Abstract

Plastic optical fibers that are a typical large-core multimode optical fiber support a great number of modes compared with conventional silica-glass multimode optical fibers. So far the WKB method has been used for most of the modal analyses of these fibers because of a great number of guided modes. We describe the accurate eigenmodal analysis of large-core multimode optical fibers with the finite-element method (FEM) and compute the propagation constants of all LP modes. In addition, the FEM has a strong advantage for arbitrary core profiles whereas the WKB method is not suitable for nonmonotonic profiles. To demonstrate the advantage, we apply the FEM to the fiber having sinusoidal fluctuations.

© 2004 Optical Society of America

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Corrections

Masashi Eguchi and Suguru Horinouchi, "Finite-element modal analysis of large-core multimode optical fibers: erratum," Appl. Opt. 43, 3158-3158 (2004)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-43-15-3158

References

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  1. Y. Koike, “High-bandwidth graded-index polymer optical fibre,” Polymer 32, 1737–1745 (1991).
    [Crossref]
  2. S. Kawakami, J. Nishizawa, “An optical waveguide with the optimum distribution of the refractive index with reference to waveform distortion,” IEEE Trans. Microwave Theory Tech. MTT-16, 814–818 (1968).
    [Crossref]
  3. D. Gloge, E. A. J. Marcatili, “Multimode theory of graded-core fibers,” Bell Syst. Tech. J. 52, 1563–1578 (1973).
  4. D. Gloge, I. P. Kaminow, H. M. Presby, “Profile dispersion in multimode fibers: measurement and analysis,” Electron. Lett. 11, 469–470 (1975).
    [Crossref]
  5. R. Olshansky, D. B. Keck, “Pulse broadening in graded-index optical fibers,” Appl. Opt. 15, 483–491 (1976).
    [Crossref] [PubMed]
  6. E. A. J. Marcatili, “Modal dispersion in optical fibers with arbitrary numerical aperture and profile dispersion,” Bell Syst. Tech. J. 56, 49–63 (1977).
  7. R. Olshansky, “Multiple-α index profiles,” Appl. Opt. 18, 683–689 (1979).
    [Crossref] [PubMed]
  8. D. Marcuse, “Calculation of bandwidth from index profiles of optical fibers. 1: Theory,” Appl. Opt. 18, 2073–2080 (1979).
    [Crossref] [PubMed]
  9. I. Kaminow, D. Marcuse, H. M. Presby, “Multimode fiber bandwidth: theory and practice,” Proc. IEEE 68, 1209–1213 (1980).
    [Crossref]
  10. T. Okoshi, K. Okamoto, “Analysis of wave propagation in inhomogeneous optical fibers using a variational method,” IEEE Trans. Microwave Theory Tech. MTT-22, 938–945 (1974).
    [Crossref]
  11. E. Bianciardi, V. Rizzoli, “Propagation in graded-core fibres: a unified numerical description,” Opt. Quantum Electron. 9, 121–133 (1977).
    [Crossref]
  12. K. Okamoto, “Comparison of calculated and measured impulse responses of optical fibers,” Appl. Opt. 18, 2199–2206 (1979).
    [Crossref] [PubMed]
  13. K. Oyamada, T. Okoshi, “High-accuracy numerical data on propagation characteristics of α-power graded-core fibers,” IEEE Trans. Microwave Theory Tech. MTT-28, 1113–1118 (1980).
    [Crossref]
  14. K. Morishita, “Numerical analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-29, 348–352 (1981).
    [Crossref]
  15. T. Ishigure, E. Nihei, Y. Koike, “Graded-index polymer optical fiber for high-speed data communication,” Appl. Opt. 33, 4261–4266 (1994).
    [Crossref] [PubMed]
  16. Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded-index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
    [Crossref]
  17. M. Eguchi, M. Koshiba, Y. Tsuji, “Dispersion compensation based on dual-mode optical fiber with inhomogeneous profile core,” J. Lightwave Technol. 14, 2387–2394 (1996).
    [Crossref]
  18. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, San Diego, Calif., 1991).

