Abstract

The power-flow equation is employed to calculate bandwidth of step-index plastic optical fibers (POFs) for different launch conditions. The outcome specifies bandwidth as a function of the mean input angle and width of the launch-beam distribution. For small distribution widths, bandwidth is shown to decrease with increasing mean input angle of the launch-beam distribution. For large distribution widths, bandwidth becomes independent of the launch angle. Launch-beam distribution, mode-dependent attenuation, and mode dispersion and coupling in POFs strongly influence the bandwidth of data transmission systems.

© 2013 Optical Society of America

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References

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  1. T. Ishigure, M. Kano, and Y. Koike, “Which is a more serious factor to the bandwidth of GI POF: differential mode attenuation or mode coupling?,” J. Lightwave Technol. 18, 959–965 (2000).
    [CrossRef]
  2. S. E. Golowich, W. White, W. A. Reed, and E. Knudsen, “Quantitative estimates of mode coupling and differential modal attenuation in perfluorinated graded-index plastic optical fiber,” J. Lightwave Technol. 21, 111–121 (2003).
    [CrossRef]
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    [CrossRef]
  4. C. Koeppen, R. F. Shi, W. D. Chen, and A. F. Garito, “Properties of plastic optical fibers,” J. Opt. Soc. Am. B 15, 727–739 (1998).
    [CrossRef]
  5. D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).
  6. J. Mateo, M. A. Losada, and J. Zubía, “Frequency response in step index plastic optical fibers obtained from the generalized power flow equation,” Opt. Express 17, 2850–2860 (2009).
    [CrossRef]
  7. D. Gloge, “Impulse response of clad optical multimode fibers,” Bell Syst. Tech. J. 52, 801–816 (1973).
  8. J. Siuzdak and G. Stepniak, “Influence of modal filtering on the bandwidth of multimode optical fibers,” Opt. Appl. 37, 31–39 (2007).
  9. H. Mrabet, I. Dayoub, R. Attia, and W. Hamouda, “Wavelength and beam launching effects on silica optical fiber in local area networks,” Opt. Commun. 283, 4234–4241 (2010).
    [CrossRef]
  10. H.-H. Lu, G.-L. Chen, Y.-W. Chuang, J. C.-C. Tsai, and C.-P. Chuang, “Improvement of radio-on-multimode fiber systems based on light injection and optoelectronic feedback techniques,” Opt. Commun. 266, 495–499 (2006).
    [CrossRef]
  11. B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response and bandwidth of step-index plastic optical fibres using the time-dependent power flow equation,” Phys. Scripta T149, 014028 (2012).
    [CrossRef]
  12. B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response of step-index plastic optical fibers using the time-dependent power flow equation,” Opt. Lasers Eng. 49, 618–622 (2011).
    [CrossRef]
  13. B. Drljača, A. Djordjevich, and S. Savović, “Frequency response in step-index plastic optical fibers obtained by numerical solution of the time-dependent power flow equation,” Opt. Laser Technol. 44, 1808–1812 (2012).
    [CrossRef]
  14. M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theor. Tech. 25, 577–585 (1977).
    [CrossRef]
  15. J. D. Anderson, Computational Fluid Dynamics (McGraw-Hill, 1995).
  16. A. Djordjevich and S. Savović, “Investigation of mode coupling in step index plastic optical fibers using the power flow equation,” IEEE Photonics Technol. Lett. 12, 1489–1491 (2000).
    [CrossRef]
  17. J. Mateo, M. A. Losada, I. Garcés, and J. Zubía, “Global characterization of optical power propagation in step-index plastic optical fibers,” Opt. Express 14, 9028–9035 (2006).
    [CrossRef]
  18. W. A. Gambling, D. N. Payne, and H. Matsumura, “Mode conversion coefficients in optical fibers,” Appl. Opt. 14, 1538–1542 (1975).
    [CrossRef]
  19. J. Dugas and G. Maurel, “Mode-coupling processes in polymethyl methacrylate-core optical fibers,” Appl. Opt. 31, 5069–5079 (1992).
    [CrossRef]
  20. L. Jeunhomme, M. Fraise, and J. P. Pocholle, “Propagation model for long step-index optical fibers,” Appl. Opt. 15, 3040–3046 (1976).
    [CrossRef]
  21. A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
    [CrossRef]
  22. N. Raptis, E. Grivas, E. Pikasis, and D. Syvridis, “Space-time block code based MIMO encoding for large core step index plastic optical fiber transmission systems,” Opt. Express 19, 10336–10350 (2011).
    [CrossRef]
  23. S. Savović and A. Djordjevich, “Influence of the angle-dependence of mode coupling on optical power distribution in step-index plastic optical fibers,” Opt. Laser Technol. 44, 180–184 (2012).
    [CrossRef]

