Abstract

For different depth and width of the intermediate layer, a power flow equation is used to calculate spatial transients and steady state of power distribution in W-type optical fibers (doubly clad fibers with three layers). A numerical solution has been obtained by the explicit finite difference method. Results show how the power distribution in W-type optical fibers varies with the depth of the intermediate layer for different values of intermediate layer width and coupling strength. We have found that with increasing depth of the intermediate layer, the fiber length at which the steady-state distribution is achieved increases. Such characterization of these fibers is consistent with their manifested effectiveness in reducing modal dispersion and improving bandwidth.

© 2012 Optical Society of America

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  1. E. J. Tyler, M. Webster, R. V. Penty, I. H. White, S. Yu, and J. Rorison, “Subcarrier modulated transmission of 2.5  Gb/s over 300 m of 62.5 μm-core diameter multimode fiber,” IEEE Photon. Technol. Lett. 14, 1743–1745 (2002).
    [CrossRef]
  2. K. M. Patel and S. E. Ralph, “Enhanched multimode fiber link performance using a spatially resolved receiver,” IEEE Photon. Tech. Lett. 14, 393–395 (2002).
    [CrossRef]
  3. X. Zhao and F. S. Choa, “Demonstration of 10  Gb/s transmission over 1.5 km-long multimde fiber using equalization techniques,” IEEE Photon. Tech. Lett. 14, 1187–1189 (2002).
    [CrossRef]
  4. J. S. Abbott, G. E. Smith, and C. M. Truesdale, “Multimode fiber link dispersion compensator,” U.S. patent 6,363,195 (26 March 2002).
  5. T. Ishigure, M. Kano, and Y. Koike, “Which is more serious factor to the bandwidth of GI POF: differential mode attenuation or mode coupling?,” J. Lightwave Technol. 18, 959–965 (2000).
    [CrossRef]
  6. S. Kawakami and S. Nishida, “Characteristics of a doubly-clad optical fiber with a low-index inner cladding,” IEEE J. Sel. Top. Quantum Electron. 10, 879–887 (1974).
    [CrossRef]
  7. K. Mikoshiba, and H. Kajioka, “Transmission characteristics of multimode W-type optical fiber: experimental study of the effect of the intermediate layer,” Appl. Opt. 17, 2836–2841 (1978).
    [CrossRef]
  8. T. Tanaka, S. Yamada, M. Sumi, and K. Mikoshiba, “Microbending losses of doubly clad (W-type) optical fibers,” Appl. Opt. 16, 2391–2394 (1977).
    [CrossRef]
  9. W. Daum, J. Krauser, P. E. Zamzow, and O. Ziemann, Polymer Optical Fibers for Data Communication (Springer, 2002).
  10. T. Yamashita and M. Kagami, “Fabrication of light-induced self-written waveguides with a W-shaped refractive index profile,” J. Lightwave Technol. 23, 2542–2548 (2005).
    [CrossRef]
  11. M. A. Losada, I. Garcés, J. Mateo, I. Salinas, J. Lou, and J. Zubía, “Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers,” J.Lightwave Technol. 20, 1160–1164 (2002).
    [CrossRef]
  12. K. Takahashi, T. Ishigure, and Y. Koike, “Index profile design for high-bandwidth W-shaped plastic optical fiber,” J. Lightwave Technol. 24, 2867–2876 (2006).
    [CrossRef]
  13. D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).
  14. M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theory Tech. 25, 577–585 (1977).
    [CrossRef]
  15. T. P. Tanaka and S. Yamada, “Numerical solution of power flow equation in multimde W-type optical fibers,” Appl. Opt. 19, 1647–1652 (1980).
    [CrossRef]
  16. T. P. Tanaka and S. Yamada, “Steady-state characteristics of multimode W-type fibers,” Appl. Opt. 18, 3261–3264(1979).
    [CrossRef]
  17. L. Jeunhomme, M. Fraise, and J. P. Pocholle, “Propagation model for long step-index optical fibers,” Appl. Opt. 15, 3040–3046 (1976).
    [CrossRef]
  18. A. Djordjevich and S. Savović, “Numerical solution of the power flow equation in step index plastic optical fibers,” J. Opt. Soc. Am. B 21, 1437–1442 (2004).
    [CrossRef]
  19. S. Savović, A. Simović, and A. Djordjevich, “Explicit finite difference solution of the power flow equation in W-type optical fibers,” Opt. Laser Technol. 44, 1786–1790 (2012).
    [CrossRef]
  20. J. D. Anderson, Computational Fluid Dynamics (McGraw-Hill, 1995).

