Abstract

We propose a full-vectorial Galerkin method for the analysis of circular symmetric fibers with arbitrary index profiles. A set of orthogonal Laguerre–Gauss functions is used to calculate the dispersion relation and mode fields of TE and TM modes. Examples are given for both standard step-index fibers and Bragg fibers. For standard step-index fiber with low or high index contrast, the Galerkin method agrees well with the analytical results. In the case of the TE mode of a Bragg fiber it agrees well with the asymptotic results.

© 2004 Optical Society of America

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References

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  1. P. Yeh, A. Yariv, and E. Marom, J. Opt. Soc. Am. 68, 1196 (1978).
  2. M. Lbanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
    [CrossRef]
  3. Y. Xu, R. K. Lee, and A. Yariv, Opt. Lett. 25, 1756 (2000).
    [CrossRef]
  4. G. Ouyang, Y. Xu, and A. Yariv, Opt. Express 9, 733 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  5. Y. Xu, G. Ouyang, R. K. Lee, and A. Yariv, J. Lightwave Technol. 20, 428 (2002).
    [CrossRef]
  6. K. Tetsuya and M. Izutsu, Opt. Express 7, 10 (2000), http://www.opticsexpress.org .
    [CrossRef]
  7. J. P. Meunier, J. Pigeon, and J. N. Massot, Opt. Quantum Electron. 13, 71 (1981).
    [CrossRef]
  8. S. Guo, “Study of dispersion compensation single mode optical fiber,” M.S. thesis (Northern Jiaotong University, Beijing, China, 1996).
  9. P. K. Mishra, I. C. Goyal, A. K. Ghatak, and E. K. Sharma, Opt. Acta 31, 1041 (1984).
    [CrossRef]
  10. H. Etzkom and T. Heun, Opt. Quantum Electron. 18, 1 (1986).
    [CrossRef]
  11. A. Sharma and S. Banarjee, J. Lightwave Technol. 7, 1919 (1989).
    [CrossRef]
  12. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).
  13. G. Arfken, Mathematical Methods for Physicists (Academic, Orlando, Fla., 1985).

2002 (1)

2001 (1)

2000 (3)

1989 (1)

A. Sharma and S. Banarjee, J. Lightwave Technol. 7, 1919 (1989).
[CrossRef]

1986 (1)

H. Etzkom and T. Heun, Opt. Quantum Electron. 18, 1 (1986).
[CrossRef]

1984 (1)

P. K. Mishra, I. C. Goyal, A. K. Ghatak, and E. K. Sharma, Opt. Acta 31, 1041 (1984).
[CrossRef]

1981 (1)

J. P. Meunier, J. Pigeon, and J. N. Massot, Opt. Quantum Electron. 13, 71 (1981).
[CrossRef]

1978 (1)

Arfken, G.

G. Arfken, Mathematical Methods for Physicists (Academic, Orlando, Fla., 1985).

Banarjee, S.

A. Sharma and S. Banarjee, J. Lightwave Technol. 7, 1919 (1989).
[CrossRef]

Etzkom, H.

H. Etzkom and T. Heun, Opt. Quantum Electron. 18, 1 (1986).
[CrossRef]

Fan, S.

M. Lbanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
[CrossRef]

Fink, Y.

M. Lbanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
[CrossRef]

Ghatak, A. K.

P. K. Mishra, I. C. Goyal, A. K. Ghatak, and E. K. Sharma, Opt. Acta 31, 1041 (1984).
[CrossRef]

Goyal, I. C.

P. K. Mishra, I. C. Goyal, A. K. Ghatak, and E. K. Sharma, Opt. Acta 31, 1041 (1984).
[CrossRef]

Guo, S.

S. Guo, “Study of dispersion compensation single mode optical fiber,” M.S. thesis (Northern Jiaotong University, Beijing, China, 1996).

Heun, T.

H. Etzkom and T. Heun, Opt. Quantum Electron. 18, 1 (1986).
[CrossRef]

Izutsu, M.

Joannopoulos, J. D.

M. Lbanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
[CrossRef]

Lbanescu, M.

M. Lbanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
[CrossRef]

Lee, R. K.