2012 (3)

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response and bandwidth of step-index plastic optical fibres using the time-dependent power flow equation,” Phys. Scripta T149, 014028 (2012).
[CrossRef]

B. Drljača, A. Djordjevich, and S. Savović, “Frequency response in step-index plastic optical fibers obtained by numerical solution of the time-dependent power flow equation,” Opt. Laser Technol. 44, 1808–1812 (2012).
[CrossRef]

S. Savović and A. Djordjevich, “Influence of the angle-dependence of mode coupling on optical power distribution in step-index plastic optical fibers,” Opt. Laser Technol. 44, 180–184 (2012).
[CrossRef]

2011 (2)

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response of step-index plastic optical fibers using the time-dependent power flow equation,” Opt. Lasers Eng. 49, 618–622 (2011).
[CrossRef]

N. Raptis, E. Grivas, E. Pikasis, and D. Syvridis, “Space-time block code based MIMO encoding for large core step index plastic optical fiber transmission systems,” Opt. Express 19, 10336–10350 (2011).
[CrossRef]

2010 (1)

H. Mrabet, I. Dayoub, R. Attia, and W. Hamouda, “Wavelength and beam launching effects on silica optical fiber in local area networks,” Opt. Commun. 283, 4234–4241 (2010).
[CrossRef]

2009 (1)

2007 (1)

J. Siuzdak and G. Stepniak, “Influence of modal filtering on the bandwidth of multimode optical fibers,” Opt. Appl. 37, 31–39 (2007).

2006 (2)

H.-H. Lu, G.-L. Chen, Y.-W. Chuang, J. C.-C. Tsai, and C.-P. Chuang, “Improvement of radio-on-multimode fiber systems based on light injection and optoelectronic feedback techniques,” Opt. Commun. 266, 495–499 (2006).
[CrossRef]

J. Mateo, M. A. Losada, I. Garcés, and J. Zubía, “Global characterization of optical power propagation in step-index plastic optical fibers,” Opt. Express 14, 9028–9035 (2006).
[CrossRef]

2003 (1)

2000 (2)

T. Ishigure, M. Kano, and Y. Koike, “Which is a more serious factor to the bandwidth of GI POF: differential mode attenuation or mode coupling?,” J. Lightwave Technol. 18, 959–965 (2000).
[CrossRef]

A. Djordjevich and S. Savović, “Investigation of mode coupling in step index plastic optical fibers using the power flow equation,” IEEE Photonics Technol. Lett. 12, 1489–1491 (2000).
[CrossRef]

1998 (2)

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[CrossRef]

C. Koeppen, R. F. Shi, W. D. Chen, and A. F. Garito, “Properties of plastic optical fibers,” J. Opt. Soc. Am. B 15, 727–739 (1998).
[CrossRef]

1996 (1)

P. E. Green, “Optical networking update,” IEEE J. Sel. Areas Commun. 14, 764–779 (1996).
[CrossRef]

1992 (1)

1977 (1)

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

1976 (1)

1975 (1)

1973 (1)

D. Gloge, “Impulse response of clad optical multimode fibers,” Bell Syst. Tech. J. 52, 801–816 (1973).

1972 (1)

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

Anderson, J. D.

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

Attia, R.

H. Mrabet, I. Dayoub, R. Attia, and W. Hamouda, “Wavelength and beam launching effects on silica optical fiber in local area networks,” Opt. Commun. 283, 4234–4241 (2010).
[CrossRef]

Chen, G.-L.

H.-H. Lu, G.-L. Chen, Y.-W. Chuang, J. C.-C. Tsai, and C.-P. Chuang, “Improvement of radio-on-multimode fiber systems based on light injection and optoelectronic feedback techniques,” Opt. Commun. 266, 495–499 (2006).
[CrossRef]

Chen, W. D.

Chuang, C.-P.

