Abstract

We show through computer simulations that the thin silica ring that surrounds the air core of a photonic-bandgap fiber introduces surface modes. The intensity profile and dispersion of these modes indicate that they are the modes of the waveguide formed by the ring surrounded by air on one side and the photonic crystal cladding on the other. The ring also induces small perturbations of the fundamental core mode. Coupling to those surface modes, which have propagation constants close to that of the core mode, are likely to induce substantial loss to the core mode. By reducing the thickness of the ring and/or by suitably selecting its radius the propagation constants of the surface modes can be moved farther from that of the core mode and the loss reduced.

© 2004 Optical Society of America

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References

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  1. D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
    [Crossref]
  2. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band-gap fibre,” Nature 424, 657–659 (2003).
    [Crossref] [PubMed]
  3. B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.
  4. T. P. Hansen, J. Broeng, C. Jakobson, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Spectral Properties, Macrobending loss, and practical handling,” IEEE J. Lightwave Technol. . 22, 11–15 (2004).
    [Crossref]
  5. H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. of Quant. Electron. 40, 551–556 (2004).
    [Crossref]
  6. M. J. F. Digonnet, H. K. Kim, J. Shin, S. Fan, and G. S. Kino, “Simple geometric criterion to predict the existence of surface modes in air-core photonic-bandgap fibers,” Opt. Express 12, 1864–1872 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1864
    [Crossref] [PubMed]
  7. J. A. West, C. M. Smith, N. F. Borrelli, D. C.. Allen, and K. W. Koch, “Surface modes in air-core photonic band-gap fibers,” Opt. Express 12, 1485–1496 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485
    [Crossref] [PubMed]
  8. F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of position of the surface plane,” Phy. Rev. B 59, p.15112 (1999).
    [Crossref]
  9. Crystal Fibre’ Air-core fiber AIR-10-1550, http://www.crystal-fibre.com
  10. Blaze Photonics’ air-core fiber HC=1500-02, http://www.blazephotonics.com.
  11. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in planewave basis,” Opt. Express 8, 173–190 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
    [Crossref] [PubMed]
  12. K. Saito, N. A. Mortensen, and M. Koshiba, “Air-core photonic band-gap fibers: the impact of surface modes,” Opt. Express 12, 394–400 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394.
    [Crossref]

2004 (5)

2003 (2)

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
[Crossref]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band-gap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

2001 (1)

1999 (1)

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of position of the surface plane,” Phy. Rev. B 59, p.15112 (1999).
[Crossref]

Allan, D. C.

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
[Crossref]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band-gap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

Allen, D. C..

Bjarklev, A.

T. P. Hansen, J. Broeng, C. Jakobson, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Spectral Properties, Macrobending loss, and practical handling,” IEEE J. Lightwave Technol. . 22, 11–15 (2004).
[Crossref]

Borrelli, N. F.

J. A. West, C. M. Smith, N. F. Borrelli, D. C.. Allen, and K. W. Koch, “Surface modes in air-core photonic band-gap fibers,” Opt. Express 12, 1485–1496 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485
[Crossref] [PubMed]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band-gap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
[Crossref]

Broeng, J.

T. P. Hansen, J. Broeng, C. Jakobson, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Spectral Properties, Macrobending loss, and practical handling,” IEEE J. Lightwave Technol. . 22, 11–15 (2004).
[Crossref]

County, F.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

Coupland, S.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

Digonnet, M. J. F.

Fan, S.

Farr, L.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

Flea, R.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

Folkenberg, J. R.

T. P. Hansen, J. Broeng, C. Jakobson, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “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. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band-gap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
[Crossref]

Halevi, P.

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of position of the surface plane,” Phy. Rev. B 59, p.15112 (1999).
[Crossref]

Hansen, T. P.

T. P. Hansen, J. Broeng, C. Jakobson, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Spectral Properties, Macrobending loss, and practical handling,” IEEE J. Lightwave Technol. . 22, 11–15 (2004).
[Crossref]

Jakobson, C.

T. P. Hansen, J. Broeng, C. Jakobson, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Spectral Properties, Macrobending loss, and practical handling,” IEEE J. Lightwave Technol. . 22, 11–15 (2004).
[Crossref]

Joannopoulos, J. D.

Johnson, S. G.

Kim, H. K.

Kino, G. S.

Koch, K. W.

J. A. West, C. M. Smith, N. F. Borrelli, D. C.. Allen, and K. W. Koch, “Surface modes in air-core photonic band-gap fibers,” Opt. Express 12, 1485–1496 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485
[Crossref] [PubMed]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band-gap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
[Crossref]

Koshiba, M.

Langford, A.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

Lawman, M.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

Mangan, B. J.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

Mason, M.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

Mortensen, N. A.

Müller, D.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band-gap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
[Crossref]

Nielsen, M. D.

