Abstract

Dispersion of the fundamental confined modes in hollow-core all-silica Bragg fibers with nanosupports is analyzed. The transfer-matrix formalism is applied. Anomalies in the group-velocity dispersion are evidenced at long wavelengths, toward the upper limit of the bandgap. The results confirm that, as in microstructured photonic crystal fibers, this anomalous dispersion is due to prevention of the confined hollow-core modes from crossing the surface modes, the avoided crossings are more apparent in the variation of group velocity with wavelength. The dependence of these avoided crossings on the hollow-core radius and the layer thicknesses is briefly analyzed.

© 2006 Optical Society of America

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References

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2004 (5)

2003 (1)

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608 (2003).
[Crossref]

2002 (1)

2001 (1)

1978 (1)

Albin, S.

Argyros, A.

Bassett, I. M.

Bjarklev, A.

Broeng, J.

Deyerl, H. J.

Engeness, T. D.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001).
[Crossref] [PubMed]

Fink, Y.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001).
[Crossref] [PubMed]

Guo, S.

Hansen, T. P.

Hoekstra, H. J. W. M.

Huang, Y.

Ibanescu, M.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001).
[Crossref] [PubMed]

Jacobs, S. A.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001).
[Crossref] [PubMed]

Jakobsen, C.

Jensen, J. B.

Joannopoulos, J. D.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001).
[Crossref] [PubMed]

Johnson, S. G.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001).
[Crossref] [PubMed]

Koshiba, M.

Large, M. C. J.

Lee, R. K.

Marom, E.

Mortensen, N. A.

Ouyang, G.

Rogowski, R. S.

Saitoh, K.

Simonsen, H.

Skorobogatiy, M.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001).
[Crossref] [PubMed]

Soljacic, M.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001).
[Crossref] [PubMed]

Sorensen, T.

Terrel, M.

Uranus, H. P.

van Eijkelenborg, M. A.

Vienne, G.

Weisberg, O.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608 (2003).
[Crossref]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001).
[Crossref] [PubMed]

Xu, Y.

Yariv, A.

Yeh, P.

J. Opt. Soc. Am. (1)

Opt. Express (7)

Phys. Rev. E (1)

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, "Analysis of mode structure in hollow dielectric waveguide fibers," Phys. Rev. E 67, 046608 (2003).
[Crossref]

Other (1)

CVI Laser Corporation,Optics and Coatings Catalog (CVI Laser Corporation, Albuquerque, N.M. 87192, 1994)

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Figures (10)

Fig. 1
Fig. 1

Cross section of a hollow-core Bragg fiber with three concentric cylindrical silica layers separated by nanoscale silica support bridges.[4] The outer, middle, and inner air layers contain 46, 35, and 24 evenly distributed nanoscale supports, respectively. The outermost thicker cladding region is also of silica. All the silica regions are shown in black.

Fig. 2
Fig. 2

(a) Mode-index plot, (b) vg c plot, and (c) GVD plot for the fundamental hollow-core modes HE11, TE01, and TM01 in fiber sample OD90 with R = 10 μm. The dashed lines in (a) denote the bandgap borders in the planar limit.

Fig. 3
Fig. 3

Mode-index plot showing the allowed TE (×) and TM (•) polarized modes with m = 0 and the allowed modes of mixed polarization (+) with m = 1 on a narrow interval toward higher wavelengths. The respective fundamental modes are also represented: TE01 (□), TM01 (◊), and HE11 (○). As guide to the eye, the points of the surface modes are joined by dotted lines. The small region delimited from 1.78 to 1.82 μm is detailed in Fig. 4.

Fig. 4
Fig. 4

(a) Mode-index plot of the allowed TE- (×) and TM- (•) polarized modes with m = 0 on the very narrow interval of wavelengths indicated in Fig. 3(a). The respective fundamental modes are also represented: TE01 (□) and TM01 (◊). (b) vg c plot of the respective fundamental modes. The dotted line in (a) indicates the wavelength (λ = 1.783 μm) at which the field amplitudes of the fundamental modes are shown in Fig. 5. The TM field amplitudes at points 1, 2, and 3 that are marked in (a) by asterisks are shown also in Fig. 6.

Fig. 5
Fig. 5

(a) Amplitude variation versus radial distance r for components H z (solid curve) and E ϕ (dashed curve) of fundamental mode TE01 at λ = 1.783 μm. (b) The same as in (a) but for components Ez (solid curve) and H ϕ (dashed curve) of fundamental mode TM01. The amplitudes are normalized to their maxima. Silica and air layers are indicated by vertical lines.

Fig. 6
Fig. 6

Amplitude variation versus radial distance for components Ez (solid curves) and H ϕ (dashed curves) of the TM-polarized mode in (a) point 1: λ = 1.7893 μm, n eff = 0.992964107; (b) point 2: λ = 1.7893 μm, n eff = 0.9945349945; and (c) point 3: λ = 1.791 μm, n eff = 0.9930786953. Points 1, 2, and 3 are marked by asterisks in Fig. 4(a). The amplitudes are normalized to their maxima. Silica and air layers are indicated by vertical lines.

Fig. 7
Fig. 7

(a) Mode-index plot showing the allowed modes of mixed polarization with m = 1 (+) and the respective fundamental mode HE11 (○) in fiber sample OD90 with R = 10 μm. (b) vg c plot of fundamental mode HE11; (c), (d) the same as in (a) and (b) but with R = 15 μm. The small region delimited in (a) from 1.8 to 1.86 μm is detailed in Fig. 8.

Fig. 8
Fig. 8

(a) Detail showing the allowed modes of mixed polarization with m = 1 (+) and the respective fundamental mode HE11 (○) at the very narrow interval of wavelengths indicated in Fig. 7(a). (b) vg c plot of fundamental mode HE11.

Fig. 9
Fig. 9

vg c of fundamental mode HE11 in hollow-core all-silica Bragg fibers with periodic claddings of different layer thicknesses but the same thickness for (a) the silica ring, (b) the air layer, and (c) the period. The respective pairs of layer thicknesses, expressed in micrometers, are shown.

Fig. 10
Fig. 10

Mode-index plots showing the allowed modes of mixed polarization with m = 1 for the same pairs of layer thicknesses as in Fig. 9. The points of the surface-mode doublets are joined by dotted lines.

Equations (7)

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[ E z H φ H z E φ ] = [ J m ( k j r ) Y m ( k j r ) 0 0 i ω ε j k j J m ( k j r ) i ω ε j k j Y m ( k j r ) m β k j     2 r J m ( k j r ) m β k j     2 r Y m ( k j r ) 0 0 J m ( k j r ) Y m ( k j r ) m β k j     2 r J m ( k j r ) m β k j     2 r Y m ( k j r ) i ω μ j k j J m ( k j r ) i ω μ j k j Y m ( k j r ) ] [ A B C D ] ,
[ M 21 M 23 M 41 M 43 ] [ A N C N ] = 0 ,
det [ M 21 M 23 M 41 M 43 ] = 0 ,
| M 11 M 13 M 21 / M 23 | 1   or
| M 31 M 41 M 33 / M 43 | 1.
v g / c = 1 / ( n e f f λ d n e ff / ) ,
GVD = ( λ / c ) d 2 n e f f / d λ 2 .

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