Abstract

Recent developments in polymer microstructured optical fibres allow for the realisation of microstructures in fibres that would be problematic to fabricate using glass-based capillary stacking. We present one class of such structures, where the holes lie on circular rings. A fibre of this type is fabricated and shown to be single moded for relatively long lengths of fibre, whereas shorter lengths are multimoded. An average index model for these fibres is developed. Comparison of its predictions to the calculated properties of the exact structure indicates that the ring structures emulate homogeneous rings of lower refractive index resulting in the ring structured fibres behaving approximately as cylindrically layered fibres.

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References

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  1. T.A. Birks, J.C. Knight, P.St.J. Russell, "Endlessly single-mode photonic crystal fibre," Opt. Lett. 22, 961-963 (1997).
    [CrossRef] [PubMed]
  2. H. Kubota, K. Suzuki, S. Kawanishi, M. Kakazawa, M. Tanaka, M. Fujita, "Low-loss, 2 km-long photonic crystal fibre with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band," Postdeadline paper CPD3, Conference on Lasers and Electro-Optics CLEO 2001, (Optical Society of America, Washington, D.C., 2001)
  3. E. Silvestre, M.V. Andres, P. Andres, "Biorthonormal-basis method for the vector description of optical fiber modes," J. Lightwave Technol 16, 923-928 (1998).
    [CrossRef]
  4. D. Mogilevtsev, T.A. Birks, P.St.J. Russell, "Localised function method for modelling defect modes in 2-D photonic crystals," J. Lightwave Technol. 17, 2078-2081 (2000).
    [CrossRef]
  5. T.M. Monro, D.J. Richardson, N.G.R. Broderick, P.J. Bennett, "Holey optical fibres: an efficient modal model," J. Lightwave Technol. 17, 1093-1102 (1999).
    [CrossRef]
  6. T.P. White, R.C. McPhedran, C.M. de Sterke, L.C. Botten, M.J. Steel, "Confinement losses in microstructured optical fibres," Opt. Lett. 26, 1660-1662 (2001).
    [CrossRef]
  7. M.A. van Eijkelenborg, M.C.J. Large, A. Argyros, J. Zagari, S.Manos, N. Issa, I. Bassett, S. Fleming, R.C. McPhedran, C.M. de Sterke, N.A.P. Nicorovici, "Microstructured polymer optical fibre," Opt. Express 9, 319-327 (2001), http://www.opticsexpress.org/oearchive/source/35051.htm.
    [CrossRef] [PubMed]
  8. J. Xu, J. Song, C Li, K. Ueda, "Cylindrically symmetric hollow fiber," Opt. Commun. 182, 343-348 (2000).
    [CrossRef]
  9. P. Yeh, A. Yariv, E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am. 68, 1196-1201 (1978).
    [CrossRef]
  10. Y. Fink, D.J. Ripin, S. Fan, C. Chen, J.D. Joannopoulos, E.L. Thomas, "Guiding optical light in air using an all-dielectric structure," J. Lightwave Technol. 17, 2039-2041(1999).
    [CrossRef]
  11. F. Brechet, P. Roy, J. Marcou, D. Pagnoux, "Singlemode propagation into depressed-core-index photonicbandgap fibre designed for zero dispersion at short wavelengths," Electron. Lett. 36, 514-515 (2000)
    [CrossRef]
  12. M. Ibanescu, Y. Fink, S. Fan, E.L. Thomas, J.D. Joannopoulos, "An all-dielectric coaxial waveguide," Science 289, 415-419 (2000)
    [CrossRef] [PubMed]
  13. G.W. Milton, The theory of composites, (Cambridge University Press, London, 2001).
  14. W.C. Chew, Waves and fields in inhomogeneous media, Chapter 3 (Van Nostrand Reinhold, New York 1990).