H.-H. Lu, G.-L. Chen, Y.-W. Chuang, J. C.-C. Tsai, and C.-P. Chuang, “Improvement of radio-on-multimode fiber systems based on light injection and optoelectronic feedback techniques,” Opt. Commun. 266, 495–499 (2006).
[CrossRef]

Chuang, Y.-W.

H.-H. Lu, G.-L. Chen, Y.-W. Chuang, J. C.-C. Tsai, and C.-P. Chuang, “Improvement of radio-on-multimode fiber systems based on light injection and optoelectronic feedback techniques,” Opt. Commun. 266, 495–499 (2006).
[CrossRef]

Dayoub, I.

H. Mrabet, I. Dayoub, R. Attia, and W. Hamouda, “Wavelength and beam launching effects on silica optical fiber in local area networks,” Opt. Commun. 283, 4234–4241 (2010).
[CrossRef]

Djordjevich, A.

S. Savović and A. Djordjevich, “Influence of the angle-dependence of mode coupling on optical power distribution in step-index plastic optical fibers,” Opt. Laser Technol. 44, 180–184 (2012).
[CrossRef]

B. Drljača, A. Djordjevich, and S. Savović, “Frequency response in step-index plastic optical fibers obtained by numerical solution of the time-dependent power flow equation,” Opt. Laser Technol. 44, 1808–1812 (2012).
[CrossRef]

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response and bandwidth of step-index plastic optical fibres using the time-dependent power flow equation,” Phys. Scripta T149, 014028 (2012).
[CrossRef]

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response of step-index plastic optical fibers using the time-dependent power flow equation,” Opt. Lasers Eng. 49, 618–622 (2011).
[CrossRef]

A. Djordjevich and S. Savović, “Investigation of mode coupling in step index plastic optical fibers using the power flow equation,” IEEE Photonics Technol. Lett. 12, 1489–1491 (2000).
[CrossRef]

Drljaca, B.

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response and bandwidth of step-index plastic optical fibres using the time-dependent power flow equation,” Phys. Scripta T149, 014028 (2012).
[CrossRef]

B. Drljača, A. Djordjevich, and S. Savović, “Frequency response in step-index plastic optical fibers obtained by numerical solution of the time-dependent power flow equation,” Opt. Laser Technol. 44, 1808–1812 (2012).
[CrossRef]

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response of step-index plastic optical fibers using the time-dependent power flow equation,” Opt. Lasers Eng. 49, 618–622 (2011).
[CrossRef]

Dugas, J.

Fraise, M.

Gambling, W. A.

Gao, R.

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[CrossRef]

Garcés, I.

Garito, A. F.

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[CrossRef]

C. Koeppen, R. F. Shi, W. D. Chen, and A. F. Garito, “Properties of plastic optical fibers,” J. Opt. Soc. Am. B 15, 727–739 (1998).
[CrossRef]

Gloge, D.

D. Gloge, “Impulse response of clad optical multimode fibers,” Bell Syst. Tech. J. 52, 801–816 (1973).

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

Golowich, S. E.

Green, P. E.

P. E. Green, “Optical networking update,” IEEE J. Sel. Areas Commun. 14, 764–779 (1996).
[CrossRef]

Grivas, E.

Hamouda, W.

H. Mrabet, I. Dayoub, R. Attia, and W. Hamouda, “Wavelength and beam launching effects on silica optical fiber in local area networks,” Opt. Commun. 283, 4234–4241 (2010).
[CrossRef]

Ishigure, T.

Jeunhomme, L.

M. Rousseau and L. Jeunhomme, “Numerical solution of the coupled-power equation in step index optical fibers,” IEEE Trans. Microwave Theor. 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]

Kano, M.

Knudsen, E.

Koeppen, C.

Koike, Y.

Losada, M. A.

Lu, H.-H.

H.-H. Lu, G.-L. Chen, Y.-W. Chuang, J. C.-C. Tsai, and C.-P. Chuang, “Improvement of radio-on-multimode fiber systems based on light injection and optoelectronic feedback techniques,” Opt. Commun. 266, 495–499 (2006).
[CrossRef]

Mateo, J.

Matsumura, H.

Maurel, G.

Mrabet, H.

H. Mrabet, I. Dayoub, R. Attia, and W. Hamouda, “Wavelength and beam launching effects on silica optical fiber in local area networks,” Opt. Commun. 283, 4234–4241 (2010).
[CrossRef]

Payne, D. N.

