Abstract

We demonstrate by numerical simulation that the general features of the loss spectrum of photonic crystal fibres (PCF) with a kagome structure can be explained by simple models consisting of thin concentric hexagons or rings of glass in air. These easily analysed models provide increased understanding of the mechanism of guidance in kagome PCF, and suggest ways in which the high-loss resonances in the loss spectrum may be shifted.

© 2007 Optical Society of America

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  1. P. St. J. Russell, "Photonic-crystal fibers," J. Lightwave Technol. 24, 4729-4749 (2006).
    [CrossRef]
  2. R. F. Cregan, B. F. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
    [CrossRef] [PubMed]
  3. 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 bandgap fibre," Nature 424, 657-659 (2003).
    [CrossRef] [PubMed]
  4. 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.
  5. F. Couny, F. Benabid, and P. S. Light, "Large-pitch kagome-structured hollow-core photonic crystal fiber," Opt. Lett. 31, 3574-3576 (2006).
    [CrossRef] [PubMed]
  6. A. Argyros and J. Pla, "Hollow-core polymer fibres with a kagome lattice: potential for transmission in the infrared," Opt. Express 15, 7713-7719 (2007).
    [CrossRef] [PubMed]
  7. T. D. Hedley, D. M. Bird, F. Benabid, J. C. Knight, P. St. J. Russell, "Modelling of a novel hollow-core photonic crystal fibre," paper QTuL4 in Proc. QELS, Baltimore MA (June 1-6, 2003)
  8. J. M. Pottage, D. M. Bird, T. D. Hedley, T. A. Birks, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Robust photonic band gaps for hollow core guidance in PCF made from high index glass," Opt. Express 11, 2854-2861 (2003).
    [CrossRef] [PubMed]
  9. T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, "Bend loss in all-solid bandgap fibres," Opt. Express 14, 5688-5698 (2006).
    [CrossRef] [PubMed]
  10. M. Koshiba and Y. Tsuji, "Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems," J. Lightwave Technol. 18, 737-743 (2000).
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  11. A. Nicolet, S. Guenneau, C. Geuzaine, and F. Zolla, "Modelling of electromagnetic waves in periodic media with finite elements," J. Comput. Appl. Math. 168, 321-329 (2004).
    [CrossRef]
  12. F. L. Teixeira, and W. C. Chew, "General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media," IEEE Microw. Guid. Wave Lett. 8, 223-225 (1998).
    [CrossRef]
  13. 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]
  14. L. Zschiedrich, S. Burger, R. Klose, A. Schädle, and F. Schmidt, "JCMmode: an adaptive finite element solver for the computation of leaky modes," Proc. SPIE 5728, 192-202 (2005).
    [CrossRef]
  15. P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, W. J. Wadsworth, T. A. Birks, J. C. Knight, and P. St. J. Russell "Realizing low loss air core photonic crystal fibers by exploiting an antiresonant core surround," Opt. Express 13, 8277-8285 (2005).
    [CrossRef] [PubMed]

2007 (1)

2006 (3)

2005 (2)

2004 (1)

A. Nicolet, S. Guenneau, C. Geuzaine, and F. Zolla, "Modelling of electromagnetic waves in periodic media with finite elements," J. Comput. Appl. Math. 168, 321-329 (2004).
[CrossRef]

2003 (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 bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

J. M. Pottage, D. M. Bird, T. D. Hedley, T. A. Birks, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Robust photonic band gaps for hollow core guidance in PCF made from high index glass," Opt. Express 11, 2854-2861 (2003).
[CrossRef] [PubMed]

2001 (1)

2000 (1)

1999 (1)

R. F. Cregan, B. F. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

1998 (1)

F. L. Teixeira, and W. C. Chew, "General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media," IEEE Microw. Guid. Wave Lett. 8, 223-225 (1998).
[CrossRef]

Allan, D. C.

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 bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

R. F. Cregan, B. F. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Argyros, A.

Benabid, F.

Bird, D. M.

Birks, T. A.

Borrelli, N. F.

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 bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Burger, S.

L. Zschiedrich, S. Burger, R. Klose, A. Schädle, and F. Schmidt, "JCMmode: an adaptive finite element solver for the computation of leaky modes," Proc. SPIE 5728, 192-202 (2005).
[CrossRef]

Chew, W. C.

F. L. Teixeira, and W. C. Chew, "General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media," IEEE Microw. Guid. Wave Lett. 8, 223-225 (1998).
[CrossRef]

Couny, F.

Cregan, R. F.

R. F. Cregan, B. F. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Engeness, T. D.

Fink, Y.

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 bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Geuzaine, C.

A. Nicolet, S. Guenneau, C. Geuzaine, and F. Zolla, "Modelling of electromagnetic waves in periodic media with finite elements," J. Comput. Appl. Math. 168, 321-329 (2004).
[CrossRef]

Guenneau, S.

A. Nicolet, S. Guenneau, C. Geuzaine, and F. Zolla, "Modelling of electromagnetic waves in periodic media with finite elements," J. Comput. Appl. Math. 168, 321-329 (2004).
[CrossRef]

Hedley, T. D.

Ibanescu, M.

Jacobs, S. A.

Joannopoulos, J. D.

Johnson, S. G.

Klose, R.