Other

T.A. Birks, J.C. Knight, P.St.J. Russell, "Endlessly single-mode photonic crystal fibre," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

H. Kubota, K. Suzuki, S. Kawanishi, M. Kakazawa, M. Tanaka, M. Fujita, "Low-loss, 2 km-long photonic crystal fibre with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band," Postdeadline paper CPD3, Conference on Lasers and Electro-Optics CLEO 2001, (Optical Society of America, Washington, D.C., 2001)

E. Silvestre, M.V. Andres, P. Andres, "Biorthonormal-basis method for the vector description of optical fiber modes," J. Lightwave Technol 16, 923-928 (1998).
[CrossRef]

D. Mogilevtsev, T.A. Birks, P.St.J. Russell, "Localised function method for modelling defect modes in 2-D photonic crystals," J. Lightwave Technol. 17, 2078-2081 (2000).
[CrossRef]

T.M. Monro, D.J. Richardson, N.G.R. Broderick, P.J. Bennett, "Holey optical fibres: an efficient modal model," J. Lightwave Technol. 17, 1093-1102 (1999).
[CrossRef]

T.P. White, R.C. McPhedran, C.M. de Sterke, L.C. Botten, M.J. Steel, "Confinement losses in microstructured optical fibres," Opt. Lett. 26, 1660-1662 (2001).
[CrossRef]

M.A. van Eijkelenborg, M.C.J. Large, A. Argyros, J. Zagari, S.Manos, N. Issa, I. Bassett, S. Fleming, R.C. McPhedran, C.M. de Sterke, N.A.P. Nicorovici, "Microstructured polymer optical fibre," Opt. Express 9, 319-327 (2001), http://www.opticsexpress.org/oearchive/source/35051.htm.
[CrossRef] [PubMed]

J. Xu, J. Song, C Li, K. Ueda, "Cylindrically symmetric hollow fiber," Opt. Commun. 182, 343-348 (2000).
[CrossRef]

P. Yeh, A. Yariv, E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am. 68, 1196-1201 (1978).
[CrossRef]

Y. Fink, D.J. Ripin, S. Fan, C. Chen, J.D. Joannopoulos, E.L. Thomas, "Guiding optical light in air using an all-dielectric structure," J. Lightwave Technol. 17, 2039-2041(1999).
[CrossRef]

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

M. Ibanescu, Y. Fink, S. Fan, E.L. Thomas, J.D. Joannopoulos, "An all-dielectric coaxial waveguide," Science 289, 415-419 (2000)
[CrossRef] [PubMed]

G.W. Milton, The theory of composites, (Cambridge University Press, London, 2001).

W.C. Chew, Waves and fields in inhomogeneous media, Chapter 3 (Van Nostrand Reinhold, New York 1990).

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Figures (4)

Fig. 1.
Fig. 1.

Optical micrograph of the cross section of the preform neck-down region. The image width corresponds to approximately 1.5 mm. Several ring structured sections can be seen with different sized holes. The structure on which the optical experiments were conducted and which was modelled is that in the lower left corner with the larger holes.

Fig. 2.
Fig. 2.

Electron micrograph of a cross section of the microstructured polymer optical fibre.

Fig. 3.
Fig. 3.

(a) A circular ring of holes is expected to behave like a circular layer of lower refractive index (b), the corresponding refractive index profile is shown in (c). Several equally spaced rings of holes of equal air-filling fraction will result in an index profile such as that shown in (d), i.e. a Bragg fibre.

Figure 4.
Figure 4.

The average index profile calculated for the structure described in the text. The averaging method used was to take the arithmetic mean of the refractive index over 360° for fixed values of the radius. This gives a value for the average between the two limits of Eq. (1). The average index profile is constructed out of 40 layers.

Tables (1)

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Table 1. Mode class and effective indices of the first five modes as calculated by the multipole method and the average index model, using the arithmetic mean of the refractive index.

Equations (2)

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( f n inc 2 + 1 f n matrix 2 ) 1 2 n av fn inc 2 + ( 1 f ) n matrix 2 .
n av = fn inc + ( 1 f ) n matrix ,

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