Abstract

The waveguiding properties of two silica-based, air-guiding photonic bandgap fiber designs are investigated with special emphasis on material effects. The nonlinear coefficients are found to be 1–2 orders of magnitude smaller than those obtained in index-guiding microstructured fibers with large mode areas. The material dispersion of silica makes a significant contribution to the total chromatic dispersion even though less than 10% of the field energy is located in the silica regions of the fibers. These findings suggest that dispersion engineering through the choice of base material may be a possibility in this type of fiber.

© 2003 Optical Society of America

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References

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  1. R. F. Cregan, B. J. 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]
  2. F. Benabid, J. C. Knight, and P. St. J. Russell, “Particle levitation and guidance in hollow-core photonic crystal fiber,” Opt. Express 10, 1195–1203 (2002).
    [Crossref] [PubMed]
  3. G. Ouyang, Y. Xu, and A. Yariv, “Theoretical study on dispersion compensation in air-core Bragg fibers,” Opt. Express 10, 899–908 (2002).
    [Crossref] [PubMed]
  4. F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2003).
    [Crossref]
  5. N. Venkataraman, M. T. Gallagher, C. M. Smith, D. Müller, J. A. West, K. W. Koch, and J. C. Fajardo, “Low loss (13 db/km) air core photonic bandgap fiber,” 28th European Conference on Optical Communication, ECOC ’02 (Technical University of Denmark, Kongens Lyngby, Denmark, 2002), post-deadline paper PD1.1.
  6. J. Broeng, S. E. Barkou, T. Søndergaard, and A. Bjarklev, “Analysis of air-guiding photonic bandgap fibers,” Opt. Lett. 25, 96–98 (2000).
    [Crossref]
  7. T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. Martijn de Sterke, “Calculations of air-guided modes in photonic crystal fibers using the multipole method,” Opt. Express 9, 721–732 (2001).
    [Crossref] [PubMed]
  8. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [Crossref] [PubMed]
  9. J. Lægsgaard, A. Bjarklev, and S. E. Barkou Libori, “Chromatic dispersion in photonic crystal fibers: fast and accurate scheme for calculation,” J. Opt. Soc. Am. B 20, 1–6 (2003).
    [Crossref]
  10. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).
  11. J. Lægsgaard, N. A. Mortensen, and A. Bjarklev, “Mode areas and field energy distribution in honeycomb photonic bandgap fibers,” J. Opt. Soc. Am. B 20, 2037–2045 (2003).
    [Crossref]
  12. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).
  13. S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of photonic bandgap guiding fibers,” in Optical Fiber Communication Conference, (OFC) (1999) (Optical Society of America, Washington, D.C., 1999), pp. 117–119.
  14. K. Okamoto, Fundamentals of Optical Waveguides (Academic, San Diego, Calif., 2000).
  15. N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Express 10, 341–348 (2002).
    [Crossref] [PubMed]

2003 (3)

2002 (3)

2001 (2)

2000 (1)

1999 (1)

R. F. Cregan, B. J. 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]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).

Allan, D. C.

R. F. Cregan, B. J. 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]

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2003).
[Crossref]

Barkou, S. E.

J. Broeng, S. E. Barkou, T. Søndergaard, and A. Bjarklev, “Analysis of air-guiding photonic bandgap fibers,” Opt. Lett. 25, 96–98 (2000).
[Crossref]

S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of photonic bandgap guiding fibers,” in Optical Fiber Communication Conference, (OFC) (1999) (Optical Society of America, Washington, D.C., 1999), pp. 117–119.

Barkou Libori, S. E.

Benabid, F.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2003).
[Crossref]

F. Benabid, J. C. Knight, and P. St. J. Russell, “Particle levitation and guidance in hollow-core photonic crystal fiber,” Opt. Express 10, 1195–1203 (2002).
[Crossref] [PubMed]

Birks, T. A.

R. F. Cregan, B. J. 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]

Bjarklev, A.

Botten, L. C.

Broeng, J.

