Abstract

In a previous paper we developed a matrix theory that applies to any cylindrically symmetric fiber surrounded by Bragg cladding. Using this formalism, along with Finite Difference Time Domain (FDTD) simulations, we study the waveguide dispersion for the m = 1 mode in an air-core Bragg fiber and showed it is possible to achieve very large negative dispersion values (~ -20,000 ps/(nm.km)) with significantly reduced absorption loss and non-linear effects.

©2002 Optical Society of America

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References

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  1. P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68, 1196–1201, (1978).
    [Crossref]
  2. Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave Technol. 17, 2039–2041, (1999).
    [Crossref]
  3. M. Miyagi, A. Hongo, Y. Aizawa, and S. Kawakami, “Fabrication of germanium-coated nickel hollow waveguides for infrared transmission,” Appl. Phys. Lett. 43, 430–432, (1983).
    [Crossref]
  4. N. Croitoru, J. Dror, and I. Gannot, “Characterization of hollow fibers for the transmission of infrared radiation,” Appl. Opt. 29, 1805–1809, (1990).
    [Crossref] [PubMed]
  5. 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]
  6. M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415–419, (2000).
    [Crossref] [PubMed]
  7. Y. Xu, R. K. Lee, and A. Yariv, “Asymptotic analysis of Bragg fibers,” Opt. Lett. 25, 1756–1758, (2000).
    [Crossref]
  8. G. Ouyang, Y. Xu, and A. Yariv, “Comparative study of air-core and coaxial Bragg fibers: single-mode transmission and dispersion characteristics,” Opt. Express 9, 733–747, (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-733
    [Crossref] [PubMed]
  9. S. G. Johnson et al., “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779, (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748
    [Crossref] [PubMed]
  10. Y. Xu, G. Ouyang, R. Lee, and A. Yariv, “Asymptotic matrix theory of Bragg fibers,” J. Lightwave Technol. 20, 428–440, (2002).
    [Crossref]
  11. A. Vengsarkar and W. A. Reed, “Dispersion-compensating single-mode fibers: efficient designs for first- and second-order compensation,” Opt. Lett. 18, 924–926, (1993).
    [Crossref] [PubMed]
  12. A. Bjarklev, T. Rasmussen, O. Lumholt, K. Rottwitt, and M. Helmer, “Optimal design of single-cladded dispersion-compensating optical fibers,” Opt. Lett. 19, 457–459, (1994).
    [Crossref] [PubMed]
  13. B. Jopson and A. Gnauck, “Dispersion compensation for optical fiber systems,” IEEE Comm. Mag. 33, 96–102, (1995).
    [Crossref]
  14. M Onishi, T Kashiwada, Y Ishiguro, M Nishimura, and H Kanamori, “High-performance dispersion-compensating fibers,” Fiber Integ. Opt. 16, 277–285, (1997).
    [Crossref]
  15. C. Bradford, “Managing chromatic dispersion increases bandwidth,” Laser Focus World, February (2001).
  16. M.R.C. Caputo and M.E. Gouvea, “Dispersion slope effects of the compensation dispersion fiber for broadband dispersion compensation in the presence of self-phase modulation,” Laser Focus World, February (2001).
  17. P. Yeh, A. Yariv, and C. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438, (1977).
    [Crossref]
  18. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307, (1966).
  19. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computat. Phys. 114, 185–200, (1994).
    [Crossref]
  20. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639, (1996).
    [Crossref]
  21. F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method.” Opt. and Quantum Electron. 31, 827–841, (1999)
    [Crossref]

2002 (1)

2001 (2)

2000 (2)

Y. Xu, R. K. Lee, and A. Yariv, “Asymptotic analysis of Bragg fibers,” Opt. Lett. 25, 1756–1758, (2000).
[Crossref]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415–419, (2000).
[Crossref] [PubMed]

1999 (3)

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]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave Technol. 17, 2039–2041, (1999).
[Crossref]

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method.” Opt. and Quantum Electron. 31, 827–841, (1999)
[Crossref]

1997 (1)

M Onishi, T Kashiwada, Y Ishiguro, M Nishimura, and H Kanamori, “High-performance dispersion-compensating fibers,” Fiber Integ. Opt. 16, 277–285, (1997).
[Crossref]

1996 (1)

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639, (1996).
[Crossref]

1995 (1)

B. Jopson and A. Gnauck, “Dispersion compensation for optical fiber systems,” IEEE Comm. Mag. 33, 96–102, (1995).
[Crossref]

1994 (2)

1993 (1)

1990 (1)

1983 (1)

M. Miyagi, A. Hongo, Y. Aizawa, and S. Kawakami, “Fabrication of germanium-coated nickel hollow waveguides for infrared transmission,” Appl. Phys. Lett. 43, 430–432, (1983).
[Crossref]

1978 (1)

1977 (1)

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307, (1966).

