Abstract

We investigate the guidance properties of low-contrast photonic band gap fibres. As predicted by the antiresonant reflecting optical waveguide (ARROW) picture, band gaps were observed between wavelengths where modes of the high-index rods in the cladding are cutoff. At these wavelengths, leakage from the core by coupling to higher-order modes of the rods was observed directly. The low index contrast allowed for bend loss to be investigated; unlike in index-guiding fibres, anomalous “centripetal” light leakage through the inside of the bend can occur.

© 2005 Optical Society of America

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References

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    [CrossRef] [PubMed]
  4. T. T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. S. H. Anawati, J. Broeng, J. Li, S.-T. Wu, �??All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers,�?? Opt. Express 12, 5857-71, <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5857.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5857.</a>
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    [CrossRef]
  17. S. R. Rengarajan, �??On higher order mode cutoff frequencies in elliptical step index fibers,�?? IEEE Transaction on Microwave Theory and Techniques 37, 1244-8 (1989).
    [CrossRef]
  18. Cladding of fibres B and C: Corning Corguide, 50 µm core diameter, 125 µm outer diameter, NA = 0.21. This fibre had a double-cladding structure, which when drawn down becomes equivalent to a step index core with an NA of 0.18. Cladding of fibre D: Thorlabs GIF625: 62.5 µm core diameter, 125 µm outer diameter, graded index, NA = 0.275. Core of fibre B: Corning SMF 28, 9 µm core diameter, 125 µm outer diameter, NA = 0.14. A different single-mode fibre with a 3.5 µm core diameter, 125 µm outer diameter and NA = 0.11 was used in the core of fibres C and D.
  19. M.-S. Chung, C.-M. Kim, �??Analysis of optical fibers with graded index profile by a combination of modified Airy functions and WKB solutions,�?? J. Lightwave Tech. 17, 2534-41 (1999).
    [CrossRef]
  20. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, 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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299."</a>
    [CrossRef] [PubMed]

Appl. Opt.

IEEE J. Lightwave Tech.

N. A. Issa, L. Poladian, �??Vector wave expansion method for leaky modes of microstructured fibers,�?? IEEE J. Lightwave Tech. 21, 1005-12 (2003)
[CrossRef]

IEEE J. Quant. Electron.

M. Heiblum, J. H. Harris, �??Analysis of curved optical waveguides by conformal transformation,�?? IEEE J. Quant. Electron. 11, 75-83 (1975).
[CrossRef]

IEEE Trans. on Microwave Theory and Tech

S. R. Rengarajan, �??On higher order mode cutoff frequencies in elliptical step index fibers,�?? IEEE Transaction on Microwave Theory and Techniques 37, 1244-8 (1989).
[CrossRef]

J. Lightwave Tech.

H. F. Taylor, �??Bending effects in optical fibers,�?? J. Lightwave Tech. 2, 617-28 (1984).
[CrossRef]

M.-S. Chung, C.-M. Kim, �??Analysis of optical fibers with graded index profile by a combination of modified Airy functions and WKB solutions,�?? J. Lightwave Tech. 17, 2534-41 (1999).
[CrossRef]

Opt. Commun.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, D. J. Richardson, �??Understanding bend losses in holey optical fibers,�?? Opt. Commun. 227, 317-335 (2003).
[CrossRef]

Opt. Express

N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, C. M. de Sterke, �??Resonances in microstructured optical waveguides,�?? Opt. Express 11, 1243-51 (2003) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1243.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1243.</a>
[CrossRef] [PubMed]

W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, 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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299."</a>
[CrossRef] [PubMed]

P. Steinvurzel, B. T. Kuhmley, T. P. White, M. J. Steel, C. M. de Sterke, B. J. Eggleton, �??Long-wavelength anti-resonant guidance in high index inclusion microstructured fibers,�?? Opt. Express 12, 5424-33, <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5424.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5424."</a>
[PubMed]

T. T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. S. H. Anawati, J. Broeng, J. Li, S.-T. Wu, �??All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers,�?? Opt. Express 12, 5857-71, <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5857.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5857.</a>
[PubMed]

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, F. Luan, P. St.J. Russell, �??Photonic bandgap with an index step of one percent,�?? Opt. Express 13, 309-14 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-309.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-309.</a>
[CrossRef] [PubMed]

Opt. Lett.