L. Zschiedrich, S. Burger, R. Klose, A. Schädle, and F. Schmidt, "JCMmode: an adaptive finite element solver for the computation of leaky modes," Proc. SPIE 5728, 192-202 (2005).
[CrossRef]

Knight, J. C.

Koch, K. W.

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 bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Koshiba, M.

Light, P. S.

Luan, F.

Mangan, B. F.

R. F. Cregan, B. F. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Mangan, B. J.

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 bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Nicolet, A.

A. Nicolet, S. Guenneau, C. Geuzaine, and F. Zolla, "Modelling of electromagnetic waves in periodic media with finite elements," J. Comput. Appl. Math. 168, 321-329 (2004).
[CrossRef]

Pearce, G. J.

Pla, J.

Pottage, J. M.

Roberts, P. J.

Russell, P. St. J.

Sabert, H.

Schädle, A.

L. Zschiedrich, S. Burger, R. Klose, A. Schädle, and F. Schmidt, "JCMmode: an adaptive finite element solver for the computation of leaky modes," Proc. SPIE 5728, 192-202 (2005).
[CrossRef]

Schmidt, F.

L. Zschiedrich, S. Burger, R. Klose, A. Schädle, and F. Schmidt, "JCMmode: an adaptive finite element solver for the computation of leaky modes," Proc. SPIE 5728, 192-202 (2005).
[CrossRef]

Skorobogatiy, M.

Smith, C. M.

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 bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Soljacic, M.

Teixeira, F. L.

F. L. Teixeira, and W. C. Chew, "General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media," IEEE Microw. Guid. Wave Lett. 8, 223-225 (1998).
[CrossRef]

Tsuji, Y.

Venkataraman, N.

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 bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Wadsworth, W. J.

Wang, A.

Weisberg, O.

West, J. A.

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 bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Williams, D. P.

Zolla, F.

A. Nicolet, S. Guenneau, C. Geuzaine, and F. Zolla, "Modelling of electromagnetic waves in periodic media with finite elements," J. Comput. Appl. Math. 168, 321-329 (2004).
[CrossRef]

Zschiedrich, L.

L. Zschiedrich, S. Burger, R. Klose, A. Schädle, and F. Schmidt, "JCMmode: an adaptive finite element solver for the computation of leaky modes," Proc. SPIE 5728, 192-202 (2005).
[CrossRef]

IEEE Microw. Guid. Wave Lett. (1)

F. L. Teixeira, and W. C. Chew, "General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media," IEEE Microw. Guid. Wave Lett. 8, 223-225 (1998).
[CrossRef]

J. Comput. Appl. Math. (1)

A. Nicolet, S. Guenneau, C. Geuzaine, and F. Zolla, "Modelling of electromagnetic waves in periodic media with finite elements," J. Comput. Appl. Math. 168, 321-329 (2004).
[CrossRef]

J. Lightwave Technol. (2)

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 bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (1)

Proc. SPIE (1)

L. Zschiedrich, S. Burger, R. Klose, A. Schädle, and F. Schmidt, "JCMmode: an adaptive finite element solver for the computation of leaky modes," Proc. SPIE 5728, 192-202 (2005).
[CrossRef]

Science (1)

R. F. Cregan, B. F. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Other (2)

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.

T. D. Hedley, D. M. Bird, F. Benabid, J. C. Knight, P. St. J. Russell, "Modelling of a novel hollow-core photonic crystal fibre," paper QTuL4 in Proc. QELS, Baltimore MA (June 1-6, 2003)

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Figures (5)

Fig. 1.
Fig. 1.

(a). Periodic kagome lattice as described in Sec. 1, where black areas represent silica and white areas represent air. b) Density of states (DOS) for the periodic kagome structure corresponding to normalized frequencies in the range k 0Λ=44-148. White regions show high DOS and darker areas show lower DOS, but the density of states is non-zero throughout. The solid horizontal line is the air line, the dashed near-vertical line is an example strut mode, and the dotted horizontal line is a mode associated with the large hexagonal air holes of the structure.

Fig. 2.
Fig. 2.

(a). A ‘full’ kagome structure, with single cell core. The hexagons shown in (b) are highlighted in black. (b) The hexagonal approximation to the full kagome structure, obtained by retaining struts that contribute to concentric hexagons around the core but omitting all others. (c) The circular approximation to the hexagonal structure, formed of concentric circles that conserve the perimeter of each hexagon (thereby conserving the amount of glass). In (b) and (c) only the core and first four cladding rings are shown.

Fig. 3.
Fig. 3.

Losses in dB/m for the fundamental mode of the ring (lines) and hexagon (points) models, with structures as shown in Fig. 2. Note the close agreement between the losses of the ring and hexagon models.

Fig. 4.
Fig. 4.

Two-layer kagome structure used for modal calculations. Grey areas represent glass and white areas represent air. The dimensions are identical to those described in Sec. 2. In order to approximate real kagome fibres as closely as possible, the sharp edges in the structure are rounded with a radius of curvature of 0.2 μm.

Fig. 5.
Fig. 5.

Loss of the fundamental mode of the two- and four-layer kagome structures, together with that of the one- and two-ring models for comparison. Note the existence of high-loss resonances in the spectra for both the model and the realistic structures.

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