Love, J. D.

W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

Marom, E.

Massot, J. N.

J. P. Meunier, J. Pigeon, and J. N. Massot, Opt. Quantum Electron. 13, 71 (1981).
[CrossRef]

Meunier, J. P.

J. P. Meunier, J. Pigeon, and J. N. Massot, Opt. Quantum Electron. 13, 71 (1981).
[CrossRef]

Mishra, P. K.

P. K. Mishra, I. C. Goyal, A. K. Ghatak, and E. K. Sharma, Opt. Acta 31, 1041 (1984).
[CrossRef]

Ouyang, G.

Pigeon, J.

J. P. Meunier, J. Pigeon, and J. N. Massot, Opt. Quantum Electron. 13, 71 (1981).
[CrossRef]

Sharma, A.

A. Sharma and S. Banarjee, J. Lightwave Technol. 7, 1919 (1989).
[CrossRef]

Sharma, E. K.

P. K. Mishra, I. C. Goyal, A. K. Ghatak, and E. K. Sharma, Opt. Acta 31, 1041 (1984).
[CrossRef]

Snyder, W.

W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

Tetsuya, K.

Thomas, E. L.

M. Lbanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
[CrossRef]

Xu, Y.

Yariv, A.

Yeh, P.

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

P. K. Mishra, I. C. Goyal, A. K. Ghatak, and E. K. Sharma, Opt. Acta 31, 1041 (1984).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Quantum Electron. (2)

J. P. Meunier, J. Pigeon, and J. N. Massot, Opt. Quantum Electron. 13, 71 (1981).
[CrossRef]

H. Etzkom and T. Heun, Opt. Quantum Electron. 18, 1 (1986).
[CrossRef]

Science (1)

M. Lbanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, Science 289, 415 (2000).
[CrossRef]

Other (3)

S. Guo, “Study of dispersion compensation single mode optical fiber,” M.S. thesis (Northern Jiaotong University, Beijing, China, 1996).

W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

G. Arfken, Mathematical Methods for Physicists (Academic, Orlando, Fla., 1985).

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Figures (2)

Fig. 1
Fig. 1

Fields Eϕ and Hϕ of TE01 and TM01, respectively, in two standard step-index fibers with low and high index contrast (N=100).

Fig. 2
Fig. 2

Effective indices neff of TE modes in a Bragg fiber and the field Eϕ of the TE01 mode at λ=1.55 µm (N=200).

Tables (1)

Tables Icon

Table 1 Normalized Propagation Constant b for Two Step-Index Fibers with Low and High Index Contrast

Equations (17)

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t2Er-2r2Eϕϕ+rErdln n2dr-Err2+k02n2-β2Er=0,
t2Eϕ+1rdln n2dr+2rErϕ-Eϕr2+k02n2-β2Eϕ=0,
t2Hr-2r2Hϕϕ-Hrr2+k02n2-β2Hr=0,
t2Hϕ-1rdln n2drrrHϕ+1rdln n2dr2+2rHrϕ-Hϕr2+k02n2-β2Hϕ=0.
d2fdr2+1rdfdr+k02n2-β2-1r2f=0.
d2gdr2+1rdgdr+k02n2-β2-1r2g-dln n2drdgdr+1rg=0.
x=σr2/a2,
hr=n2r-ncl2nco2-ncl2,  V2=k02a2nco2-ncl2, b=β/k02-ncl2nco2-ncl2.
xd2fdx2+dfdx+14V2h-V2bσ-1xf=0,
xd2gdx+dgdx+14V2h-V2bσ-1xg-dln n2dxxdgdx+12g=0.
fx=i=0N-1aiφix,  gx=i=0N-1biφix,
σV2i=0N-1aix-21+2i+mφix+i=0N-1aihx/σφix=bi=0N-1aiφix.
M1i,i=2i+m+1,
M1i+1,i=i+1i+m+11/2,
M1i-1,i=ii+m1/2,
N1i,j=0σhx/σφiφjdx.
N2i,j=xjΔ ln n22i+m+1-x2φi-ii+m1/2φi-1φjx=xj,

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