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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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)

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

IEEE Commun. Mag. (1)

B. Jopson and A. Gnauck, �??Dispersion compensation for optical fiber systems,�?? IEEE Commun. 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)

Laser Focus World (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).

Opt. Express (2)

Opt. Lett. (3)

Opt. 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. Quantum Electron. 31, 827-841, (1999)
[CrossRef]

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]

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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.

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.

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).

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.

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).

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.

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.

Equations (2)

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( + e z ) × E ( x , y , t ) = μ 0 t H ( x , y , t ) ,
( + e z ) × H ( x , y , t ) = ϵ 0 ϵ ( x , y ) t E ( x , y , t ) ,

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