J. Broeng, S. E. Barkou, T. Søndergaard, and A. Bjarklev, “Analysis of air-guiding photonic bandgap fibers,” Opt. Lett. 25, 96–98 (2000).
[Crossref]

S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of photonic bandgap guiding fibers,” in Optical Fiber Communication Conference, (OFC) (1999) (Optical Society of America, Washington, D.C., 1999), pp. 117–119.

Cregan, R. F.

R. F. Cregan, B. J. 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]

Fajardo, J. C.

N. Venkataraman, M. T. Gallagher, C. M. Smith, D. Müller, J. A. West, K. W. Koch, and J. C. Fajardo, “Low loss (13 db/km) air core photonic bandgap fiber,” 28th European Conference on Optical Communication, ECOC ’02 (Technical University of Denmark, Kongens Lyngby, Denmark, 2002), post-deadline paper PD1.1.

Gallagher, M. T.

N. Venkataraman, M. T. Gallagher, C. M. Smith, D. Müller, J. A. West, K. W. Koch, and J. C. Fajardo, “Low loss (13 db/km) air core photonic bandgap fiber,” 28th European Conference on Optical Communication, ECOC ’02 (Technical University of Denmark, Kongens Lyngby, Denmark, 2002), post-deadline paper PD1.1.

Joannopoulos, J. D.

Johnson, S. G.

Knight, J. C.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2003).
[Crossref]

F. Benabid, J. C. Knight, and P. St. J. Russell, “Particle levitation and guidance in hollow-core photonic crystal fiber,” Opt. Express 10, 1195–1203 (2002).
[Crossref] [PubMed]

R. F. Cregan, B. J. 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]

Koch, K. W.

N. Venkataraman, M. T. Gallagher, C. M. Smith, D. Müller, J. A. West, K. W. Koch, and J. C. Fajardo, “Low loss (13 db/km) air core photonic bandgap fiber,” 28th European Conference on Optical Communication, ECOC ’02 (Technical University of Denmark, Kongens Lyngby, Denmark, 2002), post-deadline paper PD1.1.

Lægsgaard, J.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).

Mangan, B. J.

R. F. Cregan, B. J. 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]

Martijn de Sterke, C.

McPhedran, R. C.

Mortensen, N. A.

Müller, D.

N. Venkataraman, M. T. Gallagher, C. M. Smith, D. Müller, J. A. West, K. W. Koch, and J. C. Fajardo, “Low loss (13 db/km) air core photonic bandgap fiber,” 28th European Conference on Optical Communication, ECOC ’02 (Technical University of Denmark, Kongens Lyngby, Denmark, 2002), post-deadline paper PD1.1.

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, San Diego, Calif., 2000).

Ouyang, G.

Roberts, P. J.

R. F. Cregan, B. J. 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]

Russell, P. St. J.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2003).
[Crossref]

F. Benabid, J. C. Knight, and P. St. J. Russell, “Particle levitation and guidance in hollow-core photonic crystal fiber,” Opt. Express 10, 1195–1203 (2002).
[Crossref] [PubMed]

R. F. Cregan, B. J. 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]

Smith, C. M.

N. Venkataraman, M. T. Gallagher, C. M. Smith, D. Müller, J. A. West, K. W. Koch, and J. C. Fajardo, “Low loss (13 db/km) air core photonic bandgap fiber,” 28th European Conference on Optical Communication, ECOC ’02 (Technical University of Denmark, Kongens Lyngby, Denmark, 2002), post-deadline paper PD1.1.

Smith, G. H.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).

Søndergaard, T.

Venkataraman, N.

N. Venkataraman, M. T. Gallagher, C. M. Smith, D. Müller, J. A. West, K. W. Koch, and J. C. Fajardo, “Low loss (13 db/km) air core photonic bandgap fiber,” 28th European Conference on Optical Communication, ECOC ’02 (Technical University of Denmark, Kongens Lyngby, Denmark, 2002), post-deadline paper PD1.1.

West, J. A.

N. Venkataraman, M. T. Gallagher, C. M. Smith, D. Müller, J. A. West, K. W. Koch, and J. C. Fajardo, “Low loss (13 db/km) air core photonic bandgap fiber,” 28th European Conference on Optical Communication, ECOC ’02 (Technical University of Denmark, Kongens Lyngby, Denmark, 2002), post-deadline paper PD1.1.