2012

S. Savović, A. Simović, and A. Djordjevich, “Explicit finite difference solution of the power flow equation in W-type optical fibers,” Opt. Laser Technol. 44, 1786–1790 (2012).
[CrossRef]

2006

2005

2004

2002

M. A. Losada, I. Garcés, J. Mateo, I. Salinas, J. Lou, and J. Zubía, “Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers,” J.Lightwave Technol. 20, 1160–1164 (2002).
[CrossRef]

E. J. Tyler, M. Webster, R. V. Penty, I. H. White, S. Yu, and J. Rorison, “Subcarrier modulated transmission of 2.5  Gb/s over 300 m of 62.5 μm-core diameter multimode fiber,” IEEE Photon. Technol. Lett. 14, 1743–1745 (2002).
[CrossRef]

K. M. Patel and S. E. Ralph, “Enhanched multimode fiber link performance using a spatially resolved receiver,” IEEE Photon. Tech. Lett. 14, 393–395 (2002).
[CrossRef]

X. Zhao and F. S. Choa, “Demonstration of 10  Gb/s transmission over 1.5 km-long multimde fiber using equalization techniques,” IEEE Photon. Tech. Lett. 14, 1187–1189 (2002).
[CrossRef]

2000

1980

1979

1978

1977

T. Tanaka, S. Yamada, M. Sumi, and K. Mikoshiba, “Microbending losses of doubly clad (W-type) optical fibers,” Appl. Opt. 16, 2391–2394 (1977).
[CrossRef]

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theory Tech. 25, 577–585 (1977).
[CrossRef]

1976

1974

S. Kawakami and S. Nishida, “Characteristics of a doubly-clad optical fiber with a low-index inner cladding,” IEEE J. Sel. Top. Quantum Electron. 10, 879–887 (1974).
[CrossRef]

1972

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).

Abbott, J. S.

J. S. Abbott, G. E. Smith, and C. M. Truesdale, “Multimode fiber link dispersion compensator,” U.S. patent 6,363,195 (26 March 2002).

Anderson, J. D.

J. D. Anderson, Computational Fluid Dynamics (McGraw-Hill, 1995).

Choa, F. S.

X. Zhao and F. S. Choa, “Demonstration of 10  Gb/s transmission over 1.5 km-long multimde fiber using equalization techniques,” IEEE Photon. Tech. Lett. 14, 1187–1189 (2002).
[CrossRef]

Daum, W.

W. Daum, J. Krauser, P. E. Zamzow, and O. Ziemann, Polymer Optical Fibers for Data Communication (Springer, 2002).

Djordjevich, A.

S. Savović, A. Simović, and A. Djordjevich, “Explicit finite difference solution of the power flow equation in W-type optical fibers,” Opt. Laser Technol. 44, 1786–1790 (2012).
[CrossRef]

A. Djordjevich and S. Savović, “Numerical solution of the power flow equation in step index plastic optical fibers,” J. Opt. Soc. Am. B 21, 1437–1442 (2004).
[CrossRef]

Fraise, M.

Garcés, I.

M. A. Losada, I. Garcés, J. Mateo, I. Salinas, J. Lou, and J. Zubía, “Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers,” J.Lightwave Technol. 20, 1160–1164 (2002).
[CrossRef]

Gloge, D.

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).

Ishigure, T.

Jeunhomme, L.

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theory Tech. 25, 577–585 (1977).
[CrossRef]

L. Jeunhomme, M. Fraise, and J. P. Pocholle, “Propagation model for long step-index optical fibers,” Appl. Opt. 15, 3040–3046 (1976).
[CrossRef]

Kagami, M.

