Abstract

We analyze the guiding problem in a realistic photonic crystal fiber, using a novel full-vector modal technique. This is a biorthogonal modal method based on the non-self-adjoint character of the electromagnetic propagation in a fiber. Dispersion curves of guided modes for different fiber structural paremeters are calculated, along with the two-dimensional transverse intensity distribution of the fundamental mode. Our results match those achieved in recent experiments in which the feasibility of this type of fiber was shown.

© 1999 Optical Society of America

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References

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  1. E. Yablonovitch, J. Opt. Soc. Am. B 10, 283 (1993).
    [CrossRef]
  2. P. St. J. Russell, T. A. Birks, and F. D. Lloyd-Lucas, in Confined Electrons and Photons, E. Burstein and C. Weisbuch, eds. (Plenum, New York, 1995), p. 585.
    [CrossRef]
  3. S. John, Phys. Rev. Lett. 58, 2486 (1987)E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
    [CrossRef] [PubMed]
  4. R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, Phys. Rev. B 48, 8434 (1993)J. N. Winn, R. D. Meade, and J. D. Joannopoulos, J. Mod. Opt. 41, 257 (1994).
    [CrossRef]
  5. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, Opt. Lett. 21, 1547 (1996)Opt. Lett. 22, 484 (1997).
    [CrossRef] [PubMed]
  6. T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
    [CrossRef] [PubMed]
  7. J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, J. Opt. Soc. Am. A 15, 748 (1998).
    [CrossRef]
  8. E. Silvestre, M. V. Andrés, and P. Andrés, J. Lightwave Technol. 16, 923 (1998).
    [CrossRef]
  9. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 595–606.

1998 (2)

1997 (1)

1996 (1)

1993 (2)

E. Yablonovitch, J. Opt. Soc. Am. B 10, 283 (1993).
[CrossRef]

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, Phys. Rev. B 48, 8434 (1993)J. N. Winn, R. D. Meade, and J. D. Joannopoulos, J. Mod. Opt. 41, 257 (1994).
[CrossRef]

1987 (1)

S. John, Phys. Rev. Lett. 58, 2486 (1987)E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Alerhand, O. L.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, Phys. Rev. B 48, 8434 (1993)J. N. Winn, R. D. Meade, and J. D. Joannopoulos, J. Mod. Opt. 41, 257 (1994).
[CrossRef]

Andrés, M. V.

Andrés, P.

Atkin, D. M.

Birks, T. A.

Brommer, K. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, Phys. Rev. B 48, 8434 (1993)J. N. Winn, R. D. Meade, and J. D. Joannopoulos, J. Mod. Opt. 41, 257 (1994).
[CrossRef]

de Sandro, J. P.

Joannopoulos, J. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, Phys. Rev. B 48, 8434 (1993)J. N. Winn, R. D. Meade, and J. D. Joannopoulos, J. Mod. Opt. 41, 257 (1994).
[CrossRef]

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987)E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Knight, J. C.

Lloyd-Lucas, F. D.

P. St. J. Russell, T. A. Birks, and F. D. Lloyd-Lucas, in Confined Electrons and Photons, E. Burstein and C. Weisbuch, eds. (Plenum, New York, 1995), p. 585.
[CrossRef]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 595–606.

Meade, R. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, Phys. Rev. B 48, 8434 (1993)J. N. Winn, R. D. Meade, and J. D. Joannopoulos, J. Mod. Opt. 41, 257 (1994).
[CrossRef]

Rappe, A. M.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, Phys. Rev. B 48, 8434 (1993)J. N. Winn, R. D. Meade, and J. D. Joannopoulos, J. Mod. Opt. 41, 257 (1994).
[CrossRef]

Silvestre, E.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 595–606.

St. J. Russell, P.

Yablonovitch, E.

J. Lightwave Technol. (1)

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

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

Opt. Lett. (2)

Phys. Rev. B (1)

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, Phys. Rev. B 48, 8434 (1993)J. N. Winn, R. D. Meade, and J. D. Joannopoulos, J. Mod. Opt. 41, 257 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

S. John, Phys. Rev. Lett. 58, 2486 (1987)E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Other (2)

P. St. J. Russell, T. A. Birks, and F. D. Lloyd-Lucas, in Confined Electrons and Photons, E. Burstein and C. Weisbuch, eds. (Plenum, New York, 1995), p. 585.
[CrossRef]

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 595–606.

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Figures (3)

Fig. 1
Fig. 1

Modal dispersion curves extending from λ=300 nm to λ=1600 nm for a single-mode photonic crystal fiber structure with a=0.3 μm and Λ=2.3 μm. Here the variations of the mode index for both polarizations coalesce in a single curve.

Fig. 2
Fig. 2

Transverse intensity distribution for the x-polarized guided mode of the photonic crystal fiber described in Fig.  1 for λ=632.8 nm.

Fig. 3
Fig. 3

Same as in Fig.  1 but with a=0.6 μm. Here the two higher-order polarization doublets are slightly shifted.

Equations (2)

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Lht=β2ht,Le¯t=β*2e¯t,
Lαγ2+k2n2δαγ-ϵαηηn2n2ϵγζζ,α,γ,ζ,η=x,y,

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