Abstract

Experimental and theoretical studies of the optical properties of large-core step-index plastic optical fibers (POF’s) and graded-index POF’s are reported. A set of criteria and analyses of physical parameters is developed in the context of major issues of POF applications in short-distance communication systems. Analyses are presented to show how the measured POF optical attenuation affects the overall performance in wavelength-division multiplexing and how the use of perfluorinated polymers can overcome limitations inherent in current POF materials. Results of POF optical bandwidth measurements by direct picosecond time-domain methods are reported, and their relationship to refractive-index profiles are theoretically analyzed by the WKB and finite-element methods. Two high-resolution optical techniques of refracted near-field and transverse interferometric methods are presented and are used to measure the index profiles of large-core POF’s. Results reveal that the index profile of currently available graded-index POF is not parabolic, which significantly limits its bandwidth compared with that of a true parabolic graded-index profile.

© 1998 Optical Society of America

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References

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  1. D. Hanson, “Wiring with plastic,” IEEE Lightwave Commun. Sys. 3, 34 (1992).
  2. P. E. Green, Jr., “Optical networking update,” IEEE J. Sel. Areas Commun. 14, 764 (1996).
    [CrossRef]
  3. T. Kaino, “Polymer optical fibers,” in Polymers for Lightwave and Integrated Optics, L. Hornak, ed. (Dekker, Dordrecht, The Netherlands, 1992).
  4. See, for example, R. Olshansky, “Propagation in glass optical waveguides,” Rev. Mod. Phys. 51, 341 (1979).
    [CrossRef]
  5. Y. Koike, “Graded-index and single-mode polymer optical fibers,” Mater. Res. Soc. Symp. Proc. 247, 817 (1992).
    [CrossRef]
  6. R. F. Shi, W. D. Chen, and A. F. Garito, “Measurement of graded-index plastic optical fibers,” in Proceedings of the Fourth International Conference on Plastic Optical Fibers and Applications (Information Gatekeepers, Boston, Mass., 1995), pp. 59–62.
  7. T. Kaino, M. Fujiki and K. Jinguji, “Preparation of plastic optical fibers,” Rev. Electron. Commun. Lab. 32, 478–488 (1984).
  8. W. Groh, “Overtone absorption in macromolecules for polymer optical fibers,” Makromol. Chem. 189, 2861 (1988).
    [CrossRef]
  9. W. H. Buck and P. R. Resnick, “Properties of amorphous fluoropolymers based on 2, 2-bitrifluoromethyl-4, 5-difluoro-1, 3-dioxole,” presented at the 183rd Meeting of the Electrochemical Society, Honolulu, Hawaii, May 16–21, 1993.
  10. See, for example, T. Okoshi, Optical Fibers (Academic, New York, 1982).
  11. D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10, 2252 (1971).
    [CrossRef] [PubMed]
  12. K. Okamoto, “Comparison of calculated and measured impulse responses of optical fibers,” Appl. Opt. 18, 2199 (1979).
    [CrossRef] [PubMed]
  13. K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fiber refractive index profiles,” Opt. Quantum Electron. 11, 185 (1977).
    [CrossRef]
  14. M. Young, “Optical fiber index profiles by the refracted-ray method (refracted near-field scanning),” Appl. Opt. 20, 3415 (1981).
    [CrossRef] [PubMed]
  15. W. D. Chen, “High speed plastic optical fibers for data communications,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa. 1996).
  16. R. Olshansky and D. B. Keck, “Pulse broadening in graded-index optical fibers,” Appl. Opt. 15, 483 (1976).
    [CrossRef] [PubMed]
  17. T. Ishigure, E. Nihei, and Y. Koike, “Optimum refractive-index profile of the graded-index polymer optical fiber, toward gigabit data links,” Appl. Opt. 35, 2048 (1996).
    [CrossRef] [PubMed]
  18. D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767 (1972).
    [CrossRef]
  19. G. Jiang, R. F. Shi, and A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photonics Technol. Lett. 9, 1128 (1997).
    [CrossRef]
  20. D. Marcuse, Principles of Optical Fiber Measurements (Academic, New York, 1981).
  21. L. Boggs, H. M. Presby, and D. Marcuse, “Rapid automatic index profiling of whole-fiber samples: Part I,” Bell Syst. Tech. J. 58, 867 (1979).
    [CrossRef]
  22. H. M. Presby, D. Marcuse, L. Boggs, and H. W. Astle, “Rapid automatic index profiling of whole-fiber samples: Part II,” Bell Syst. Tech. J. 58, 883 (1979).
    [CrossRef]
  23. K. Oyamada and T. Okoshi, “High-accuracy numerical data on propagation characteristics of α-power graded-core fibers,” IEEE Trans. Microwave Theory Tech. MTT-28, 1113 (1980).
    [CrossRef]