Kajioka, H.

Kano, M.

Kawakami, S.

S. Kawakami and S. Nishida, “Characteristics of a doubly-clad optical fiber with a low-index inner cladding,” IEEE J. Sel. Top. Quantum Electron. 10, 879–887 (1974).
[CrossRef]

Koike, Y.

Krauser, J.

W. Daum, J. Krauser, P. E. Zamzow, and O. Ziemann, Polymer Optical Fibers for Data Communication (Springer, 2002).

Losada, M. A.

M. A. Losada, I. Garcés, J. Mateo, I. Salinas, J. Lou, and J. Zubía, “Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers,” J.Lightwave Technol. 20, 1160–1164 (2002).
[CrossRef]

Lou, J.

M. A. Losada, I. Garcés, J. Mateo, I. Salinas, J. Lou, and J. Zubía, “Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers,” J.Lightwave Technol. 20, 1160–1164 (2002).
[CrossRef]

Mateo, J.

M. A. Losada, I. Garcés, J. Mateo, I. Salinas, J. Lou, and J. Zubía, “Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers,” J.Lightwave Technol. 20, 1160–1164 (2002).
[CrossRef]

Mikoshiba, K.

Nishida, S.

S. Kawakami and S. Nishida, “Characteristics of a doubly-clad optical fiber with a low-index inner cladding,” IEEE J. Sel. Top. Quantum Electron. 10, 879–887 (1974).
[CrossRef]

Patel, K. M.

K. M. Patel and S. E. Ralph, “Enhanched multimode fiber link performance using a spatially resolved receiver,” IEEE Photon. Tech. Lett. 14, 393–395 (2002).
[CrossRef]

Penty, R. V.

E. J. Tyler, M. Webster, R. V. Penty, I. H. White, S. Yu, and J. Rorison, “Subcarrier modulated transmission of 2.5  Gb/s over 300 m of 62.5 μm-core diameter multimode fiber,” IEEE Photon. Technol. Lett. 14, 1743–1745 (2002).
[CrossRef]

Pocholle, J. P.

Ralph, S. E.

K. M. Patel and S. E. Ralph, “Enhanched multimode fiber link performance using a spatially resolved receiver,” IEEE Photon. Tech. Lett. 14, 393–395 (2002).
[CrossRef]

Rorison, J.

E. J. Tyler, M. Webster, R. V. Penty, I. H. White, S. Yu, and J. Rorison, “Subcarrier modulated transmission of 2.5  Gb/s over 300 m of 62.5 μm-core diameter multimode fiber,” IEEE Photon. Technol. Lett. 14, 1743–1745 (2002).
[CrossRef]

Rousseau, M.

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theory Tech. 25, 577–585 (1977).
[CrossRef]

Salinas, I.

M. A. Losada, I. Garcés, J. Mateo, I. Salinas, J. Lou, and J. Zubía, “Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers,” J.Lightwave Technol. 20, 1160–1164 (2002).
[CrossRef]

Savovic, S.

S. Savović, A. Simović, and A. Djordjevich, “Explicit finite difference solution of the power flow equation in W-type optical fibers,” Opt. Laser Technol. 44, 1786–1790 (2012).
[CrossRef]

A. Djordjevich and S. Savović, “Numerical solution of the power flow equation in step index plastic optical fibers,” J. Opt. Soc. Am. B 21, 1437–1442 (2004).
[CrossRef]

Simovic, A.

S. Savović, A. Simović, and A. Djordjevich, “Explicit finite difference solution of the power flow equation in W-type optical fibers,” Opt. Laser Technol. 44, 1786–1790 (2012).
[CrossRef]

Smith, G. E.

J. S. Abbott, G. E. Smith, and C. M. Truesdale, “Multimode fiber link dispersion compensator,” U.S. patent 6,363,195 (26 March 2002).

Sumi, M.

Takahashi, K.

Tanaka, T.

Tanaka, T. P.

Truesdale, C. M.

