = ln ε ( x , y ) = a , b = 0 P P ab ln cos 2 π a x D cos 2 π b y D ,
P ab = ε F ( k a + P , b + P ) + ε F ( k a + P , b + P ) + ε F ( k a + P , b + P ) + ε F ( k a + P , b + P ) ,
for a = 0 or b = 0 , P ab = ε F ( k a + P , b + P ) + ε F ( k a + P , b + P ) ,
for a = 0 and b = 0 , P 00 = ε F ( k P , P ) ,
( t 2 β 2 + k 0 2 ε ) e x = x ( e x ln ε x + e y ln ε y )
( t 2 β 2 + k 0 2 ε ) e y = y ( e x ln ε x + e y ln ε y ) ,
e x ( x , y ) mn = a , b = 0 F 1 ε ab x ψ 2 a + m ( x ) ψ 2 b + n ( y ) , e y ( x , y ) m ¯ n ¯ = a , b = 0 F 1 ε ab y ψ 2 a + m ¯ ( x ) ψ 2 b + n ¯ ( y ) ,
ψ i ( s ) = 2 i 2 π 1 4 i ! ϖ s exp ( s 2 2 ϖ s 2 ) H i ( s ϖ s ) ,
L mn [ ε x ε y ] [ [ I abcd ( 1 ) + k 2 I abcd ( 2 ) + I abcd ( 3 ) x ] mn [ I abcd ( 4 ) x ] mn [ I abcd ( 4 ) y ] mn ¯ [ I abcd ( 1 ) + k 2 I abcd ( 2 ) + I abcd ( 3 ) y ] mn ¯ ] [ ε x ε y ] = β 2 [ ε x ε y ] ,
[ I abcd ( 1 ) ] mn = + ψ 2 a + m ( x ) ψ 2 b + n ( y ) t 2 [ ψ 2 c + m ( x ) ψ 2 d + n ( y ) ] d x d y ,
[ I abcd ( 2 ) ] mn = + ε ψ 2 a + m ( x ) ψ 2 b + n ( y ) ψ 2 c + m ( x ) ψ 2 d + n ( y ) d x d y ,
[ I abcd ( 3 ) x ] mn = + ψ 2 a + m ( x ) ψ 2 b + n ( y ) x [ ψ 2 c + m ( x ) ψ 2 d + n ( y ) ln ε x ] d x d y ,
[ I abcd ( 3 ) y ] mn = + ψ 2 a + m ( x ) ψ 2 b + n ( y ) y [ ψ 2 c + m ( x ) ψ 2 d + n ( y ) ln ε y ] d x d y ,
[ I abcd ( 4 ) x ] mn = + ψ 2 a + m ( x ) ψ 2 b + n ( y ) x [ ψ 2 c + m ¯ ( x ) ψ 2 d + n ¯ ( y ) ln ε y ] d x d y ,
[ I abcd ( 4 ) y ] mn = + ψ 2 a + m ( x ) ψ 2 b + n ( y ) y [ ψ 2 c + m ¯ ( x ) ψ 2 d + n ¯ ( y ) ln ε x ] d x d y .

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