White, T. P.

Xu, Y.

Yariv, A.

J. Opt. Soc. Am. B (2)

Opt. Express (5)

Opt. Lett. (1)

Science (2)

R. F. Cregan, B. J. 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]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2003).
[Crossref]

Other (5)

N. Venkataraman, M. T. Gallagher, C. M. Smith, D. Müller, J. A. West, K. W. Koch, and J. C. Fajardo, “Low loss (13 db/km) air core photonic bandgap fiber,” 28th European Conference on Optical Communication, ECOC ’02 (Technical University of Denmark, Kongens Lyngby, Denmark, 2002), post-deadline paper PD1.1.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1996).

S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of photonic bandgap guiding fibers,” in Optical Fiber Communication Conference, (OFC) (1999) (Optical Society of America, Washington, D.C., 1999), pp. 117–119.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, San Diego, Calif., 2000).

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Figures (6)

Fig. 1
Fig. 1

Schematic picture of one of the structures (with d/Λ=0.88) under study. The black circles are airholes while the white areas are the silica regions. Only the core and innermost cladding region are shown.

Fig. 2
Fig. 2

(a) Field energy fraction in silica, and (b) effective area as calculated from Eq. (3). The effective area curve for the fiber with d/Λ=0.88 [solid curve in (b)] has been multiplied by 10 to facilitate comparison.

Fig. 3
Fig. 3

Dispersion curves for the fundamental guided mode of three air-guiding PBG fibers with various values of d and Λ: (a) d/Λ=0.88, Λ=0.8 μm, (b) d/Λ=0.88, Λ=2.4 μm, (c) d/Λ=0.95, Λ=1.0 μm. Solid curves report waveguide dispersion (DW) calculated at n=1.45, dashed curves report waveguide dispersion at values of n suitable for the wavelength interval spanned by the transmission window, and dotted curves denote results of self-consistent calculations.

Fig. 4
Fig. 4

Material dispersion Dmat (solid curves), defined in Eq. (11), for the two fiber designs guiding at short wavelengths. The dashed curves report the difference between the dotted and dashed curves in Fig. 3 for comparison.

Fig. 5
Fig. 5

Plots of the quantity RD, defined in Eq. (12), for two air-guiding PBG fiber designs (a) and two index-guiding fibers (b) having a cladding structure similar (although with smaller airholes) to the air-guiding PBG fibers.

Fig. 6
Fig. 6

Dispersion curves for two fibers with added absorption resonances in the base material at either λ=500 nm (P500) or λ=640 nm (P640) compared to the undoped result.

Equations (17)

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Δneff=P n2PAeff.
Aeff=|E|2dA2|E|4dA.
Aeff=n1ng02EDdA2SiO2|ED|2dA.
D=-ω22πcd2βdω2=ω22πcvg2dvgdω,
vg=dωdβ.
vg=vg01+ω2 Eddln dω  ,
vg0=c Re[E*×H ]zH, H.
dvgdω=vgvg01vg0vg0β+vg0ddω-vgEd2dln dω+ω2dEddωdln dω+Edd2ln dω2.
vg0=-Ed2 vg0-ω2Edβ,
dvgdω=vg(vg0)2vg0β-(vg)2vg0 Eddln dω1+ω4 Eddln dω+ω2d2ln dω2-(vg)2vg0 ω Edωdln dω1+ω4 Eddln dω.
D=DwSC-ω2Ed2πcvg0dln dω1+ω4 Eddln dω+ω2d2ln dω2-ω32πcvg0Edωdln dω×1+ω4 Eddln dωDwSC+Dmat,
RD=ω  ln Edωdln dωdln dω+ω2d2ln dω21+ω4 Eddln dω  .
(λ)=1+i=14aiλ2-λi2,
a1=0.6965325μm-2,λ1=0.066μm;
a2=0.4083099μm-2,λ2=0.118μm;
a3=0.8968766μm-2,λ3=9.896μm;
a4=0.001μm-2,

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