Abstract

Experimental measurements of all-solid photonic bandgap fibres with an array of high-index rods in a low-index background revealed an unexpected variation of bend loss across different bandgaps. This behaviour was confirmed by calculations of photonic band structure, and explained with reference to the differing field distributions of the modes of the cladding rods. Our understanding was confirmed by further experiments, leading to proposals for the improvement of these fibres.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
  2. Y. Fink, D. J. Ripin, S. H. Fan, C. P. 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]
  3. 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]
  4. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, 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. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, F. Luan, and P. St. J. Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309-314 (2005).
    [CrossRef] [PubMed]
  8. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. St. J. Russell, "Guidance properties of low-contrast photonic bandgap fibres," Opt. Express 13, 2503-2511 (2005).
    [CrossRef] [PubMed]
  9. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay, "Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm," Opt. Express 13, 8452-8459 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  16. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. St. J. Russell, "Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibers," Opt. Express 12, 299-309 (2004).
    [CrossRef] [PubMed]
  17. G. J. Pearce, T. D. Hedley, and D. M. Bird, "Adaptive curvilinear coordinates in a plane-wave solution of Maxwell's equations in photonic crystals," Phys. Rev. B 71, 195108 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
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  24. P. Steinvurzel, E. D. Moore, E. C. Mägi, B. T. Kuhmley, and B. J. Eggleton, "Long period grating resonances in photonic bandgap fiber," Opt. Express 14, 3007-3014 (2006).
    [CrossRef] [PubMed]
  25. We would like to thank one of this paper's reviewers for bringing to our attention the applicability of our work to these other results.
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2006 (2)

2005 (5)

2004 (6)

2003 (3)

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

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Resonances in microstructured optical waveguides," Opt. Express 11, 1243-1251 (2003).
[CrossRef] [PubMed]

2002 (1)

1999 (2)

Y. Fink, D. J. Ripin, S. H. Fan, C. P. 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]

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]

1997 (1)

1989 (1)

J. D. Love, "Application of a low-loss criterion to optical waveguides and devices," IEE Proc. J 136, 225-228 (1989).

1979 (1)

W. A. Gambling, H. Matsumura, and C. M. Ragdale, "Curvature and microbending losses in single-mode optical fibres," Opt. Quantum Electron. 11, 43-59 (1979).
[CrossRef]

Allan, D. C.

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

Allen, D. C.

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]

Argyros, A.

Biancalana, F.

Bigot, L.

Bird, D. M.

Birks, T. A.

Bjarklev, A.

T. P. Handen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, "Air-guiding photonic bandgap fibers: spectral properties, macrobending loss, and practical handling," IEEE J. Lightwave Technol. 22, 11-15 (2004).
[CrossRef]

Borrelli, N. F.

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

Bouwmans, G.

Broeng, J.

T. P. Handen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, "Air-guiding photonic bandgap fibers: spectral properties, macrobending loss, and practical handling," IEEE J. Lightwave Technol. 22, 11-15 (2004).
[CrossRef]

Chen, C. P.

Y. Fink, D. J. Ripin, S. H. Fan, C. P. 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]

Cordeiro, C. M. B.

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. Allen, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

de Sterke, C. M.

Douay, M.

Dunn, S. C.

Eggleton, B. J.

Fan, S. H.

Y. Fink, D. J. Ripin, S. H. Fan, C. P. 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]

Fink, Y.

Y. Fink, D. J. Ripin, S. H. Fan, C. P. 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]

Folkenberg, J. R.

T. P. Handen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, "Air-guiding photonic bandgap fibers: spectral properties, macrobending loss, and practical handling," IEEE J. Lightwave Technol. 22, 11-15 (2004).
[CrossRef]

Gallagher, M. T.

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

Gambling, W. A.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, "Curvature and microbending losses in single-mode optical fibres," Opt. Quantum Electron. 11, 43-59 (1979).
[CrossRef]

George, A. K.

Handen, T. P.

T. P. Handen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, "Air-guiding photonic bandgap fibers: spectral properties, macrobending loss, and practical handling," IEEE J. Lightwave Technol. 22, 11-15 (2004).
[CrossRef]

Hedley, T. D.

Hu, J.

Jakobsen, C.

T. P. Handen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, "Air-guiding photonic bandgap fibers: spectral properties, macrobending loss, and practical handling," IEEE J. Lightwave Technol. 22, 11-15 (2004).
[CrossRef]

Joannopoulos, J. D.

Y. Fink, D. J. Ripin, S. H. Fan, C. P. 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]

Joly, N.

Knight, J. C.

Koch, K. W.

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

Kuhmley, B. T.

Lægsgaard, J.

J. Lægsgaard, "Gap formation and guided modes in photonic band gap fibres with high-index rods," J. Opt. A: Pure Appl. Opt. 6, 798-804 (2004).
[CrossRef]

Leon-Saval, S. G.

Litchinitser, N. M.

