Abstract

Fresnel fibres with silica zones resembling omnidirectional structures with self-imaging properties are proposed. Numerical simulation is carried out on a large air hole Fresnel fibre with a triadic Cantor fractal zone cross-section (FZC). The results show the transmission bandgap of these fibres widens and the practical confinement loss decreases with increasing orders of self-imaging. For an order of S = 4 a bandwidth ∆λ = 0.69 μm and a confinement loss of 0.11 dB/km @ 1.1 μm is calculated.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2007 (1)

2005 (1)

2004 (2)

2003 (5)

2002 (2)

J. Canning, "Diffraction-free mode generation and propagation in optical waveguides," Opt. Commun. 207, 35-39 (2002).
[CrossRef]

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, "External reflection from omnidirectional dielectric mirror fibers," Science 296, 511-513 (2002).
[CrossRef]

2001 (1)

S. V. Khukhlevsky, "Optical waveguide fields as free space waves," Europhys. Lett. 54, 461 (2001).
[CrossRef]

1998 (4)

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

A. D. Jaggard and D. L. Jaggard, "Cantor ring diffractals," Opt. Commun. 158, 141-148 (1998).
[CrossRef]

D. L. Jaggard and A. D. Jaggard, "Cantor ring arrays," Microwave Opt. Technol. Lett. 19, 121-125 (1998).
[CrossRef]

A. D. Jaggard and D. L. Jagaard, "Scattering from fractal superlattices with variable lacunarity," J. Opt. Soc. Am. A. 15, 1626-1635 (1998).
[CrossRef]

1987 (1)

J. Durnin, J. J. MiceliJr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

1979 (1)

M. V. Berry, "Diffractals," J. Phys. A 12, 781-797 (1979).
[CrossRef]

Berry, M. V.

M. V. Berry, "Diffractals," J. Phys. A 12, 781-797 (1979).
[CrossRef]

Bjarklev, A.

Broeng, J.

Buckley, E.

Canning, J.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Deyerl, H. J.

Digweed-Lyytikäinen, K.

Durnin, J.

J. Durnin, J. J. MiceliJr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. MiceliJr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Fan, S.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Fink, Y.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, "External reflection from omnidirectional dielectric mirror fibers," Science 296, 511-513 (2002).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Folkenberg, J. R.

Furlan, W. D.

Ganguly, S.

D. H. Werner and S. Ganguly, "An overview of fractal antenna engineering research," IEEE Antenn. Propag. Mag. 45, 38-57 (2003).
[CrossRef]

Gibson, B. C.

Hansen, T.

Hansen, T. P.

Hart, S. D.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, "External reflection from omnidirectional dielectric mirror fibers," Science 296, 511-513 (2002).
[CrossRef]

Hisatomi, M.

Huang, Y.

Huntington, S. T.

Issa, N. A.

Jagaard, D. L.

A. D. Jaggard and D. L. Jagaard, "Scattering from fractal superlattices with variable lacunarity," J. Opt. Soc. Am. A. 15, 1626-1635 (1998).
[CrossRef]

Jaggard, A. D.

A. D. Jaggard and D. L. Jagaard, "Scattering from fractal superlattices with variable lacunarity," J. Opt. Soc. Am. A. 15, 1626-1635 (1998).
[CrossRef]

D. L. Jaggard and A. D. Jaggard, "Cantor ring arrays," Microwave Opt. Technol. Lett. 19, 121-125 (1998).
[CrossRef]

A. D. Jaggard and D. L. Jaggard, "Cantor ring diffractals," Opt. Commun. 158, 141-148 (1998).
[CrossRef]

Jaggard, D. L.

A. D. Jaggard and D. L. Jaggard, "Cantor ring diffractals," Opt. Commun. 158, 141-148 (1998).
[CrossRef]

D. L. Jaggard and A. D. Jaggard, "Cantor ring arrays," Microwave Opt. Technol. Lett. 19, 121-125 (1998).
[CrossRef]

Jakobsen, C.

Jensen, J.

Joannopoulos, J. D.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, "External reflection from omnidirectional dielectric mirror fibers," Science 296, 511-513 (2002).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Khukhlevsky, S. V.