T. P. Hansen, J. Broeng, C. Jakobson, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Spectral Properties, Macrobending loss, and practical handling,” IEEE J. Lightwave Technol. . 22, 11–15 (2004).
[Crossref]

Ramos-Mendieta, F.

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of position of the surface plane,” Phy. Rev. B 59, p.15112 (1999).
[Crossref]

Roberts, P. J.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

Sabert, H.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

Saito, K.

Shin, J.

Simonsen, H. R.

T. P. Hansen, J. Broeng, C. Jakobson, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Spectral Properties, Macrobending loss, and practical handling,” IEEE J. Lightwave Technol. . 22, 11–15 (2004).
[Crossref]

Skovgaard, P. M. W.

T. P. Hansen, J. Broeng, C. Jakobson, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Spectral Properties, Macrobending loss, and practical handling,” IEEE J. Lightwave Technol. . 22, 11–15 (2004).
[Crossref]

Smith, C. M.

J. A. West, C. M. Smith, N. F. Borrelli, D. C.. Allen, and K. W. Koch, “Surface modes in air-core photonic band-gap fibers,” Opt. Express 12, 1485–1496 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485
[Crossref] [PubMed]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band-gap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
[Crossref]

Venkataraman, N.

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
[Crossref]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band-gap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

Vienne, G.

T. P. Hansen, J. Broeng, C. Jakobson, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Spectral Properties, Macrobending loss, and practical handling,” IEEE J. Lightwave Technol. . 22, 11–15 (2004).
[Crossref]

West, J. A.

J. A. West, C. M. Smith, N. F. Borrelli, D. C.. Allen, and K. W. Koch, “Surface modes in air-core photonic band-gap fibers,” Opt. Express 12, 1485–1496 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485
[Crossref] [PubMed]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band-gap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
[Crossref]

Williams, D. P.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

Zhang, Peihong

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
[Crossref]

IEEE J. Lightwave Technol. (1)

T. P. Hansen, J. Broeng, C. Jakobson, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Spectral Properties, Macrobending loss, and practical handling,” IEEE J. Lightwave Technol. . 22, 11–15 (2004).
[Crossref]

IEEE J. of Quant. Electron. (1)

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. of Quant. Electron. 40, 551–556 (2004).
[Crossref]

Nature (1)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band-gap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

Opt. Express (4)

Phy. Rev. B (1)

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of position of the surface plane,” Phy. Rev. B 59, p.15112 (1999).
[Crossref]

Proc. of SPIE (1)

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, Peihong Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers,” Proc. of SPIE 5000, 161–174 (2003).
[Crossref]

Other (3)

Crystal Fibre’ Air-core fiber AIR-10-1550, http://www.crystal-fibre.com

Blaze Photonics’ air-core fiber HC=1500-02, http://www.blazephotonics.com.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, and H. Sabert, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” Conf. on Optical Fiber Communications, (LA, USA, 2004), paper PDP24.

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Figures (9)

Fig. 1.
Fig. 1.

(a) Cross-section of an air-core photonic-bandgap fiber with a core radius such (R=0.9Λ) that the core does not support surface modes, and (b) same fiber with a thin silica ring around the core.

Fig. 2.
Fig. 2.

(a) Cross-section of a generic preform for an air-core photonic-bandgap fiber, consisting of a stack of silica tubes with the seven center tubes removed to form the fiber’s air-core, and (b) photograph of a fiber drawn from such a preform.

Fig. 3.
Fig. 3.

Calculated ω-k diagram of the air-core fiber of (a) Fig. 1(a) (no ring), and (b) Fig. 1(b) (ring present).

Fig. 4.
Fig. 4.

Intensity contour lines of the fundamental core mode of (a) the fiber of Fig. 1(a) (no ring), and (b) the fiber of Fig. 1(b) (ring present), both calculated at kzΛ/2π=1.7. The relative intensity on the contours varies from 0.1 to 0.9 in increments of 0.1.

Fig. 5.
Fig. 5.

Intensity contour lines of two exemplary surface modes of the fiber of Fig. 1(b) (ring around the core).

Fig. 6.
Fig. 6.

(a) Cross-section of an air-core photonic-bandgap fiber with a core radius such (R=1.13Λ) that the core supports surface modes, and (b) same fiber with a thin silica ring around the core.

Fig. 7.
Fig. 7.

Calculated ω-k diagram of the air-core fiber of (a) Fig. 6(a) (no ring), and (b) Fig. 6(b) (ring present).

Fig. 8.
Fig. 8.

Dispersion curves of core modes and surface modes, and intensity profiles of four exemplary surface modes simulated with the simplified air-core fiber geometry in references 7 and 12.

Fig. 9.
Fig. 9.

Photonic crystal terminated by a thin slab used to model very thin PBF core ring.

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