Abstract

Aperture, attenuation, and far-field radiation diagrams have been studied on short lengths of commercial polymethyl methacrylate- (PMMA-) core optical fibers. The spectral attenuation of the PMMA constituting the core has been carefully measured and compared with the attenuation that may be calculated from optical properties of PMMA. Accurate extrinsic attenuation spectra have been obtained. Moreover, the dependence of the far-field radiation diagram on the fiber length and on the launching incidence of a laser beam has been studied on this side of the mode-equilibrium length. The analysis of these diagrams, first performed with the Gloge mode-coupling model, has been improved with the hypothesis that the mode-coupling processes are a result of light diffraction by structural anomalies in the core. The average size and form of these structural anomalies has been evaluated. They may be longitudinal microcracks of the PMMA coming from stress relaxation, which occurs during the fiber-drawing process.

© 1992 Optical Society of America

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References

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  1. J. Dugas, M. Sotom, L. Martin, J. M. Cariou, “Accurate characterization of the transmittivity of large-diameter multimode optical fibers,” Appl. Opt. 26, 4198–4208 (1987).
    [CrossRef] [PubMed]
  2. D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).
  3. L. Jeunhomme, J. P. Pocholle, “Mode coupling coefficient in a multimode optical fiber,” Electron. Lett. 11, 18–23 (1975).
    [CrossRef]
  4. L. Jeunhomme, M. Fraise, J. P. Pocholle, “Propagation modes for long step-index optical fibers,” Appl. Opt. 15, 3040–3046 (1976).
    [CrossRef] [PubMed]
  5. M. Rousseau, L. Jeunhomme, “Numerical solution of coupled power equation in step-index optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-25, 577–585 (1977).
    [CrossRef]
  6. M. Sotom, “Etude experimentale de l’ouverture angulaire de fibres optiques multimodes,” M.S. thesis (Institut des Sciences Appliquées, Toulouse, France, 1986).
  7. J. Dugas, M. Sotom, E. Douhé, L. Martin, P. Destruel, “Accurate determination of thermal variation of the aperture of step index optical fibers,” Appl. Opt. 27, 4822–4825 (1988).
    [CrossRef] [PubMed]
  8. A. W. Snyder, D. J. Mitchell, “Leaky rays on circular optical fibers,” J. Opt. Soc. Am. 64, 599–607 (1974).
    [CrossRef]
  9. A. W. Snyder, D. J. Mitchell, C. Pask, “Failure of geometric optics for analysis of circular optical fibers,” J. Opt. Soc. Am. 64, 608–614 (1974).
    [CrossRef]
  10. T. Kaino, M. Fujiki, K. Jinguji, “Preparation of plastic optical fibers,” Rev. Elec. Com. Lab. 32, 478–482 (1984).
  11. T. Kaino, “Absorption losses of low loss plastic optical fibers,” Jpn. J. Appl. Phys. 24, 1661–1665 (1985).
    [CrossRef]
  12. J. W. Ellis, “Heats of linkage of C—H and N—H bonds from vibration spectra,” Phys. Rev. 33, 27–36 (1929).
    [CrossRef]
  13. T. Kaino, “Influence of water absorption on plastic optical fibers,” Appl. Opt. 24, 4192–4195 (1985).
    [CrossRef] [PubMed]

1988 (1)

1987 (1)

1985 (2)

T. Kaino, “Absorption losses of low loss plastic optical fibers,” Jpn. J. Appl. Phys. 24, 1661–1665 (1985).
[CrossRef]

T. Kaino, “Influence of water absorption on plastic optical fibers,” Appl. Opt. 24, 4192–4195 (1985).
[CrossRef] [PubMed]

1984 (1)

T. Kaino, M. Fujiki, K. Jinguji, “Preparation of plastic optical fibers,” Rev. Elec. Com. Lab. 32, 478–482 (1984).

1977 (1)

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

1976 (1)

1975 (1)

L. Jeunhomme, J. P. Pocholle, “Mode coupling coefficient in a multimode optical fiber,” Electron. Lett. 11, 18–23 (1975).
[CrossRef]

1974 (2)

1972 (1)

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

1929 (1)

J. W. Ellis, “Heats of linkage of C—H and N—H bonds from vibration spectra,” Phys. Rev. 33, 27–36 (1929).
[CrossRef]

Cariou, J. M.

Destruel, P.

Douhé, E.

Dugas, J.

Ellis, J. W.

J. W. Ellis, “Heats of linkage of C—H and N—H bonds from vibration spectra,” Phys. Rev. 33, 27–36 (1929).
[CrossRef]

Fraise, M.

Fujiki, M.

T. Kaino, M. Fujiki, K. Jinguji, “Preparation of plastic optical fibers,” Rev. Elec. Com. Lab. 32, 478–482 (1984).

Gloge, D.

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

Jeunhomme, L.

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

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

L. Jeunhomme, J. P. Pocholle, “Mode coupling coefficient in a multimode optical fiber,” Electron. Lett. 11, 18–23 (1975).
[CrossRef]

Jinguji, K.

T. Kaino, M. Fujiki, K. Jinguji, “Preparation of plastic optical fibers,” Rev. Elec. Com. Lab. 32, 478–482 (1984).

Kaino, T.

T. Kaino, “Absorption losses of low loss plastic optical fibers,” Jpn. J. Appl. Phys. 24, 1661–1665 (1985).
[CrossRef]

T. Kaino, “Influence of water absorption on plastic optical fibers,” Appl. Opt. 24, 4192–4195 (1985).
[CrossRef] [PubMed]

T. Kaino, M. Fujiki, K. Jinguji, “Preparation of plastic optical fibers,” Rev. Elec. Com. Lab. 32, 478–482 (1984).

Martin, L.