Pikasis, E.

Pocholle, J. P.

Raptis, N.

Reed, W. A.

Rousseau, M.

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

Savovic, S.

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response and bandwidth of step-index plastic optical fibres using the time-dependent power flow equation,” Phys. Scripta T149, 014028 (2012).
[CrossRef]

B. Drljača, A. Djordjevich, and S. Savović, “Frequency response in step-index plastic optical fibers obtained by numerical solution of the time-dependent power flow equation,” Opt. Laser Technol. 44, 1808–1812 (2012).
[CrossRef]

S. Savović and A. Djordjevich, “Influence of the angle-dependence of mode coupling on optical power distribution in step-index plastic optical fibers,” Opt. Laser Technol. 44, 180–184 (2012).
[CrossRef]

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response of step-index plastic optical fibers using the time-dependent power flow equation,” Opt. Lasers Eng. 49, 618–622 (2011).
[CrossRef]

A. Djordjevich and S. Savović, “Investigation of mode coupling in step index plastic optical fibers using the power flow equation,” IEEE Photonics Technol. Lett. 12, 1489–1491 (2000).
[CrossRef]

Shi, R. F.

Siuzdak, J.

J. Siuzdak and G. Stepniak, “Influence of modal filtering on the bandwidth of multimode optical fibers,” Opt. Appl. 37, 31–39 (2007).

Stepniak, G.

J. Siuzdak and G. Stepniak, “Influence of modal filtering on the bandwidth of multimode optical fibers,” Opt. Appl. 37, 31–39 (2007).

Syvridis, D.

Tsai, J. C.-C.

H.-H. Lu, G.-L. Chen, Y.-W. Chuang, J. C.-C. Tsai, and C.-P. Chuang, “Improvement of radio-on-multimode fiber systems based on light injection and optoelectronic feedback techniques,” Opt. Commun. 266, 495–499 (2006).
[CrossRef]

Wang, J.

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[CrossRef]

White, W.

Zubía, J.

Appl. Opt. (3)

Bell Syst. Tech. J. (2)

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

D. Gloge, “Impulse response of clad optical multimode fibers,” Bell Syst. Tech. J. 52, 801–816 (1973).

IEEE J. Sel. Areas Commun. (1)

P. E. Green, “Optical networking update,” IEEE J. Sel. Areas Commun. 14, 764–779 (1996).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

A. Djordjevich and S. Savović, “Investigation of mode coupling in step index plastic optical fibers using the power flow equation,” IEEE Photonics Technol. Lett. 12, 1489–1491 (2000).
[CrossRef]

IEEE Trans. Microwave Theor. Tech. (1)

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

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Opt. Appl. (1)

J. Siuzdak and G. Stepniak, “Influence of modal filtering on the bandwidth of multimode optical fibers,” Opt. Appl. 37, 31–39 (2007).

Opt. Commun. (2)

H. Mrabet, I. Dayoub, R. Attia, and W. Hamouda, “Wavelength and beam launching effects on silica optical fiber in local area networks,” Opt. Commun. 283, 4234–4241 (2010).
[CrossRef]

H.-H. Lu, G.-L. Chen, Y.-W. Chuang, J. C.-C. Tsai, and C.-P. Chuang, “Improvement of radio-on-multimode fiber systems based on light injection and optoelectronic feedback techniques,” Opt. Commun. 266, 495–499 (2006).
[CrossRef]

Opt. Express (3)

Opt. Laser Technol. (2)

B. Drljača, A. Djordjevich, and S. Savović, “Frequency response in step-index plastic optical fibers obtained by numerical solution of the time-dependent power flow equation,” Opt. Laser Technol. 44, 1808–1812 (2012).
[CrossRef]

S. Savović and A. Djordjevich, “Influence of the angle-dependence of mode coupling on optical power distribution in step-index plastic optical fibers,” Opt. Laser Technol. 44, 180–184 (2012).
[CrossRef]

Opt. Lasers Eng. (1)

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response of step-index plastic optical fibers using the time-dependent power flow equation,” Opt. Lasers Eng. 49, 618–622 (2011).
[CrossRef]

Phys. Scripta (1)

B. Drljača, S. Savović, and A. Djordjevich, “Calculation of the frequency response and bandwidth of step-index plastic optical fibres using the time-dependent power flow equation,” Phys. Scripta T149, 014028 (2012).
[CrossRef]

Science (1)

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[CrossRef]

Other (1)

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

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Figures (6)

Fig. 1.
Fig. 1.