1997 (1)

G. Jiang, R. F. Shi, and A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photonics Technol. Lett. 9, 1128 (1997).
[CrossRef]

1996 (2)

1992 (1)

Y. Koike, “Graded-index and single-mode polymer optical fibers,” Mater. Res. Soc. Symp. Proc. 247, 817 (1992).
[CrossRef]

1988 (1)

W. Groh, “Overtone absorption in macromolecules for polymer optical fibers,” Makromol. Chem. 189, 2861 (1988).
[CrossRef]

1981 (1)

1980 (1)

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

1979 (4)

L. Boggs, H. M. Presby, and D. Marcuse, “Rapid automatic index profiling of whole-fiber samples: Part I,” Bell Syst. Tech. J. 58, 867 (1979).
[CrossRef]

H. M. Presby, D. Marcuse, L. Boggs, and H. W. Astle, “Rapid automatic index profiling of whole-fiber samples: Part II,” Bell Syst. Tech. J. 58, 883 (1979).
[CrossRef]

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

See, for example, R. Olshansky, “Propagation in glass optical waveguides,” Rev. Mod. Phys. 51, 341 (1979).
[CrossRef]

1977 (1)

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fiber refractive index profiles,” Opt. Quantum Electron. 11, 185 (1977).
[CrossRef]

1976 (1)

1972 (1)

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

1971 (1)

Astle, H. W.

H. M. Presby, D. Marcuse, L. Boggs, and H. W. Astle, “Rapid automatic index profiling of whole-fiber samples: Part II,” Bell Syst. Tech. J. 58, 883 (1979).
[CrossRef]

Boggs, L.

H. M. Presby, D. Marcuse, L. Boggs, and H. W. Astle, “Rapid automatic index profiling of whole-fiber samples: Part II,” Bell Syst. Tech. J. 58, 883 (1979).
[CrossRef]

L. Boggs, H. M. Presby, and D. Marcuse, “Rapid automatic index profiling of whole-fiber samples: Part I,” Bell Syst. Tech. J. 58, 867 (1979).
[CrossRef]

Garito, A. F.

G. Jiang, R. F. Shi, and A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photonics Technol. Lett. 9, 1128 (1997).
[CrossRef]

Gloge, D.

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

D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10, 2252 (1971).
[CrossRef] [PubMed]

Green Jr., P. E.

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

Groh, W.

W. Groh, “Overtone absorption in macromolecules for polymer optical fibers,” Makromol. Chem. 189, 2861 (1988).
[CrossRef]

Ishigure, T.

Jiang, G.

G. Jiang, R. F. Shi, and A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photonics Technol. Lett. 9, 1128 (1997).
[CrossRef]

Keck, D. B.

Koike, Y.

Marcuse, D.

L. Boggs, H. M. Presby, and D. Marcuse, “Rapid automatic index profiling of whole-fiber samples: Part I,” Bell Syst. Tech. J. 58, 867 (1979).
[CrossRef]

H. M. Presby, D. Marcuse, L. Boggs, and H. W. Astle, “Rapid automatic index profiling of whole-fiber samples: Part II,” Bell Syst. Tech. J. 58, 883 (1979).
[CrossRef]

Nihei, E.

Okamoto, K.

Okoshi, T.

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

Olshansky, R.