J. S. Abbott, G. E. Smith, and C. M. Truesdale, “Multimode fiber link dispersion compensator,” U.S. patent 6,363,195 (26 March 2002).

Tyler, E. J.

E. J. Tyler, M. Webster, R. V. Penty, I. H. White, S. Yu, and J. Rorison, “Subcarrier modulated transmission of 2.5  Gb/s over 300 m of 62.5 μm-core diameter multimode fiber,” IEEE Photon. Technol. Lett. 14, 1743–1745 (2002).
[CrossRef]

Webster, M.

E. J. Tyler, M. Webster, R. V. Penty, I. H. White, S. Yu, and J. Rorison, “Subcarrier modulated transmission of 2.5  Gb/s over 300 m of 62.5 μm-core diameter multimode fiber,” IEEE Photon. Technol. Lett. 14, 1743–1745 (2002).
[CrossRef]

White, I. H.

E. J. Tyler, M. Webster, R. V. Penty, I. H. White, S. Yu, and J. Rorison, “Subcarrier modulated transmission of 2.5  Gb/s over 300 m of 62.5 μm-core diameter multimode fiber,” IEEE Photon. Technol. Lett. 14, 1743–1745 (2002).
[CrossRef]

Yamada, S.

Yamashita, T.

Yu, S.

E. J. Tyler, M. Webster, R. V. Penty, I. H. White, S. Yu, and J. Rorison, “Subcarrier modulated transmission of 2.5  Gb/s over 300 m of 62.5 μm-core diameter multimode fiber,” IEEE Photon. Technol. Lett. 14, 1743–1745 (2002).
[CrossRef]

Zamzow, P. E.

W. Daum, J. Krauser, P. E. Zamzow, and O. Ziemann, Polymer Optical Fibers for Data Communication (Springer, 2002).

Zhao, X.

X. Zhao and F. S. Choa, “Demonstration of 10  Gb/s transmission over 1.5 km-long multimde fiber using equalization techniques,” IEEE Photon. Tech. Lett. 14, 1187–1189 (2002).
[CrossRef]

Ziemann, O.

W. Daum, J. Krauser, P. E. Zamzow, and O. Ziemann, Polymer Optical Fibers for Data Communication (Springer, 2002).

Zubía, J.

M. A. Losada, I. Garcés, J. Mateo, I. Salinas, J. Lou, and J. Zubía, “Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers,” J.Lightwave Technol. 20, 1160–1164 (2002).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).

IEEE J. Sel. Top. Quantum Electron.

S. Kawakami and S. Nishida, “Characteristics of a doubly-clad optical fiber with a low-index inner cladding,” IEEE J. Sel. Top. Quantum Electron. 10, 879–887 (1974).
[CrossRef]

IEEE Photon. Tech. Lett.

K. M. Patel and S. E. Ralph, “Enhanched multimode fiber link performance using a spatially resolved receiver,” IEEE Photon. Tech. Lett. 14, 393–395 (2002).
[CrossRef]

X. Zhao and F. S. Choa, “Demonstration of 10  Gb/s transmission over 1.5 km-long multimde fiber using equalization techniques,” IEEE Photon. Tech. Lett. 14, 1187–1189 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

E. J. Tyler, M. Webster, R. V. Penty, I. H. White, S. Yu, and J. Rorison, “Subcarrier modulated transmission of 2.5  Gb/s over 300 m of 62.5 μm-core diameter multimode fiber,” IEEE Photon. Technol. Lett. 14, 1743–1745 (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theory Tech. 25, 577–585 (1977).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

J.Lightwave Technol.

M. A. Losada, I. Garcés, J. Mateo, I. Salinas, J. Lou, and J. Zubía, “Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers,” J.Lightwave Technol. 20, 1160–1164 (2002).
[CrossRef]

Opt. Laser Technol.

S. Savović, A. Simović, and A. Djordjevich, “Explicit finite difference solution of the power flow equation in W-type optical fibers,” Opt. Laser Technol. 44, 1786–1790 (2012).
[CrossRef]

Other

J. D. Anderson, Computational Fluid Dynamics (McGraw-Hill, 1995).

W. Daum, J. Krauser, P. E. Zamzow, and O. Ziemann, Polymer Optical Fibers for Data Communication (Springer, 2002).

J. S. Abbott, G. E. Smith, and C. M. Truesdale, “Multimode fiber link dispersion compensator,” U.S. patent 6,363,195 (26 March 2002).

