Abstract

Spectral interferometry with a supercontinuum is used for the first experimental measurement, to our knowledge, of phase dispersion of the fundamental mode in multiple bandgaps of a photonic bandgap fiber. The dispersion data show a strong influence of the Bragg scattering from the crystal structure surrounding the core. A simple two-dimensional model that includes the effects of a wavelength-dependent angle of propagation, where the angle is determined by the Bragg-scattering condition, and the effects of thin-film-like resonant scattering planes in the fiber is found to explain the observations qualitatively.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. F. Cregan, B. J. Mangan, J. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science (Washington, DC, U.S.) 285, 1537–1539 (1999).
    [CrossRef]
  2. J. Tirapu, T. Lopetegi, M. A. G. Laso, M. J. Erro, F. Falcone, and M. Sorolla, “Study of the delay characteristics of 1-D photonic bandgap microstrip structures,” Microwave Opt. Technol. Lett. 23, 346–349 (1999).
    [CrossRef]
  3. M. Notomi, K. Yamata, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]
  4. J. A. West, J. C. Fajardo, M. T. Gallagher, K. W. Koch, N. F. Borrelli, and D. C. Allan, “Demonstration of an IR-optimized air-core photonic band-gap fiber,” in European Conference on Optical Communication (IEEE, New York, 2000), pp. 41–42.
  5. J. A. West, N. Venkataraman, C. M. Smith, and M. T. Gallagher, “Photonic crystal fibers,” in European Conference on Optical Communication (IEEE, New York, 2001), pp. 582–585.
  6. S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of PBG guiding fibers,” in Optical Fiber Communication Conference, Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FG5.
  7. J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibers,” J. Opt. A: Pure Appl. Opt. 1, 477–482 (1999).
    [CrossRef]
  8. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. 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]
  9. J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic bandgap guidance in optical fibers,” Science (Washington, DC, U.S.) 282, 1476–1478 (1998).
    [CrossRef]
  10. C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).
  11. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air–silica microstructure optical fi-bers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
    [CrossRef]
  12. R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, “Tunable photonic band gap fiber,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 466–468.
  13. M. V. Klein and T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986).
  14. J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in tapered and photonic crystal fibers,” in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), p. 47.

2001 (2)

M. Notomi, K. Yamata, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. 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]

2000 (1)

1999 (3)

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibers,” J. Opt. A: Pure Appl. Opt. 1, 477–482 (1999).
[CrossRef]

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

J. Tirapu, T. Lopetegi, M. A. G. Laso, M. J. Erro, F. Falcone, and M. Sorolla, “Study of the delay characteristics of 1-D photonic bandgap microstrip structures,” Microwave Opt. Technol. Lett. 23, 346–349 (1999).
[CrossRef]

1998 (1)

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic bandgap guidance in optical fibers,” Science (Washington, DC, U.S.) 282, 1476–1478 (1998).
[CrossRef]

1973 (1)

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).

Allan, D. C.

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

Barbeito, P. M.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibers,” J. Opt. A: Pure Appl. Opt. 1, 477–482 (1999).
[CrossRef]

Barkou, S. E.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibers,” J. Opt. A: Pure Appl. Opt. 1, 477–482 (1999).
[CrossRef]

Birks, T. A.

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

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic bandgap guidance in optical fibers,” Science (Washington, DC, U.S.) 282, 1476–1478 (1998).
[CrossRef]

Bjarklev, A.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibers,” J. Opt. A: Pure Appl. Opt. 1, 477–482 (1999).
[CrossRef]

Broeng, J.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibers,” J. Opt. A: Pure Appl. Opt. 1, 477–482 (1999).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic bandgap guidance in optical fibers,” Science (Washington, DC, U.S.) 282, 1476–1478 (1998).
[CrossRef]

Cregan, R. F.

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

Engeness, T.

Erro, M. J.

J. Tirapu, T. Lopetegi, M. A. G. Laso, M. J. Erro, F. Falcone, and M. Sorolla, “Study of the delay characteristics of 1-D photonic bandgap microstrip structures,” Microwave Opt. Technol. Lett. 23, 346–349 (1999).
[CrossRef]

Falcone, F.

J. Tirapu, T. Lopetegi, M. A. G. Laso, M. J. Erro, F. Falcone, and M. Sorolla, “Study of the delay characteristics of 1-D photonic bandgap microstrip structures,” Microwave Opt. Technol. Lett. 23, 346–349 (1999).
[CrossRef]

Fink, Y.

Froehly, C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).

Ibanescu, M.

Jacobs, S.

Joannopoulos, J. D.

Johnson, S. G.

Knight, J.

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

Knight, J. C.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic bandgap guidance in optical fibers,” Science (Washington, DC, U.S.) 282, 1476–1478 (1998).
[CrossRef]

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).

Laso, M. A. G.

J. Tirapu, T. Lopetegi, M. A. G. Laso, M. J. Erro, F. Falcone, and M. Sorolla, “Study of the delay characteristics of 1-D photonic bandgap microstrip structures,” Microwave Opt. Technol. Lett. 23, 346–349 (1999).
[CrossRef]

Lopetegi, T.