See, for example, R. Olshansky, “Propagation in glass optical waveguides,” Rev. Mod. Phys. 51, 341 (1979).
[CrossRef]

R. Olshansky and D. B. Keck, “Pulse broadening in graded-index optical fibers,” Appl. Opt. 15, 483 (1976).
[CrossRef] [PubMed]

Oyamada, K.

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

Presby, H. M.

H. M. Presby, D. Marcuse, L. Boggs, and H. W. Astle, “Rapid automatic index profiling of whole-fiber samples: Part II,” Bell Syst. Tech. J. 58, 883 (1979).
[CrossRef]

L. Boggs, H. M. Presby, and D. Marcuse, “Rapid automatic index profiling of whole-fiber samples: Part I,” Bell Syst. Tech. J. 58, 867 (1979).
[CrossRef]

Shi, R. F.

G. Jiang, R. F. Shi, and A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photonics Technol. Lett. 9, 1128 (1997).
[CrossRef]

White, K. I.

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fiber refractive index profiles,” Opt. Quantum Electron. 11, 185 (1977).
[CrossRef]

Young, M.

Appl. Opt. (5)

Bell Syst. Tech. J. (3)

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

L. Boggs, H. M. Presby, and D. Marcuse, “Rapid automatic index profiling of whole-fiber samples: Part I,” Bell Syst. Tech. J. 58, 867 (1979).
[CrossRef]

H. M. Presby, D. Marcuse, L. Boggs, and H. W. Astle, “Rapid automatic index profiling of whole-fiber samples: Part II,” Bell Syst. Tech. J. 58, 883 (1979).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

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

IEEE Photonics Technol. Lett. (1)

G. Jiang, R. F. Shi, and A. F. Garito, “Mode coupling and equilibrium mode distribution conditions in plastic optical fibers,” IEEE Photonics Technol. Lett. 9, 1128 (1997).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

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

Makromol. Chem. (1)

W. Groh, “Overtone absorption in macromolecules for polymer optical fibers,” Makromol. Chem. 189, 2861 (1988).
[CrossRef]

Mater. Res. Soc. Symp. Proc. (1)

Y. Koike, “Graded-index and single-mode polymer optical fibers,” Mater. Res. Soc. Symp. Proc. 247, 817 (1992).
[CrossRef]

Opt. Quantum Electron. (1)

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fiber refractive index profiles,” Opt. Quantum Electron. 11, 185 (1977).
[CrossRef]

Rev. Mod. Phys. (1)

See, for example, R. Olshansky, “Propagation in glass optical waveguides,” Rev. Mod. Phys. 51, 341 (1979).
[CrossRef]

Other (8)

D. Hanson, “Wiring with plastic,” IEEE Lightwave Commun. Sys. 3, 34 (1992).

T. Kaino, “Polymer optical fibers,” in Polymers for Lightwave and Integrated Optics, L. Hornak, ed. (Dekker, Dordrecht, The Netherlands, 1992).

R. F. Shi, W. D. Chen, and A. F. Garito, “Measurement of graded-index plastic optical fibers,” in Proceedings of the Fourth International Conference on Plastic Optical Fibers and Applications (Information Gatekeepers, Boston, Mass., 1995), pp. 59–62.

T. Kaino, M. Fujiki and K. Jinguji, “Preparation of plastic optical fibers,” Rev. Electron. Commun. Lab. 32, 478–488 (1984).

W. H. Buck and P. R. Resnick, “Properties of amorphous fluoropolymers based on 2, 2-bitrifluoromethyl-4, 5-difluoro-1, 3-dioxole,” presented at the 183rd Meeting of the Electrochemical Society, Honolulu, Hawaii, May 16–21, 1993.

See, for example, T. Okoshi, Optical Fibers (Academic, New York, 1982).

W. D. Chen, “High speed plastic optical fibers for data communications,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa. 1996).

D. Marcuse, Principles of Optical Fiber Measurements (Academic, New York, 1981).

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Figures (25)

Fig. 1
Fig. 1

Schematic of a five-channel WDM system. Five narrow-linewidth lasers transmit the distinct channels, which are multiplexed onto a single fiber. After traveling a long distance the signals are demultiplexed, regenerated, and remultiplexed back onto a fiber for further transmission. At the terminal end the channels are demultiplexed and are individually detected and processed.