1996 (1)

M. Eguchi, M. Koshiba, Y. Tsuji, “Dispersion compensation based on dual-mode optical fiber with inhomogeneous profile core,” J. Lightwave Technol. 14, 2387–2394 (1996).
[Crossref]

1995 (1)

Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded-index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
[Crossref]

1994 (1)

1991 (1)

Y. Koike, “High-bandwidth graded-index polymer optical fibre,” Polymer 32, 1737–1745 (1991).
[Crossref]

1981 (1)

K. Morishita, “Numerical analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-29, 348–352 (1981).
[Crossref]

1980 (2)

K. Oyamada, T. Okoshi, “High-accuracy numerical data on propagation characteristics of α-power graded-core fibers,” IEEE Trans. Microwave Theory Tech. MTT-28, 1113–1118 (1980).
[Crossref]

I. Kaminow, D. Marcuse, H. M. Presby, “Multimode fiber bandwidth: theory and practice,” Proc. IEEE 68, 1209–1213 (1980).
[Crossref]

1979 (3)

1977 (2)

E. A. J. Marcatili, “Modal dispersion in optical fibers with arbitrary numerical aperture and profile dispersion,” Bell Syst. Tech. J. 56, 49–63 (1977).

E. Bianciardi, V. Rizzoli, “Propagation in graded-core fibres: a unified numerical description,” Opt. Quantum Electron. 9, 121–133 (1977).
[Crossref]

1976 (1)

1975 (1)

D. Gloge, I. P. Kaminow, H. M. Presby, “Profile dispersion in multimode fibers: measurement and analysis,” Electron. Lett. 11, 469–470 (1975).
[Crossref]

1974 (1)

T. Okoshi, K. Okamoto, “Analysis of wave propagation in inhomogeneous optical fibers using a variational method,” IEEE Trans. Microwave Theory Tech. MTT-22, 938–945 (1974).
[Crossref]

1973 (1)

D. Gloge, E. A. J. Marcatili, “Multimode theory of graded-core fibers,” Bell Syst. Tech. J. 52, 1563–1578 (1973).

1968 (1)

S. Kawakami, J. Nishizawa, “An optical waveguide with the optimum distribution of the refractive index with reference to waveform distortion,” IEEE Trans. Microwave Theory Tech. MTT-16, 814–818 (1968).
[Crossref]

Bianciardi, E.

E. Bianciardi, V. Rizzoli, “Propagation in graded-core fibres: a unified numerical description,” Opt. Quantum Electron. 9, 121–133 (1977).
[Crossref]

Eguchi, M.

M. Eguchi, M. Koshiba, Y. Tsuji, “Dispersion compensation based on dual-mode optical fiber with inhomogeneous profile core,” J. Lightwave Technol. 14, 2387–2394 (1996).
[Crossref]

Gloge, D.

D. Gloge, I. P. Kaminow, H. M. Presby, “Profile dispersion in multimode fibers: measurement and analysis,” Electron. Lett. 11, 469–470 (1975).
[Crossref]

D. Gloge, E. A. J. Marcatili, “Multimode theory of graded-core fibers,” Bell Syst. Tech. J. 52, 1563–1578 (1973).

Ishigure, T.

Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded-index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
[Crossref]

T. Ishigure, E. Nihei, Y. Koike, “Graded-index polymer optical fiber for high-speed data communication,” Appl. Opt. 33, 4261–4266 (1994).
[Crossref] [PubMed]

Kaminow, I.

I. Kaminow, D. Marcuse, H. M. Presby, “Multimode fiber bandwidth: theory and practice,” Proc. IEEE 68, 1209–1213 (1980).
[Crossref]

Kaminow, I. P.

D. Gloge, I. P. Kaminow, H. M. Presby, “Profile dispersion in multimode fibers: measurement and analysis,” Electron. Lett. 11, 469–470 (1975).
[Crossref]

Kawakami, S.

S. Kawakami, J. Nishizawa, “An optical waveguide with the optimum distribution of the refractive index with reference to waveform distortion,” IEEE Trans. Microwave Theory Tech. MTT-16, 814–818 (1968).
[Crossref]

Keck, D. B.

Koike, Y.

Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded-index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
[Crossref]

T. Ishigure, E. Nihei, Y. Koike, “Graded-index polymer optical fiber for high-speed data communication,” Appl. Opt. 33, 4261–4266 (1994).
[Crossref] [PubMed]

Y. Koike, “High-bandwidth graded-index polymer optical fibre,” Polymer 32, 1737–1745 (1991).
[Crossref]

Koshiba, M.

M. Eguchi, M. Koshiba, Y. Tsuji, “Dispersion compensation based on dual-mode optical fiber with inhomogeneous profile core,” J. Lightwave Technol. 14, 2387–2394 (1996).
[Crossref]

Marcatili, E. A. J.

E. A. J. Marcatili, “Modal dispersion in optical fibers with arbitrary numerical aperture and profile dispersion,” Bell Syst. Tech. J. 56, 49–63 (1977).

D. Gloge, E. A. J. Marcatili, “Multimode theory of graded-core fibers,” Bell Syst. Tech. J. 52, 1563–1578 (1973).

Marcuse, D.

I. Kaminow, D. Marcuse, H. M. Presby, “Multimode fiber bandwidth: theory and practice,” Proc. IEEE 68, 1209–1213 (1980).
[Crossref]

D. Marcuse, “Calculation of bandwidth from index profiles of optical fibers. 1: Theory,” Appl. Opt. 18, 2073–2080 (1979).
[Crossref] [PubMed]

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, San Diego, Calif., 1991).

Morishita, K.

K. Morishita, “Numerical analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-29, 348–352 (1981).
[Crossref]

Nihei, E.

Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded-index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
[Crossref]

T. Ishigure, E. Nihei, Y. Koike, “Graded-index polymer optical fiber for high-speed data communication,” Appl. Opt. 33, 4261–4266 (1994).
[Crossref] [PubMed]

Nishizawa, J.

S. Kawakami, J. Nishizawa, “An optical waveguide with the optimum distribution of the refractive index with reference to waveform distortion,” IEEE Trans. Microwave Theory Tech. MTT-16, 814–818 (1968).
[Crossref]

Okamoto, K.

K. Okamoto, “Comparison of calculated and measured impulse responses of optical fibers,” Appl. Opt. 18, 2199–2206 (1979).
[Crossref] [PubMed]

T. Okoshi, K. Okamoto, “Analysis of wave propagation in inhomogeneous optical fibers using a variational method,” IEEE Trans. Microwave Theory Tech. MTT-22, 938–945 (1974).
[Crossref]

Okoshi, T.

K. Oyamada, T. Okoshi, “High-accuracy numerical data on propagation characteristics of α-power graded-core fibers,” IEEE Trans. Microwave Theory Tech. MTT-28, 1113–1118 (1980).
[Crossref]

T. Okoshi, K. Okamoto, “Analysis of wave propagation in inhomogeneous optical fibers using a variational method,” IEEE Trans. Microwave Theory Tech. MTT-22, 938–945 (1974).
[Crossref]

Olshansky, R.

Oyamada, K.

K. Oyamada, T. Okoshi, “High-accuracy numerical data on propagation characteristics of α-power graded-core fibers,” IEEE Trans. Microwave Theory Tech. MTT-28, 1113–1118 (1980).
[Crossref]

Presby, H. M.

I. Kaminow, D. Marcuse, H. M. Presby, “Multimode fiber bandwidth: theory and practice,” Proc. IEEE 68, 1209–1213 (1980).
[Crossref]

D. Gloge, I. P. Kaminow, H. M. Presby, “Profile dispersion in multimode fibers: measurement and analysis,” Electron. Lett. 11, 469–470 (1975).
[Crossref]

Rizzoli, V.

E. Bianciardi, V. Rizzoli, “Propagation in graded-core fibres: a unified numerical description,” Opt. Quantum Electron. 9, 121–133 (1977).
[Crossref]

Tsuji, Y.

M. Eguchi, M. Koshiba, Y. Tsuji, “Dispersion compensation based on dual-mode optical fiber with inhomogeneous profile core,” J. Lightwave Technol. 14, 2387–2394 (1996).
[Crossref]

Appl. Opt. (5)

Bell Syst. Tech. J. (2)

E. A. J. Marcatili, “Modal dispersion in optical fibers with arbitrary numerical aperture and profile dispersion,” Bell Syst. Tech. J. 56, 49–63 (1977).