Pure Appl. Opt.

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

Science

P.St.J. Russell, �??Photonic crystal fibers,�?? Science 299, 69-74 (2004).

R. F. Cregan, B. J. Managan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, D. C. Allen, �??Single-mode photonic band gap guidance of light in air,�?? Science 285, 1537-9 (1999).
[CrossRef] [PubMed]

Other

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

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton University Press, 1995).

Cladding of fibres B and C: Corning Corguide, 50 µm core diameter, 125 µm outer diameter, NA = 0.21. This fibre had a double-cladding structure, which when drawn down becomes equivalent to a step index core with an NA of 0.18. Cladding of fibre D: Thorlabs GIF625: 62.5 µm core diameter, 125 µm outer diameter, graded index, NA = 0.275. Core of fibre B: Corning SMF 28, 9 µm core diameter, 125 µm outer diameter, NA = 0.14. A different single-mode fibre with a 3.5 µm core diameter, 125 µm outer diameter and NA = 0.11 was used in the core of fibres C and D.

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Figures (6)

Fig. 1.
Fig. 1.

(a) A typical bandgap fibre cross-section, a schematic of an elliptical rod, and calculated intensity distributions of some modes of a rod. For elliptical rods, some modes split into odd/even versions about the minor axis. The modes are shown in the correct order for small deviations from circularity (b/a > 0.6). (b) The calculated confinement loss for a bandgap fibre with n r=1.465, n m=1.45 (1% index contrast), d/Λ=0.4 and circular rods, for different numbers of rings of rods around the 7-cell core. The cutoffs of modes of the rods are indicated. (c) and (d) The calculated confinement loss for the same fibre with 5 rings but for elliptical rods with b/a=0.8 and 0.6.

Fig. 2.
Fig. 2.

Scanning electron micrographs of samples of fibres (left to right) B, C and D. Elliptical deformations are clearly seen in C and D. The black regions in C and D are (random) air bubbles that, apart from possibly contributing to the loss, did not appear to affect the guidance properties of the fibres.

Fig. 3.
Fig. 3.

(a) Transmission in the first two bandgaps of fibre B (Λ=7.5 µm, length 0.15 m) for illumination of the core alone. Insets are filtered images of the fibre endface for wide illumination. (b) Transmission in the first 4 bandgaps of a sample of fibre C (Λ=10 µm, length 0.4 m). Insets are modes excited in the rods by focusing light into the core at the high-loss wavelengths for a sample of fibre C. (c) Transmission of fibre D (Λ=6 µm, length 0.4 m). Insets show the two modes supported by the core (LP01 and oLP11) at λ=1064 nm. The high-order mode cutoffs are indicated, corresponding to high-loss wavelengths. Spectra have been normalised to give 0 dB transmission in the first bandgap.

Fig. 4.
Fig. 4.

(a) Cutback loss measurement on 15 m of a sample of fibre C with Λ=5 µm. Inset: typical near-field image of the fundamental mode in the first bandgap. (b) Normalised transmission of fibre C tapered from Λ=11.5 to 6.6 µm over 2.0 m to give a transmission window of 50 nm FWHM. For comparison, the transmission windows of uniform sections with Λ=6.6 and 11.5 µm were approximately 300 and 600 nm wide respectively.

Fig. 5.
Fig. 5.

(a) Schematic index profile of straight and bent step-index fibres. The red line is the core mode’s n eff and is resonant with radiation modes in the cladding only on the outside of the bend. (b) A calculated plot of the n eff of the first two bands of a bandgap fibre, with the low-index line in red. (The core mode line will be only slightly below the low-index line, the exact trajectory being dependent on the size of the core.) (c) Schematic variation of the band n eff across a slightly bent bandgap fibre, for wavelengths at (left to right) the blue edge, middle and red edge of the bandgap.

Fig. 6.
Fig. 6.

(a) Transmission spectra of a bandgap fibre for different bend radii. (b) Average loss as a function of bend radius for wavelength ranges at both edges and the middle of the bandgap, 600–700 nm corresponding to the blue edge, 770–980 nm to the middle and 1100–1270 nm to the red edge.

Equations (3)

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V = 2 π N A r λ ,
N A = ( n r 2 n m 2 ) 1 2 .
n ( x ) = n o ( x ) [ 1 + ( 1 χ ) x R ] ,

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