Fig. 2
Fig. 2

Schematic of an eight-terminal star network in which each terminal, or user, transmits a signature wavelength and can read all eight wavelengths, which allows each user to communicate with any other user.

Fig. 3
Fig. 3

Schematic experimental setup for POF attenuation measurements: PD, photodiode; PC, computer.

Fig. 4
Fig. 4

Attenuation spectra of (a) SI (1000 μm in diameter) and (b) GI (750 μm in diameter) PMMA-based POF’s. The loss at 650 nm is 110 dB/km for the SI POF and 158 dB/km for the GI POF. The slight increase in the short-wavelength region for GI POF loss spectrum is due to the involvement of benzyl benzoate.

Fig. 5
Fig. 5

Attenuation spectra of PMMA-based SI (dashed curve) and GI (dotted curve) POF’s and a theoretical perfluorinated POF (solid curve, bottom).

Fig. 6
Fig. 6

Absorption spectrum of silica GOF with transmission windows at 1330 and 1550 nm.

Fig. 7
Fig. 7

Schematic experimental setup for time-domain POF bandwidth measurement. The fast-pulse detector is an optical sampling oscilloscope from Hamamatsu. M.O.’s, microscope objectives.

Fig. 8
Fig. 8

Schematic illustration of a mode scrambler to achieve equilibrium mode distribution condition in POF’s.

Fig. 9
Fig. 9

Optical pulse width from a 64-m GI POF as a function of incidence angle. Open and filled circles are results when guided modes are unscrambled and scrambled, respectively.

Fig. 10
Fig. 10

Optical pulses from the diode (left) and a 12.2-m SI POF. The pulse broadening is due to the intermodal dispersion in the fiber.

Fig. 11
Fig. 11

Optical pulse from the diode (left) and a 98.8-m GI POF. The pulse broadening is due to the intermodal dispersion in the fiber.

Fig. 12
Fig. 12

Calculated impulse response function for a SI fiber. The spike near the cutoff is due to those cutoff modes that were not included in the WKB approximation.

Fig. 13
Fig. 13

Calculated relative group-delay time as a function of normalized propagation constant for a fiber possessing the refractive-index profile shown in Eq. (23). The normalized frequency number V is 60.

Fig. 14
Fig. 14

Calculated radial part of the electric-field distribution for three guided modes (v, l), where v is the azimuthal number and l is the sequential number.

Fig. 15
Fig. 15

Schematic of the experimental setup for refracted near-field measurement of POF refractive-index profiles: A, chopper; B, polarizer; C, quarter-wave plate; D, 10 microscope objective; E, pinhole (25 μm in diameter); F, microscope objective; PD, photodiode; LD, laser diode. The back end of the fiber is illuminated with a He–Ne laser so that the front end can be observed with an eyepiece.

Fig. 16
Fig. 16

Blocking disk assembly of the refracted near-field measurement technique of Fig. 15.

Fig. 17
Fig. 17

Measured refractive-index profile of current GI POF (dashed curve) and its polynomial fit (solid curve). The measured curve consists of three regions: A, index-matching liquid; B, cladding, C, core.

Fig. 18
Fig. 18

Measured refractive-index profile of current GI POF (dotted curve) and its alpha fit (solid curve) with α=3.67.

Fig. 19
Fig. 19

Calculated impulse response function based on the measured refractive-index profile of current GI POF (100 m). The response function has two parts: a sharp peak corresponding to the modes confined in the central-core region, and a long tail representing the remaining modes, which have large intermodal dispersion.

Fig. 20
Fig. 20

Transfer function of the impulse response function of Fig. 19 based on the measured refractive-index profile of current GI POF (100 m). The bandwidth–length product is 450 GHz–100 m.

Fig. 21
Fig. 21

Schematic of the light paths in the TIM experiment.

Fig. 22
Fig. 22

Schematic of the observed interference fringes of the TIM measurement (a) before and (b) after insertion of the POF sample.

