Abstract

We propose a simple geometric criterion based on the size of the core relative to the photonic crystal to quickly determine whether an air-core photonic-bandgap fiber with a given geometry supports surface modes. Comparison to computer simulations show that when applied to fibers with a triangular-pattern cladding and a circular air core, this criterion accurately predicts the existence of a finite number of discrete ranges of core radii that support no surface modes. This valuable tool obviates the need for time-consuming and costly simulations, and it can be easily applied to fibers with an arbitrary photonic-crystal structure and core profile.

© 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 Vol. 5000, pp. 161-174 (2003).
    [CrossRef]
  2. D. Müller, D. C. Allan, N. F. Borrelli, K. T. Gahagan, M. T. Gallagher, C. M. Smith, N. Venkataraman, and K. W. Koch, �??Measurement of photonic band-gap fiber transmission from 1.0 to 3.0 µm and impact of surface mode coupling,�?? Conf. on Lasers and Electro-Optics, Baltimore, USA, June 2003, paper QtuL2, (2003).
  3. 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," to appear in IEEE J. of Quantum Electronics (May 2004).
  4. K. Saito, N. A. Mortensen, and M. Koshiba, "Air-core photonic band-gap fibers: the impact of surface modes," Opt. Express Vol. 12, No. 3, 394-400 (Feb. 2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394.</a>
    [CrossRef]
  5. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borreill, D. C. Allan, K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature Vol. 424, No. 6949, pp. 657-659 (2003).
    [CrossRef]
  6. F. Ramos-Mendieta and P. Halevi, �??Surface electromagnetic waves in two-dimensional photonic crystals: effect of position of the surface plane,�?? Phy. Rev. B Vol. 59, p. 15112 (1999).
    [CrossRef]
  7. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the flow of light, (Princeton U. Press, Princeton, N.J, 1995), pp. 73-76.
  8. A. Yariv, and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation, (John Wiley & Sons, New York, 1984), p. 210.
  9. S. G. Johnson, and J. D. Joannopoulos, �??Block-iterative frequency-domain methods for Maxwell's equations in planewave basis,�?? Opt. Expr. Vol. 8, No. 3, pp. 173-190 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.">http://www.opticsexpress.org/abstract. cfm?URI=OPEX-8-3-173.</a>
    [CrossRef]

CLEO 2003 (1)

D. Müller, D. C. Allan, N. F. Borrelli, K. T. Gahagan, M. T. Gallagher, C. M. Smith, N. Venkataraman, and K. W. Koch, �??Measurement of photonic band-gap fiber transmission from 1.0 to 3.0 µm and impact of surface mode coupling,�?? Conf. on Lasers and Electro-Optics, Baltimore, USA, June 2003, paper QtuL2, (2003).

Nature (1)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borreill, D. C. Allan, K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature Vol. 424, No. 6949, pp. 657-659 (2003).
[CrossRef]

Opt. Expr. (1)

S. G. Johnson, and J. D. Joannopoulos, �??Block-iterative frequency-domain methods for Maxwell's equations in planewave basis,�?? Opt. Expr. Vol. 8, No. 3, pp. 173-190 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.">http://www.opticsexpress.org/abstract. cfm?URI=OPEX-8-3-173.</a>
[CrossRef]

Opt. Express (1)

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 Vol. 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 Vol. 5000, pp. 161-174 (2003).
[CrossRef]

Other (3)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the flow of light, (Princeton U. Press, Princeton, N.J, 1995), pp. 73-76.

A. Yariv, and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation, (John Wiley & Sons, New York, 1984), p. 210.

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," to appear in IEEE J. of Quantum Electronics (May 2004).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Example of a surface mode calculated for a triangular-pattern PBF with an air hole radius ρ = 0.47Λ and a core radius of 1.15 Λ, and (b) the highest frequency bulk mode of the same fiber in the absence of core. Both were calculated at kz Λ/2π= 1.7.

Fig. 2.
Fig. 2.

Example of a circular core (a) that intersects corners of the photonic-crystal cladding (surface modes expected), and (b) that intersects only membranes of the photonic crystal (no surface modes expected).

Fig. 3.
Fig. 3.

Schematic of the rod (small black circle) inscribed within a corner of a photonic-crystal cladding (larger open circles), drawn for ρ = 0.47Λ.

Fig. 4.
Fig. 4.

The gray regions represent the ranges of core radii that intersect rods, and thus support surface modes, and the white regions between them the surface-mode-free bands. See text for details.

Fig. 5.
Fig. 5.

Dependence of the number of surface modes on core radius predicted by numerical simulations (dashed curves with triangles) and by the proposed geometric criterion (solid curve).

Fig. 6.
Fig. 6.

Evolution of the surface-mode-free bands with increasing hole radius predicted by the geometric criterion.

Tables (1)

Tables Icon

Table 1. Location of the 14 bands of core radii that support no surface modes in triangular PBFs with ρ = 0.47Λ (see text for details).

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