Aizawa, Y.

M. Miyagi, A. Hongo, Y. Aizawa, and S. Kawakami, “Fabrication of germanium-coated nickel hollow waveguides for infrared transmission,” Appl. Phys. Lett. 43, 430–432, (1983).
[Crossref]

Alimenti, F.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method.” Opt. and Quantum Electron. 31, 827–841, (1999)
[Crossref]

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]

Bassi, P.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method.” Opt. and Quantum Electron. 31, 827–841, (1999)
[Crossref]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computat. Phys. 114, 185–200, (1994).
[Crossref]

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.

Bradford, C.

C. Bradford, “Managing chromatic dispersion increases bandwidth,” Laser Focus World, February (2001).

Caputo, M.R.C.

M.R.C. Caputo and M.E. Gouvea, “Dispersion slope effects of the compensation dispersion fiber for broadband dispersion compensation in the presence of self-phase modulation,” Laser Focus World, February (2001).

Chen, C.

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]

Croitoru, N.

Dror, J.

Fan, S.

Fink, Y.

Gannot, I.

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639, (1996).
[Crossref]

Gnauck, A.

B. Jopson and A. Gnauck, “Dispersion compensation for optical fiber systems,” IEEE Comm. Mag. 33, 96–102, (1995).
[Crossref]

Gouvea, M.E.

M.R.C. Caputo and M.E. Gouvea, “Dispersion slope effects of the compensation dispersion fiber for broadband dispersion compensation in the presence of self-phase modulation,” Laser Focus World, February (2001).

Helmer, M.

Hong, C.

Hongo, A.

M. Miyagi, A. Hongo, Y. Aizawa, and S. Kawakami, “Fabrication of germanium-coated nickel hollow waveguides for infrared transmission,” Appl. Phys. Lett. 43, 430–432, (1983).
[Crossref]

Ibanescu, M.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415–419, (2000).
[Crossref] [PubMed]

Ishiguro, Y

M Onishi, T Kashiwada, Y Ishiguro, M Nishimura, and H Kanamori, “High-performance dispersion-compensating fibers,” Fiber Integ. Opt. 16, 277–285, (1997).
[Crossref]

Joannopoulos, J. D.

Johnson, S. G.

Jopson, B.

B. Jopson and A. Gnauck, “Dispersion compensation for optical fiber systems,” IEEE Comm. Mag. 33, 96–102, (1995).
[Crossref]

Kanamori, H

M Onishi, T Kashiwada, Y Ishiguro, M Nishimura, and H Kanamori, “High-performance dispersion-compensating fibers,” Fiber Integ. Opt. 16, 277–285, (1997).
[Crossref]

Kashiwada, T

M Onishi, T Kashiwada, Y Ishiguro, M Nishimura, and H Kanamori, “High-performance dispersion-compensating fibers,” Fiber Integ. Opt. 16, 277–285, (1997).
[Crossref]

Kawakami, S.

M. Miyagi, A. Hongo, Y. Aizawa, and S. Kawakami, “Fabrication of germanium-coated nickel hollow waveguides for infrared transmission,” Appl. Phys. Lett. 43, 430–432, (1983).
[Crossref]

Knight, J. 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]

Lee, R.

Lee, R. K.

Lumholt, O.

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]

Marom, E.

Mezzanotte, P.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method.” Opt. and Quantum Electron. 31, 827–841, (1999)
[Crossref]

Miyagi, M.

M. Miyagi, A. Hongo, Y. Aizawa, and S. Kawakami, “Fabrication of germanium-coated nickel hollow waveguides for infrared transmission,” Appl. Phys. Lett. 43, 430–432, (1983).
[Crossref]

Nishimura, M

M Onishi, T Kashiwada, Y Ishiguro, M Nishimura, and H Kanamori, “High-performance dispersion-compensating fibers,” Fiber Integ. Opt. 16, 277–285, (1997).
[Crossref]

Onishi, M

M Onishi, T Kashiwada, Y Ishiguro, M Nishimura, and H Kanamori, “High-performance dispersion-compensating fibers,” Fiber Integ. Opt. 16, 277–285, (1997).
[Crossref]

Ouyang, G.

Rasmussen, T.

Reed, W. A.

Ripin, D. J.

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]

Roselli, L.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method.” Opt. and Quantum Electron. 31, 827–841, (1999)
[Crossref]

Rottwitt, K.

Russell, P. St. 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]

Sorrentino, R.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method.” Opt. and Quantum Electron. 31, 827–841, (1999)
[Crossref]

Tartarini, G.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method.” Opt. and Quantum Electron. 31, 827–841, (1999)
[Crossref]

Thomas, E. L.

Vengsarkar, A.

Xu, Y.