Fig. 23
Fig. 23

Geometry of the path traveled by a ray of light as it passes through the fiber sample.

Fig. 24
Fig. 24

Diagram of the sample stage for the TIM measurement. A fiber sample is placed upon a quartz plate and immersed in index-matching liquid on the sample side of the stage. The reference side comprises the same index-matching fluid and an identical quartz plate.

Fig. 25
Fig. 25

Comparison of the GI POF index-of-refraction profile measured by the TIM (solid curve) with that measured by the near-field refracted ray technique (dashed curve).

Tables (2)

Tables Icon

Table 1 Transmission Windows for Silica Glass and PMMA POF

Tables Icon

Table 2 Transmission Windows for SI and GI PMMA POF

Equations (42)

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αt=-10L log10(P2/P1),
[A(λboundary)-A(λmin)]*L=3dB,
L=20dB/A(λmin)
τ=τ22-τ12.
BW=0.44τ L,
N.A.=λf1πaf2,
Λ=πd2Δ,
uJv(u)-w Kv(w)Kv(w) Jv(u)=0,
u=[(k02nf2-β2)a]1/2,
w=V2-u2;
V=[(k02nf2-k02nc2)]1/2a=2Δnfk0a,
τ=nfc 1-2ΔΘ1-2Δ u2V21/2,
Θ=ψ(w)-1ϕβ2(w)-v2u2+ψ(w).
ϕβ(w)=w Kv(w)Kv(w),
ψ(w)=Kv-1(w)Kv+1(w)Kv2(w).
1r ddr r dRdr+n2(r)k02-β2-v2r2R=0,
m(β, k0)=0r2[n2(r)k02-β2)rdr,
τ=-1c m/k0m/β,
h(τ)=p(m) dmdτ,
h(τ)1/τ3nf/cτnf2/(ncc).
h(τ)1-3δτ/τf,0δτ(nf/c)Δ.
Ri=R(ri),i=0, 1, 2, , N.
n(r)=nfra/2,[nfp2-(nfp2-nc2)(r/a)2]1/2a/2ra,ncr>a,
nfp=4nf2-nc231/2
P[sin2 θ1 max-sin2 θ2min+nL2-n2(r)],
n(r)=nf1-δn10(r/a)2-δn11(r/a)4ra1,nf2-δn20(r/a)2-δn21(r/a)4a1ra,ncr>a.
p(m)=1-(m/Mc)mMc0m>Mc,
L/Lc=BW1/BW2,
Δϕ=kl1l2[n(l)-nL]dl,
SD=Δϕ2π,
S00=12-3v22-u212N2+(5-3q0-2q1)× V2120N2Δ,
S01=-12+v22-u212N2+(5-2q0-3q1) V2120N2Δ,
S11=4v2 ln 2-2(v2-1)-2u23N2+(40-3q0-30q1-7q2) v2120N2Δ,
Sii=(i-1)2v2 ln ii-1+(i+1)2v2 ln i+1i-2i(v2-1)-2iu23N2+[40i-(5i-2)qi-1-30iqi-(5i+2)qi+1] V2120N2Δ(i=2, 3, , N-1),
Si,i+1=i+12(v2-1)-i(i+1)v2 ln i+1i-(2i+1)u212N2+[5(2i+1)-(5i+2)qi-(5i+3)qi+1] V2120N2Δ(i=1, 2, , N-1),
SN,N=(N-1)2v2 ln NN-1-N-12(v2-1)+v(v+1)+wKv-1(w)Kv(w)-(4N-1)u212N2+[5(4N-1)-(5N-2)qN-1-3(5N-1)qN]v2120N2Δ,
qi=ni2nf2(i=0, 1, 2, , N),
τ=-1c f/k0f/β,
fk0=fu uk0+fV Vk0,
fβ=fu uβ+fV Vβ=fu uβ,
τ=nfc 1+2Δ uv (f/V)(f/u)1-2Δ u2V21/2.
T=1+2Δ uv (f/V)(f/u)1-2Δ u2V21/2-1.

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