Abstract

We propose a simple analytical theory for low-index core photonic bandgap optical waveguides based on an antiresonant reflecting guidance mechanism. We identify a new regime of guidance in which the spectral properties of these structures are largely determined by the thickness of the high-index layers and the refractive-index contrast and are not particularly sensitive to the period of the cladding layers. The attenuation properties are controlled by the number of high/low-index cladding layers. Numerical simulations with the beam propagation method confirm the predictions of the analytical model. We discuss the implications of the results for photonic bandgap fibers.

© 2002 Optical Society of America

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References

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  1. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  2. M. Ibanescu, Y. Fink, S. Fran, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
    [CrossRef] [PubMed]
  3. 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]
  4. B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T. A. Strasser, Opt. Lett. 24, 1460 (1999).
    [CrossRef]
  5. M. A. Duduay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, Appl. Phys. Lett. 49, 13 (1986).
    [CrossRef]
  6. P. Yeh, A. Yariv, and E. Marom, J. Opt. Soc. Am. 68, 1196 (1978).
  7. R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, in Optical Fiber Communications Conference (OFC2002) (to be published).
  8. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, San Diego, Calif., 1991).
  9. E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
    [CrossRef]

2000 (1)

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

1999 (2)

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]

B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T. A. Strasser, Opt. Lett. 24, 1460 (1999).
[CrossRef]

1986 (1)

M. A. Duduay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, Appl. Phys. Lett. 49, 13 (1986).
[CrossRef]

1978 (1)

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[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]

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]

Bise, R. T.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, in Optical Fiber Communications Conference (OFC2002) (to be published).

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]

Duduay, M. A.

M. A. Duduay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, Appl. Phys. Lett. 49, 13 (1986).
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T. A. Strasser, Opt. Lett. 24, 1460 (1999).
[CrossRef]

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, in Optical Fiber Communications Conference (OFC2002) (to be published).

Fink, Y.

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

Fran, S.

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

Ibanescu, M.

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

Joannopoulos, J. D.

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

Kerbage, C.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, in Optical Fiber Communications Conference (OFC2002) (to be published).

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]

Koch, T. L.

M. A. Duduay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, Appl. Phys. Lett. 49, 13 (1986).
[CrossRef]

Kokubun, Y.

M. A. Duduay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, Appl. Phys. Lett. 49, 13 (1986).
[CrossRef]

Kranz, K. S.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, in Optical Fiber Communications Conference (OFC2002) (to be published).

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]

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, San Diego, Calif., 1991).

Marom, E.

Pfeiffer, L.

M. A. Duduay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, Appl. Phys. Lett. 49, 13 (1986).
[CrossRef]

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]

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]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Spalter, S.

Strasser, T. A.

Thomas, E. L.

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

Trevor, D. J.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, in Optical Fiber Communications Conference (OFC2002) (to be published).

Westbrook, P. S.

Windeler, R. S.

B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T. A. Strasser, Opt. Lett. 24, 1460 (1999).
[CrossRef]

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, in Optical Fiber Communications Conference (OFC2002) (to be published).

Yariv, A.

P. Yeh, A. Yariv, and E. Marom, J. Opt. Soc. Am. 68, 1196 (1978).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

P. Yeh, A. Yariv, and E. Marom, J. Opt. Soc. Am. 68, 1196 (1978).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Appl. Phys. Lett. (1)

M. A. Duduay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, Appl. Phys. Lett. 49, 13 (1986).
[CrossRef]

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Science (2)

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

Other (3)

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, in Optical Fiber Communications Conference (OFC2002) (to be published).

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, San Diego, Calif., 1991).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

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Figures (4)

Fig. 1
Fig. 1

Schematics of (a) a 1D ARROW structure, (b), its 2D equivalent, and (c) a microstructured optical fiber.

Fig. 2
Fig. 2

Calculated transmission spectra for 1D 10-layer structures over the ranges (a) 0.615 µm and (b) 0.61 µm. Insets, fundamental mode profiles for three different wavelengths. The straight lines in (b) correspond to analytical predictions from Eq. (1), and the curves with open circles correspond to a one-layer structure.

Fig. 3
Fig. 3

Schematics of (a) a hollow waveguide, (b) a one-layer ARROW structure, and (c) a two-layer ARROW structure.

Fig. 4
Fig. 4

Schematic of (top) the ARROW structure and (bottom) its transmission spectrum.

Equations (4)

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

λm=2n1dmn2/n12-11/2,  m=1,2,.
λl=4n1d2l+1n2/n12-11/2,  l=0,1,2,.
b=2l+1a2,  l=0,1,2,.
λ/d>2n22-n12,

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