S. V. Khukhlevsky, "Optical waveguide fields as free space waves," Europhys. Lett. 54, 461 (2001).
[CrossRef]

Lee, R.

Love, J. D.

Lyytikainen, K.

Maskaly, G. R.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, "External reflection from omnidirectional dielectric mirror fibers," Science 296, 511-513 (2002).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. MiceliJr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Michel, J.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Monsoriu, J. A.

Mortensen, N.

Nielsen, M. D.

Parker, M. C.

Poladian, L.

Prideaux, P. H.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, "External reflection from omnidirectional dielectric mirror fibers," Science 296, 511-513 (2002).
[CrossRef]

Saavedra, G.

Simonsen, H.

Simonsen, H. R.

Skovgaard, P. M. W.

Sorensen, T.

Steblina, V.

Temelkuran, B.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, "External reflection from omnidirectional dielectric mirror fibers," Science 296, 511-513 (2002).
[CrossRef]

Terrel, M.

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Vienne, G.

Walker, S. D.

Werner, D. H.

D. H. Werner and S. Ganguly, "An overview of fractal antenna engineering research," IEEE Antenn. Propag. Mag. 45, 38-57 (2003).
[CrossRef]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Xu, Y.

Yariv, A.

Europhys. Lett. (1)

S. V. Khukhlevsky, "Optical waveguide fields as free space waves," Europhys. Lett. 54, 461 (2001).
[CrossRef]

IEEE Antenn. Propag. Mag. (1)

D. H. Werner and S. Ganguly, "An overview of fractal antenna engineering research," IEEE Antenn. Propag. Mag. 45, 38-57 (2003).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. A. (1)

A. D. Jaggard and D. L. Jagaard, "Scattering from fractal superlattices with variable lacunarity," J. Opt. Soc. Am. A. 15, 1626-1635 (1998).
[CrossRef]

J. Phys. A (1)

M. V. Berry, "Diffractals," J. Phys. A 12, 781-797 (1979).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

D. L. Jaggard and A. D. Jaggard, "Cantor ring arrays," Microwave Opt. Technol. Lett. 19, 121-125 (1998).
[CrossRef]

Opt. Commun. (2)

A. D. Jaggard and D. L. Jaggard, "Cantor ring diffractals," Opt. Commun. 158, 141-148 (1998).
[CrossRef]

J. Canning, "Diffraction-free mode generation and propagation in optical waveguides," Opt. Commun. 207, 35-39 (2002).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

J. Durnin, J. J. MiceliJr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Science (2)

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, "External reflection from omnidirectional dielectric mirror fibers," Science 296, 511-513 (2002).
[CrossRef]

Other (6)

B. B. Mandelbrot, Fractal Geometry of Nature (San Fransisco, California: Freeman - 1983).

C. Martelli and J. Canning, "Fresnel fibres for sensing," in: 18th International Conference on Optical Fiber Sensors, 2006, Cancún. Postdeadline Papers Proceedings of OFS-18, (2006).

J. Ojeda-Castenada and C. Gomez-Reino, Selected Papers on Zone Plates; (SPIE Milestone Series 1996), Vol. MS 128

M. W. Takeda, S. Kirihara, Y. Miyamoto, K. Sakoda, and K. Honda, "Localization of electromagnetic waves in three-dimensional fractal cavities," Phys. Rev. Lett. 92, 093902-1 - 093902-4 (2004).

V. Kochergin, Omnidirectional Optical Filters (Boston: Kluwer Academic Publishers, 2003).

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibers (Kluwer Academic Publishers, Dordrecht, 2003).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Generation of Cantor bar with five stages of growth (S).

Fig. 2
Fig. 2

The cross-section of a Fresnel fibre with triadic Cantor fractal zones at different exponent orders representing increasing stages in the evolution of the fractal.

Fig. 3.
Fig. 3.

Confinement loss of the fundamental-like mode for Fresnel fibres with Cantor fractal zones at different orders of evolution stages.

Fig. 4.
Fig. 4.

Modal field profile of the lowest order air guided mode for the Fresnel fibres with fractal zones cross sections.

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