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Figures (8)

Fig. 1.
Fig. 1.

Refractive index profile of a W-type fiber [15].

Fig. 2.
Fig. 2.

Leaky mode loss for different intermediate layer depths.

Fig. 3.
Fig. 3.

Spatial transient of power distributions for Δq=0.525%, δ=0.2 and for the coupling coefficient D=2.3×107rad2/m (centrally launched input). Shown by dashed lines are the power distributions resulting when only the guided modes are excited and are excited equally (the θp excitation). Solid curves in the figures represent power distribution when guided and leaky modes are equally excited at the input fiber end (the θq excitation).

Fig. 4.
Fig. 4.

Spatial transient of power distributions for Δq=0.595%, δ=0.2 and for the coupling coefficient D=2.3×107rad2/m (centrally launched input). Shown by dashed lines are the power distributions resulting when only the guided modes are excited and are excited equally (the θp excitation). Solid curves in the figures represent power distribution when guided and leaky modes are equally excited at the input fiber end (the θq excitation).

Fig. 5.
Fig. 5.

Spatial transient of power distributions for Δq=0.7%, δ=0.2 and for the coupling coefficient D=2.3×107rad2/m (centrally launched input). Shown by dashed lines are the power distributions resulting when only the guided modes are excited and are excited equally (the θp excitation). Solid curves in the figures represent power distribution when guided and leaky modes are equally excited at the input fiber end (the θq excitation).

Fig. 6.
Fig. 6.

Spatial transient of power distributions for Δq=0.805%, δ=0.2 and for the coupling coefficient D=2.3×107rad2/m (centrally launched input). Shown by dashed lines are the power distributions resulting when only the guided modes are excited and are excited equally (the θp excitation). Solid curves in the figures represent power distribution when guided and leaky modes are equally excited at the input fiber end (the θq excitation).

Fig. 7.
Fig. 7.

Spatial transient of power distributions for Δq=0.875%, δ=0.2 and for the coupling coefficient D=2.3×107rad2/m (centrally launched input). Shown by dashed lines are the power distributions resulting when only the guided modes are excited and are excited equally (the θp excitation). Solid curves in the figures represent power distribution when guided and leaky modes are equally excited at the input fiber end (the θq excitation).

Fig. 8.
Fig. 8.

Fiber length zs at which the steady-state distribution is achieved. (Curves are drawn for visual aid.)

Tables (1)

Tables Icon

Table 1. W-type Fiber Length zs at which the Steady-state Distribution Is Achieved for Different Values of the Coupling Coefficient D, Intermediate Layer Width δ, and Intermediate Layer Depth Δq

Equations (9)

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

P(θ,z)z=α(θ)P(θ,z)+Dθθ(θP(θ,z)θ).
P(θ,z)z=α(θ)P(θ,z)+DθP(θ,z)θ+D2P(θ,z)θ2,
αL(θ)=4(θ2θp2)1/2a(1θ2)1/2θ2(θq2θ2)θq2(θq2θp2)exp[2δan0k0(θq2θ2)1/2],
αd(θ)={0θθpαL(θ)θp<θ<θqθθq.
Pk,l+1=(ΔzDΔθ2ΔzD2θkΔθ)Pk1,l+(12ΔzDΔθ2(αd)kΔz)Pk,l+(ΔzD2θkΔθ+ΔzDΔθ2)Pk+1,l,
(αd)k={0θkθp4(θk2θp2)1/2a(1θk2)1/2θk2(θq2θk2)θq2(θq2θp2)exp[2δan0k0(θq2θk2)1/2]θp<θk<θqθkθq.
limθ01θθ(θPθ)=22Pθ2|θ=0.
P(θ,0)=1,for0θθp;z=0,
P(θ,0)=1,for0θθq;z=0.

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