Lopez, F.

Love, J. D.

J. D. Love, "Application of a low-loss criterion to optical waveguides and devices," IEE Proc. J 136, 225-228 (1989).

Luan, F.

Mägi, E. C.

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. Allen, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Matsumura, H.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, "Curvature and microbending losses in single-mode optical fibres," Opt. Quantum Electron. 11, 43-59 (1979).
[CrossRef]

McPhedran, R. C.

Moore, E. D.

Muller, D.

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

Nielsen, M. D.

T. P. Handen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, "Air-guiding photonic bandgap fibers: spectral properties, macrobending loss, and practical handling," IEEE J. Lightwave Technol. 22, 11-15 (2004).
[CrossRef]

Pearce, G. J.

G. J. Pearce, T. D. Hedley, and D. M. Bird, "Adaptive curvilinear coordinates in a plane-wave solution of Maxwell's equations in photonic crystals," Phys. Rev. B 71, 195108 (2005).
[CrossRef]

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, P. and St. J. Russell, "All-solid photonic band gap fiber," Opt. Lett. 29, 2369-2371 (2004).
[CrossRef] [PubMed]

Pottage, J. M.

Provino, L.

Quiquempois, Y.

Ragdale, C. M.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, "Curvature and microbending losses in single-mode optical fibres," Opt. Quantum Electron. 11, 43-59 (1979).
[CrossRef]

Ripin, D. J.

Y. Fink, D. J. Ripin, S. H. Fan, C. P. 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]

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. Allen, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Russell, P. St. J.

Shum, P.

Simonsen, H. R.

T. P. Handen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, "Air-guiding photonic bandgap fibers: spectral properties, macrobending loss, and practical handling," IEEE J. Lightwave Technol. 22, 11-15 (2004).
[CrossRef]

Skovgaard, P. M. W.

T. P. Handen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, "Air-guiding photonic bandgap fibers: spectral properties, macrobending loss, and practical handling," IEEE J. Lightwave Technol. 22, 11-15 (2004).
[CrossRef]

Smith, C. M.

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

Steel, M. J.

Steinvurzel, P.

Thomas, E. L.

Y. Fink, D. J. Ripin, S. H. Fan, C. P. 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]

Usner, B.

Venkataraman, N.

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

Vienne, G.

T. P. Handen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, "Air-guiding photonic bandgap fibers: spectral properties, macrobending loss, and practical handling," IEEE J. Lightwave Technol. 22, 11-15 (2004).
[CrossRef]

Wadsworth, W. J.

Wang, A.

West, J. A.

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

White, T. P.

Yan, M.

IEE Proc. J (1)

J. D. Love, "Application of a low-loss criterion to optical waveguides and devices," IEE Proc. J 136, 225-228 (1989).

IEEE J. Lightwave Technol. (2)

Y. Fink, D. J. Ripin, S. H. Fan, C. P. 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]

T. P. Handen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, "Air-guiding photonic bandgap fibers: spectral properties, macrobending loss, and practical handling," IEEE J. Lightwave Technol. 22, 11-15 (2004).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

J. Lægsgaard, "Gap formation and guided modes in photonic band gap fibres with high-index rods," J. Opt. A: Pure Appl. Opt. 6, 798-804 (2004).
[CrossRef]

Nature (2)

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

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

Opt. Express (8)

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, F. Luan, and P. St. J. Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309-314 (2005).
[CrossRef] [PubMed]

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. St. J. Russell, "Guidance properties of low-contrast photonic bandgap fibres," Opt. Express 13, 2503-2511 (2005).
[CrossRef] [PubMed]

G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay, "Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm," Opt. Express 13, 8452-8459 (2005).
[CrossRef] [PubMed]

N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Resonances in microstructured optical waveguides," Opt. Express 11, 1243-1251 (2003).
[CrossRef] [PubMed]

P. Steinvurzel, B. T. Kuhmley, T. P. White, M. J. Steel, C. M. de Sterke, andd B. J. Eggleton, "Long-wavelength anti-resonant guidance in high index inclusion microstructured fibers," Opt. Express 12, 5424-5433 (2004).
[CrossRef] [PubMed]

W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. St. J. Russell, "Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibers," Opt. Express 12, 299-309 (2004).
[CrossRef] [PubMed]

T. A. Birks, D. M. Bird, T. D. Hedley, J. M. Pottage, and P. St. J. Russell, "Scaling laws and vector effects in bandgap-guiding fibres," Opt. Express 12, 69-74 (2004).
[CrossRef] [PubMed]

P. Steinvurzel, E. D. Moore, E. C. Mägi, B. T. Kuhmley, and B. J. Eggleton, "Long period grating resonances in photonic bandgap fiber," Opt. Express 14, 3007-3014 (2006).
[CrossRef] [PubMed]

Opt. Lett. (5)

Opt. Quantum Electron. (1)