J. Tirapu, T. Lopetegi, M. A. G. Laso, M. J. Erro, F. Falcone, and M. Sorolla, “Study of the delay characteristics of 1-D photonic bandgap microstrip structures,” Microwave Opt. Technol. Lett. 23, 346–349 (1999).
[CrossRef]

Mangan, B. J.

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

Notomi, M.

M. Notomi, K. Yamata, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Ranka, J. K.

Roberts, P. J.

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

Russell, P. S. J.

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

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic bandgap guidance in optical fibers,” Science (Washington, DC, U.S.) 282, 1476–1478 (1998).
[CrossRef]

Shinya, A.

M. Notomi, K. Yamata, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Skorobogatiy, M.

Soljacic, M.

Sondergaard, T.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibers,” J. Opt. A: Pure Appl. Opt. 1, 477–482 (1999).
[CrossRef]

Sorolla, M.

J. Tirapu, T. Lopetegi, M. A. G. Laso, M. J. Erro, F. Falcone, and M. Sorolla, “Study of the delay characteristics of 1-D photonic bandgap microstrip structures,” Microwave Opt. Technol. Lett. 23, 346–349 (1999).
[CrossRef]

Stentz, A. J.

Takahashi, C.

M. Notomi, K. Yamata, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamata, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Tirapu, J.

J. Tirapu, T. Lopetegi, M. A. G. Laso, M. J. Erro, F. Falcone, and M. Sorolla, “Study of the delay characteristics of 1-D photonic bandgap microstrip structures,” Microwave Opt. Technol. Lett. 23, 346–349 (1999).
[CrossRef]

Vienot, J. C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).

Weisberg, O.

Windeler, R. S.

Yamata, K.

M. Notomi, K. Yamata, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Yokohama, I.

M. Notomi, K. Yamata, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

J. Opt. (Paris) (1)

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).

J. Opt. A: Pure Appl. Opt. (1)

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibers,” J. Opt. A: Pure Appl. Opt. 1, 477–482 (1999).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

J. Tirapu, T. Lopetegi, M. A. G. Laso, M. J. Erro, F. Falcone, and M. Sorolla, “Study of the delay characteristics of 1-D photonic bandgap microstrip structures,” Microwave Opt. Technol. Lett. 23, 346–349 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

M. Notomi, K. Yamata, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Science (Washington, DC, U.S.) (2)

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic bandgap guidance in optical fibers,” Science (Washington, DC, U.S.) 282, 1476–1478 (1998).
[CrossRef]

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

Other (6)

J. A. West, J. C. Fajardo, M. T. Gallagher, K. W. Koch, N. F. Borrelli, and D. C. Allan, “Demonstration of an IR-optimized air-core photonic band-gap fiber,” in European Conference on Optical Communication (IEEE, New York, 2000), pp. 41–42.

J. A. West, N. Venkataraman, C. M. Smith, and M. T. Gallagher, “Photonic crystal fibers,” in European Conference on Optical Communication (IEEE, New York, 2001), pp. 582–585.

S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of PBG guiding fibers,” in Optical Fiber Communication Conference, Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper FG5.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, “Tunable photonic band gap fiber,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 466–468.

M. V. Klein and T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986).

J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in tapered and photonic crystal fibers,” in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), p. 47.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

(a) Unnormalized transmission spectrum of the PBG fiber, with (solid curve), and without (dashed curve) high-index liquid in the fiber holes. The inset is a cross section of the fiber; the dark regions are the liquid-filled air holes. (b) Spectral interferometry setup.

Fig. 2
Fig. 2

Dots are the group delay recovered from measurements on a 130-mm-long PBG fiber over one of its bandgaps. The solid curve through the dots is a polynomial fit to the data. Curve (b) shows Is(ω)/Ir(ω). Curve (c) is the total normalized transmission. The insets show the near-field mode patterns recorded on the short and long-wavelength sides of the bandgap with a spectral width of 1 nm.

Fig. 3
Fig. 3

Dispersion measured over three different bandgaps of the fiber (dots). Curve (b), Is(ω)/Ir(ω). Curve (c), total transmission shown for comparison. The dip in curve (b) for the bandgap centered at 810 nm is likely due to modulational instability in the continuum-generating fiber14 and occurs only at high powers around the Ti:sapphire pump wavelength. The data in this wavelength range are taken at low power. The absence of the dip in the total transmission curve (c) indicates that it is not caused by the presence of multiple modes.

Fig. 4
Fig. 4

Position of minimum group delay (squares), and the long-wavelength edge of the bandgap (circles), versus temperature change and refractive index of the liquid.

Fig. 5
Fig. 5

(a) Geometry of propagation in a waveguide surrounded with a thin-film Bragg crystal. (b) Dispersion under the condition that the transverse wave vector is a constant (equal to the total wave vector at 808 nm) for all wavelengths. The dashed curve shows the reflectivity; R, dispersion on reflection off the film; L, dispersion of the longitudinal component; T, total dispersion.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

I(ω)=Ir(ω)+Is(ω)+2Ir(ω)Is(ω)cos[Φ(ω)],
τ(ω)=dΦ(ω)dωδΦ(ω)δω=2πωi-ωi+1,
Ψ(ω)=k sin[θ(ω)]L+k cos[θ(ω)]D+ϕr(ω),
d2Ψ(ω)dω2=L d2dω2 {k sin[θ(ω)]}+d2ϕr(ω)dω2.

Metrics