Yariv, A.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307, (1966).

Yeh, P.

Zepparelli, F.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method.” Opt. and Quantum Electron. 31, 827–841, (1999)
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Miyagi, A. Hongo, Y. Aizawa, and S. Kawakami, “Fabrication of germanium-coated nickel hollow waveguides for infrared transmission,” Appl. Phys. Lett. 43, 430–432, (1983).
[Crossref]

Fiber Integ. Opt. (1)

M Onishi, T Kashiwada, Y Ishiguro, M Nishimura, and H Kanamori, “High-performance dispersion-compensating fibers,” Fiber Integ. Opt. 16, 277–285, (1997).
[Crossref]

IEEE Comm. Mag. (1)

B. Jopson and A. Gnauck, “Dispersion compensation for optical fiber systems,” IEEE Comm. Mag. 33, 96–102, (1995).
[Crossref]

IEEE Trans. Antennas Propag. (2)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307, (1966).

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639, (1996).
[Crossref]

J. Computat. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computat. Phys. 114, 185–200, (1994).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (2)

Opt. and Quantum Electron. (1)

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the compact-2D-FDTD method.” Opt. and Quantum Electron. 31, 827–841, (1999)
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

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]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415–419, (2000).
[Crossref] [PubMed]

Other (2)

C. Bradford, “Managing chromatic dispersion increases bandwidth,” Laser Focus World, February (2001).

M.R.C. Caputo and M.E. Gouvea, “Dispersion slope effects of the compensation dispersion fiber for broadband dispersion compensation in the presence of self-phase modulation,” Laser Focus World, February (2001).

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Figures (7)

Fig. 1.
Fig. 1. Schematic of an air-core Bragg fiber. The fiber cladding consists of alternating layers of dielectric media with high and low refractive indices.

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Fig. 2.
Fig. 2. Bragg fiber band diagram based on asymptotic computations. For clarity only the TM and TM-like modes with lowest radial number are plotted here, as all other modes have all been “pushed” out of the band gap. The TM band structure of the corresponding Bragg stack serves as the background and the dotted line shown is the light line. Boundary conditions are matched at the air core boundary. The structural parameters are given as follows: n 1 = 4.6, n 2 = 1.5, r 1 = 10, r 2 = 2, and rcore = 30, all in normalized units. Note in the frequency window (0.762, 0.782) the m = 1 band not only exhibits single-mode behavior but also possesses negative dispersion values.

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Fig. 3.
Fig. 3. Dispersion value D for the m = 1 band based on asymptotic computations. The second order derivative ∂ 2 β ∂ ω 2 is calculated by a direct differential method (i.e., no curve fitting is involved). Fiber structure and boundary matching surface follow those of Fig. 2. Shaded area (1526, 1566) is made to match the frequency window (0.762, 0.782) (also in Fig. 2) by choosing the normalized operating frequency to be 0.77(c/(r 1+r 2)), which translates to 1.55μm in MKS units. Note at λ = 1.55μm, dispersion value D ≈ -25,000ps/(nm.km).

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Fig. 4.
Fig. 4. Bragg fiber band diagram for the m=1 mode. The asymptotic curve is copied from Fig. 2 and the FDTD structure is defined with 12 cladding pairs.

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Fig. 5.
Fig. 5. The Hz field distribution of an m = 1 mode based on FDTD simulation. The parameters of the Bragg fiber are given in the caption of Fig. 2. The Bragg cladding consists of 12 cladding pairs and the whole fiber is immersed in air. The frequency and propagation constant of the mode are respectively ω = 0.777(c/(r 1+r 2)) and β = 0.5(1/(r 1+r 2).

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Fig. 6.
Fig. 6. Bragg fiber band diagram based on asymptotic computations. Just as in Fig. 2, only the TM-like bands with the lowest radial number are plotted. Boundary conditions are matched at the 50th cladding layer. The fiber structural parameters are given in the caption of Fig. 2. Note that the m = 4 band was missing in Fig. 2.

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Fig. 7.
Fig. 7. The radial profile of Eθ field of guided Bragg fiber modes. The white area is the fiber core and the shaded layers represent the cladding layers. All structural parameters are given in the caption of Fig. 2. The vertical dashed line shows the boundary of a fiber structure with 12 cladding pairs, used in the FDTD simulations in Sec. 3. The frequency of the mode is ω = 0.77(1/(r 1+r 2)), the chosen normalized operating frequency.

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Equations (2)

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( ∇ ⊥ + iβ e → z ) × E → ( x , y , t ) = − μ 0 ∂ ∂ t H → ( x , y , t ) ,
( ∇ ⊥ + iβ e → z ) × H → ( x , y , t ) = ϵ 0 ϵ ( x , y ) ∂ ∂ t E → ( x , y , t ) ,

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