Bandwidth versus fiber length for GH fiber for four Gaussian input angles θ0=0° (solid curve), 5° (dashed curve), 10° (dotted curve), and 15° (dot-dashed curve) with FWHMz=0=7.5°: numerical results.

Fig. 2.
Fig. 2.

Bandwidth versus fiber length for HFBR fiber for four Gaussian input angles θ0=0° (solid curve), 5° (dashed curve), 10° (dotted curve), and 15° (dot-dashed curve) with FWHMz=0=7.5°: numerical results.

Fig. 3.
Fig. 3.

Bandwidth versus fiber length for GH fiber for four Gaussian input angles θ0=0° (solid curve), 5° (dashed curve), 10° (dotted curve), and 15° (dotted-dashed curve) with FWHMz=0=19°: numerical results.

Fig. 4.
Fig. 4.

Bandwidth versus fiber length for HFBR fiber for four Gaussian input angles θ0=0° (solid curve), 5° (dashed curve), 10° (dotted curve), and 15° (dot-dashed curve) with FWHMz=0=19°: numerical results.

Fig. 5.
Fig. 5.

Bandwidth versus fiber length for GH fiber for four Gaussian input angles θ0=0° (solid curve), 5° (dashed curve), 10° (dotted curve), and 15° (dot-dashed curve) with FWHMz=0=30°: numerical results.

Fig. 6.
Fig. 6.

Bandwidth versus fiber length for HFBR fiber for four Gaussian input angles θ0=0° (solid curve), 5° (dashed curve), 10° (dotted curve), and 15° (dot-dashed curve) with FWHMz=0=30°: numerical results.

Equations (19)

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

P(θ,z,t)z+tzP(θ,z,t)t=α(θ)P(θ,z,t)+1θθ[θD(θ)P(θ,z,t)θ],
P(θ,z,t)z+tzP(θ,z,t)t=Aθ2P(θ,z,t)+Dθθ[θP(θ,z,t)θ].
dzdt=cn(1+θ2/2).
P(θ,z,t)z=Aθ2P(θ,z,t)n2cθ2P(θ,z,t)t+Dθθ(θP(θ,z,t)θ).
p(θ,z,ω)=P(θ,z,t)ejωtdt,
p(θ,z,ω)z=[Aθ2+jωn2cθ2]p(θ,z,ω)+Dθp(θ,z,ω)θ+D(θ2p(θ,z,ω)θ2),
p(θc,z,ω)=0,Dp(θ,z,ω)θ|θ=0=0,
P(θ,z=0)=exp[(θθ0)2σ2],
prz=Aθ2pr+Dθprθ+D2prθ2+ωn2cθ2pi,
piz=Aθ2pi+Dθpiθ+D2piθ2ωn2cθ2pr.
H(z,ω)=2π0θcθ[pr(θ,z,ω)+jpi(θ,z,ω)]dθ2π0θcθ[pr(θ,0,ω)+jpi(θ,0,ω)]dθ.
(p(θ,z,ω)θ)k,l=pk+1,lpk1,l2Δθ+O(Δθ)2,
(2p(θ,z,ω)θ2)k,l=pk+1,l2pk,l+pk1,l(Δθ)2+O(Δθ)2,
(p(θ,z,ω)z)k,l=pk,l+1pk,lΔz+O(Δz),
pk,l+1r=(ΔzDΔθ2ΔzD2θkΔθ)pk1,lr+(12ΔzDΔθ2ΔzAθk2)pk,lr+(ΔzD2θkΔθ+ΔzDΔθ2)pk+1,lr+ωnΔz2cθk2pk,li
pk,l+1i=(ΔzDΔθ2ΔzD2θkΔθ)pk1,li+(12ΔzDΔθ2ΔzAθk2)pk,li+(ΔzD2θkΔθ+ΔzDΔθ2)pk+1,liωnΔz2cθk2pk,lr.
pN,lr=0,pN,li=0andp0,lr=p1,lr,p0,li=p1,li,
limθ01θθ(θpθ)=22pθ2|θ=0.
pk,l=0r=exp[(θkθ0)2σ2],0θkθc

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