W. A. Gambling, H. Matsumura, and C. M. Ragdale, "Curvature and microbending losses in single-mode optical fibres," Opt. Quantum Electron. 11, 43-59 (1979).
[CrossRef]

Phys. Rev. B (1)

G. J. Pearce, T. D. Hedley, and D. M. Bird, "Adaptive curvilinear coordinates in a plane-wave solution of Maxwell's equations in photonic crystals," Phys. Rev. B 71, 195108 (2005).
[CrossRef]

Science (1)

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 (4)

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, D. J. Trevor, "Tunable photonic band gap fiber," in Optical Fiber Communications Conference, Postconference edition, 70 of OSA Trends in Optics and Photonics Series Technical Digest (Optical Society of America, Washington D.C. 2002) pp. 466-468.

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

P. W. Barber, R. K. Chang, eds., Optical Effects Associated With Small Particles (World Scientific, 1988).

We would like to thank one of this paper's reviewers for bringing to our attention the applicability of our work to these other results.

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Figures (8)

Fig. 1.
Fig. 1.

SEM image of an all-solid silica bandgap fibre. The light-coloured regions are the Ge-doped raised-index rods. The fibre’s bandgap-guiding core is the site of a missing rod in the centre.

Fig. 2.
Fig. 2.

Transmission spectra (against frequency, with an auxiliary wavelength scale at the top) of 2 m of the fibre of Fig. 1 subject to different bend radii R. We observed transmission in bandgaps 3 to 7 (marked) in the straight fibre. At a bend radius of 15 cm there is dramatic loss in gaps 4 and 6 but little in gaps 3 and 5. When the bend radius is decreased to 7.5 cm some light is lost in all bandgaps, gap 3 being the least affected.

Fig. 3.
Fig. 3.

Calculated DOS for a triangular lattice of graded-index rods in a low-index background as described in Section 2. The axes are effective index n eff =β/k and normalised frequency kΛ, with the cutoff line n eff =n BG =1.458 marked. Red regions represent bandgaps (zero DOS) and are numbered in order of increasing kΛ. The grey-scale shading of non-zero DOS (low DOS in black, high DOS in white) highlights the continuity of features within and across bands. The yellow curve is the core line in bandgaps 3–6 for a core formed by the omission of one rod. The designations of the scalar rod modes from which the bands evolve are labelled in the form LP lm . Also defined are the downward and upward effective index mismatches Δn- and Δn+ between the core line and the bands, to aid the discussion in Section 4. Across each bandgap, Δn- is smaller than Δn+ except near the long-wavelength edge.

Fig. 4.
Fig. 4.

Schematic plots of effective index n eff against displacement r from the fibre axis along the radius of curvature. The index n fm of the fundamental core mode is marked in red. (top) A step-index fibre when (a) straight and (b) bent, where Δn is the mismatch between n fm and the cladding index n cl . A radiation caustic appears where n eff =n fm , at a distance from the axis proportional to Δn and the radius of curvature R. (bottom) The cladding bands of a bandgap fibre when (c) straight and (d) bent. Two radiation caustics appear, one on each side of the axis, again at distances proportional to R and the appropriate Δn. Bend loss is predominantly to the radiation caustic closer to the core, determined by whichever Δn is smaller.

Fig. 5.
Fig. 5.

Critical bend radius R c calculated from the data in Fig. 3 using Eq. (2) for gaps 3–6.

Fig. 6.
Fig. 6.

Calculated unnormalised intensity distributions |Ψ|2 at cutoff for the first four LP l2 modes of a step-index rod with radius ρ, showing the different rates of decay |Ψ|2~1/r 2l into the background. For l=0 and l=1 this integrates so that the fraction of the power in the core at cutoff is zero, but for higher values of l the field decays quickly enough for a non-zero fraction 1 - 1/l of the power to exist within the rod even at cutoff. The plot also illustrates how only l=0 modes have non-zero intensity in the centre of the rod. (The m=2 modes were chosen for this illustration because of their prominence in Fig. 3, and also because the LP01 mode has no cutoff.)

Fig. 7.
Fig. 7.

(upper) Images (on a logarithmic grey scale) of the light patterns in the cladding excited by bend loss, for the wavelengths near the bandgap edges indicated at the top. The plots show whether light is coupled to l=0 or l=1 rod modes by the bend, depending on whether the patterns have central peaks. (lower) Calculated patterns expected at the same wavelengths, together with the inferred LP designations of the rod modes from which the adjacent band of cladding states is formed.

Fig. 8.
Fig. 8.

Light patterns across the fibre after bending, for wavelengths near the blue (left) and red (right) edges of gap 5. The top of each image is towards the outside of the bend. Near the red edge of the bandgap, bend loss is towards the inside of the bend.

Equations (2)

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R c 8 π 2 k 2 ρ 3 n cl 2 W 3 ,
R c 4 π λ n BG 2 n fm 2 n edge 2 3 2 .

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