D. Gloge, E. A. J. Marcatili, “Multimode theory of graded-core fibers,” Bell Syst. Tech. J. 52, 1563–1578 (1973).

Electron. Lett. (1)

D. Gloge, I. P. Kaminow, H. M. Presby, “Profile dispersion in multimode fibers: measurement and analysis,” Electron. Lett. 11, 469–470 (1975).
[Crossref]

IEEE Trans. Microwave Theory Tech. (4)

S. Kawakami, J. Nishizawa, “An optical waveguide with the optimum distribution of the refractive index with reference to waveform distortion,” IEEE Trans. Microwave Theory Tech. MTT-16, 814–818 (1968).
[Crossref]

K. Oyamada, T. Okoshi, “High-accuracy numerical data on propagation characteristics of α-power graded-core fibers,” IEEE Trans. Microwave Theory Tech. MTT-28, 1113–1118 (1980).
[Crossref]

K. Morishita, “Numerical analysis of pulse broadening in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-29, 348–352 (1981).
[Crossref]

T. Okoshi, K. Okamoto, “Analysis of wave propagation in inhomogeneous optical fibers using a variational method,” IEEE Trans. Microwave Theory Tech. MTT-22, 938–945 (1974).
[Crossref]

J. Lightwave Technol. (2)

Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded-index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
[Crossref]

M. Eguchi, M. Koshiba, Y. Tsuji, “Dispersion compensation based on dual-mode optical fiber with inhomogeneous profile core,” J. Lightwave Technol. 14, 2387–2394 (1996).
[Crossref]

Opt. Quantum Electron. (1)

E. Bianciardi, V. Rizzoli, “Propagation in graded-core fibres: a unified numerical description,” Opt. Quantum Electron. 9, 121–133 (1977).
[Crossref]

Polymer (1)

Y. Koike, “High-bandwidth graded-index polymer optical fibre,” Polymer 32, 1737–1745 (1991).
[Crossref]

Proc. IEEE (1)

I. Kaminow, D. Marcuse, H. M. Presby, “Multimode fiber bandwidth: theory and practice,” Proc. IEEE 68, 1209–1213 (1980).
[Crossref]

Other (1)

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, San Diego, Calif., 1991).

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Figures (6)

Fig. 1
Fig. 1

Convergence behavior in the calculation of the effective index for the LP0M modes at ν = 320.571: (a) step-index profile and (b) parabolic-index profile.

Fig. 2
Fig. 2

Convergence behavior in the calculation of the effective index for the LP0M modes at ν = 534.284: (a) step-index profile and (b) parabolic-index profile.

Fig. 3
Fig. 3

Total number of guided modes versus the ν value. The filled circles represent the results computed with the WKB method.

Fig. 4
Fig. 4

Normalized propagation constant b versus the principal mode number at ν = 534.284: (a) step-index profile, (b) parabolic-index profile, (c) triangular-index profile.

Fig. 5
Fig. 5

Refractive-index profile with sinusoidal fluctuations for (a) f(r) = r/ a and (b) f(r) = 1 - r/ a.

Fig. 6
Fig. 6

Maximum effective-index difference among the LP modes in each principal mode group versus the principal mode number at ν = 534.284.

Equations (13)

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1rddrr dϕdr+k02n2-β2-l2r2ϕ=0,
F=-Γ ϕ*ψdΓ,Ωdϕ*drdϕdr+l2r2+β2-k02n2ϕ*ϕdΩ
Kϕ-k02Tϕ=ψ,
K=2π eer dNdrdNTdr+l2rNNT+β2rNNTdr,
T=2π ee n2rNNTdr,
ψ=002πaψa,
ψa=wKlwaKlw ϕa,
Aϕ=0,
A=K+00000000-2πwlw-Kl+1wKlw-k02T.
|A|=0.
Klw=2l-1Kl-1ww+Kl-2w.
C l-1!w2l,
nr=n11-2Δra2-0.05fr×sin2π×50 ra1/2.

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