Abstract

Using an asymptotic analysis, we analytically calculate the dispersion and the field distribution of guided modes in an all-dielectric coaxial fiber. We compare the analytical results with those obtained from numerical calculations and find excellent agreement between them. We demonstrate that both the Bragg reflection and the total internal reflection play important roles in providing confinement and determining the dispersion characteristics of the coaxial fiber modes.

© 2002 Optical Society of America

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  1. P. Yeh, A. Yariv, and E. Marom, J. Opt. Soc. Am. 68, 1196 (1978).
  2. J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
    [CrossRef] [PubMed]
  5. Y. Xu, R. K. Lee, and A. Yariv, Opt. Lett. 25, 1756 (2000).
    [CrossRef]
  6. Y. Xu, G. X. Ouyang, R. K. Lee, and A. Yariv, J. Lightwave Technol. 20, 428 (2002).
    [CrossRef]
  7. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
    [CrossRef] [PubMed]
  8. F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, Opt. Quantum Electron. 31, 827 (1999).
    [CrossRef]
  9. S. D. Gedney, IEEE Trans. Antennas Propag. 44, 1630 (1996).
    [CrossRef]
  10. C. M. Furse and O. P. Gandhi, IEEE Microwave Guided Wave Lett. 5, 326 (1995).
    [CrossRef]

2002 (1)

2000 (2)

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

Y. Xu, R. K. Lee, and A. Yariv, Opt. Lett. 25, 1756 (2000).
[CrossRef]

1999 (2)

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, Opt. Quantum Electron. 31, 827 (1999).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

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. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[CrossRef] [PubMed]

1996 (1)

S. D. Gedney, IEEE Trans. Antennas Propag. 44, 1630 (1996).
[CrossRef]

1995 (1)

C. M. Furse and O. P. Gandhi, IEEE Microwave Guided Wave Lett. 5, 326 (1995).
[CrossRef]

1978 (1)

Alimenti, F.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, Opt. Quantum Electron. 31, 827 (1999).
[CrossRef]

Allan, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Bassi, P.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, Opt. Quantum Electron. 31, 827 (1999).
[CrossRef]

Birks, T. A.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[CrossRef] [PubMed]

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[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]

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Fan, S.

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

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

Fink, Y.

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

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

Furse, C. M.

C. M. Furse and O. P. Gandhi, IEEE Microwave Guided Wave Lett. 5, 326 (1995).
[CrossRef]

Gandhi, O. P.

C. M. Furse and O. P. Gandhi, IEEE Microwave Guided Wave Lett. 5, 326 (1995).
[CrossRef]

Gedney, S. D.

S. D. Gedney, IEEE Trans. Antennas Propag. 44, 1630 (1996).
[CrossRef]

Ibanescu, M.

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

Joannopoulos, J. D.

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

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

Knight, J. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[CrossRef] [PubMed]

Lee, R. K.

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Marom, E.

Mezzanotte, P.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, Opt. Quantum Electron. 31, 827 (1999).
[CrossRef]

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]

Ouyang, G. X.

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Roselli, L.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, Opt. Quantum Electron. 31, 827 (1999).
[CrossRef]

Russell, P. St. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[CrossRef] [PubMed]

Sorrentino, R.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, Opt. Quantum Electron. 31, 827 (1999).
[CrossRef]

Tartarini, G.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, Opt. Quantum Electron. 31, 827 (1999).
[CrossRef]

Thomas, E. L.

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

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

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]

Xu, Y.

Yariv, A.

Yeh, P.

Zepparelli, F.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, Opt. Quantum Electron. 31, 827 (1999).
[CrossRef]

IEEE Microwave Guided Wave Lett. (1)

C. M. Furse and O. P. Gandhi, IEEE Microwave Guided Wave Lett. 5, 326 (1995).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

S. D. Gedney, IEEE Trans. Antennas Propag. 44, 1630 (1996).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, Opt. Quantum Electron. 31, 827 (1999).
[CrossRef]

Science (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]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[CrossRef] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

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

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Figures (3)

Fig. 1
Fig. 1

(a) Cross section of a dielectric coaxial fiber. For the high-index cladding medium, we choose ncl1=4.6 and lcl1=1/3Λ, whereas for the low-index cladding medium ncl2=1.6 and lcl2=2/3Λ. Λ is the total thickness of the Bragg cladding pair. For the center core and the coaxial region, we choose nco=4.6 and lco=0.4Λ and ncoax=1 and lcoax=1.0Λ, respectively. (b) Cross section of a metallic coaxial cable.

Fig. 2
Fig. 2

(a) Dispersion of the coaxial fiber defined in the caption of Fig. 1. The shaded region indicate the existence of propagating TM cladding modes in the omnidirectional reflector. The thick solid curves are results obtained from asymptotic analysis. The filled circles represent the two-dimensional FDTD results. The center core of the coaxial fiber resembles a conventional optical fiber and supports three guided modes: HE, TE, and TM modes. Their dispersions are shown as dashed curves. The single-mode windows for the TM band are illustrated in the figure as two boxes. (b) Hz field distributions of the lower m=1 band at β=0.1532π/Λ and ω=0.1872πc/Λ. (c) Hz field distributions of the lower m=1 band at β=0.6112π/Λ and w=0.2292πc/Λ. In (b) and (c), the field distributions are normalized relative to the maximum Hz value. The scale bar indicates the relative values of the Hz fields in (b) and (c).

Fig. 3
Fig. 3

(a) Absolute value of dispersion parameter D of the coaxial fiber TM band. Wavelength λ is normalized such that the TM band crosses air light line β=ω/c at 1.55 µm. At λ=1.598 µm [or ω=0.2022πc/Λ], dispersion parameter D becomes zero, which is shown as the dashed line. The two single-mode windows in Fig. 2 are shown as shaded regions. To the left of the dashed line, D is negative, whereas D is positive to the left of the dashed line. (b) Dispersion parameter D within the vicinity of D=0. (c) Hθ field of the TM coaxial fiber mode at D=0. The unshaded, light, and dark regions represent air ncoax=1, the low-index dielectric medium ncl2=1.6, and the high-index dielectric medium ncl1=4.6, respectively.

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