Abstract

Scaling laws for photonic bandgaps in photonic crystal fibres are described. Although only strictly valid for small refractive index contrast, they successfully identify corresponding features in structures with large index contrast. Furthermore, deviations from the scaling laws distinguish features that are vector phenomena unique to electromagnetic waves from those that would be expected for generic scalar waves.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. T. A. Birks, P. J. Roberts, P. St.J. Russell, D. M. Atkin, T. J. Shepherd, "Full 2D photonic band gaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
    [CrossRef]
  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-dielectric structure," IEEE J. Lightwave Technol. 17, 2039-2041 (1999).
    [CrossRef]
  4. F. Brechet, P. Roy, J. Marcou and D. Pagnoux, "Singlemode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths," Electron. Lett. 36, 514-515 (2000).
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  5. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allen and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton and D. J. Trevor, "Tunable photonic band gap fiber," Proc. Optical Fiber Communication Conference (2002) pp. 466-468.
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  11. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).
  12. J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals (Princeton University Press, 1995), pp. 19-20.
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    [CrossRef]

CLEO 2003

J. Riishede, J. Broeng and A. Bjarklev, "All silica photonic bandgap fiber," Proc. Conference on Lasers and Electro-Optics (2003), paper CTuC5.

Electron. Lett.

T. A. Birks, P. J. Roberts, P. St.J. Russell, D. M. Atkin, T. J. Shepherd, "Full 2D photonic band gaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

F. Brechet, P. Roy, J. Marcou and D. Pagnoux, "Singlemode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths," Electron. Lett. 36, 514-515 (2000).
[CrossRef]

IEEE J. Lightwave Technol.

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," IEEE J. Lightwave Technol. 17, 2039-2041 (1999).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

J. Riishede, N. A. Mortensen and J. Laegsgaard, "A 'poor man's approach' to modelling micro-structured optical fibres," J. Opt. A: Pure Appl. Opt. 5, 534-538 (2003).
[CrossRef]

Nature

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allen and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

OFC 2002

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton and D. J. Trevor, "Tunable photonic band gap fiber," Proc. Optical Fiber Communication Conference (2002) pp. 466-468.

Opt. Express

Opt. Lett.

Phys. Rev. E

P. R. Villeneuve and M. Piché, "Photonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. E 46, 4946-4972 (1992).

Science

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, P. J. Roberts and D. C. Allen, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Other

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals (Princeton University Press, 1995), pp. 19-20.

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagram illustrating our new way of mapping the states of a photonic crystal, on normalised axes v 2 (or v) against w 2. Propagation is forbidden in the regions coloured red.

Fig. 2.
Fig. 2.

Plots of DOS on normalised axes for d/Λ=(a) 0.96 and (b) 0.80, and for n=(i) 1.02 and (ii) 1.45 (the “scalar” and “vector” cases respectively). Regions with no propagating states (DOS≡0) are coloured red for emphasis. These correspond to cutoff (bottom right, β>kneff ), evanescent states (bottom left, β2<0) and bandgaps (elsewhere). The arrows on the top edge locate the resonances of the circular low-index regions, whose loci would be vertical lines on these plots.

Fig. 3.
Fig. 3.

Plots of DOS on the low-index line as index contrast n is varied, for d/Λ=(a) 0.96 and (b) 0.80. The colour map for DOS is the same as that in Fig. 2. The shrinking bandgap around v=12 in (a) is the fundamental bandgap used in current air-guiding silica PCFs. The growing bandgap around v=12 in (b) is the robust type II bandgap of [13].

Equations (7)

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

k t 1 k t 2 = k 2 n 1 2 β 2 k 2 n 2 2 β 2
( t 2 + k 2 n 0 2 β 2 ) h = ( t × h ) × ( t ln n 0 2 ) ,
f ( X , Y ) = { 0 low index regions 1 high index regions ,
T 2 Ψ + ( v 2 f w 2 ) Ψ = 0 ,
v 2 = Λ 2 k 2 ( n 1 2 n 2 2 ) .
w 2 = Λ 2 ( β 2 k 2 n 2 2 )
w 2 = ( 2 j l m d Λ ) 2 ,

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