Mitchell, D. J.

Pask, C.

Pocholle, J. P.

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

L. Jeunhomme, J. P. Pocholle, “Mode coupling coefficient in a multimode optical fiber,” Electron. Lett. 11, 18–23 (1975).
[CrossRef]

Rousseau, M.

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

Snyder, A. W.

Sotom, M.

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

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

Electron. Lett. (1)

L. Jeunhomme, J. P. Pocholle, “Mode coupling coefficient in a multimode optical fiber,” Electron. Lett. 11, 18–23 (1975).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

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

J. Opt. Soc. Am. (2)

Jpn. J. Appl. Phys. (1)

T. Kaino, “Absorption losses of low loss plastic optical fibers,” Jpn. J. Appl. Phys. 24, 1661–1665 (1985).
[CrossRef]

Phys. Rev. (1)

J. W. Ellis, “Heats of linkage of C—H and N—H bonds from vibration spectra,” Phys. Rev. 33, 27–36 (1929).
[CrossRef]

Rev. Elec. Com. Lab. (1)

T. Kaino, M. Fujiki, K. Jinguji, “Preparation of plastic optical fibers,” Rev. Elec. Com. Lab. 32, 478–482 (1984).

Other (1)

M. Sotom, “Etude experimentale de l’ouverture angulaire de fibres optiques multimodes,” M.S. thesis (Institut des Sciences Appliquées, Toulouse, France, 1986).

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Figures (15)

Fig. 1
Fig. 1

Variations of the relative transmitted power P(θ)/P(0) versus the launching incidence θ of the laser beam for various fiber lengths for (a) the TB1000 fiber and (b) the EK40 fiber.

Fig. 2
Fig. 2

Variations of the angular aperture θ M (measured from the launching incidence for which the transmitted power is 50% of the transmitted power at θ = 0) versus fiber length.

Fig. 3
Fig. 3

Variations of the maximum transmitted power when the launching incidence is normal versus the fiber length. The slope directly gives the core-material attenuation coefficient α c .

Fig. 4
Fig. 4

Spectral attenuation α c (λ) of the core material.

Fig. 5
Fig. 5

Example of the record of the far-field radiation diagram given by a 1-m-long TB1000 fiber when the launching angle of the laser beam is ~ 23°.

Fig. 6
Fig. 6

Variation of the angular width of the ring versus the launching incidence θ of the laser beam for a 1-m-long TB1000 fiber.

Fig. 7
Fig. 7

Variations of the angular width of the ring versus the fiber length. Filled circles and triangles represent the experimental values and curves were calculated by using either Gloge’s model for mode coupling or a diffraction process.

Fig. 8
Fig. 8

PMMA-attenuation calculated spectrum.

Fig. 9
Fig. 9

Extrinsic core attenuation spectra calculated by substracting the curve of Fig. 8 from the measured spectra of Fig. 4.

Fig. 10
Fig. 10

Evolution of the product (far-field diagram peak intensity × angular width × sin θ) versus the launching angle θ for a 1-m-long TB1000 fiber, showing that the total transmitted power is independent of the launching angle as long as this angle does not exceed 25°.

Fig. 11
Fig. 11

Theoretical progressive broadening of transmitted ring in the far-field diagram in Gloge’s model of mode coupling. The launched beam has an incidence of 20°.

Fig. 12
Fig. 12

Theoretical evolution of the angular ring width in the far-field diagram in Gloge’s model of mode coupling versus the fiber length for various values of the μ coefficient. The launched beam has an incidence of 20° and its initial width is 1.5°.

Fig. 13
Fig. 13

Effect of launched beam angular width (1°, 1.5°, and 2°) on the theoretical variations of the angular ring width in the far-field diagram in Gloge’s model of mode coupling versus the fiber length. The launched beam has an incidence of 20° and μ = 0.53.

Fig. 14
Fig. 14

Effect of the launching incidence of the laser beam on the theoretical variations of the angular ring width in the far-field diagram in Gloge’s model of mode coupling versus the fiber length. The launched beam has an angular width of 1.5° and μ = 0.53.

Fig. 15
Fig. 15

Comparison of the calculated (curve) and experimental (triangles) values of the angular ring width in the far-field diagram versus the launching incidence of the laser beam in the model of the diffraction by 37-μm-long and 7-μm-diam. rods.

Tables (3)

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Table 1 Experimental Positions and Intensities of Various Vibration Peaks

Tables Icon

Table 2 Calculated Values of A and B Coefficients

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Table 3 Best-Fitting Values of C and τ Coefficients

Equations (11)

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λ n = 10 7 / ( A n - B n 2 ) ,
I ( n ) = C exp ( - τ n ) ,
α R ( λ ) = 13 ( 633 / λ ) 4 .
P ( θ i , z ) z = - α ( θ i ) P ( θ i , z ) + δ θ i 2 1 θ i θ i [ θ i d ( θ i ) P ( θ i , z ) θ i ] ,
P ( θ i , z ) z = D θ i θ i [ θ i P ( θ i , z ) θ i ] .
P ( θ i , 0 ) = exp - 4 ln ( 2 ) [ θ i ( - θ i 0 ) δ θ 0 ] 2 ,
μ = ( 2 / D ) ( Δ θ 2 / Δ z ) ,
( sin 2 u / u 2 ) [ 2 J 1 ( v ) / v ] 2 ,
u = ( π L n / λ ) [ cos ( θ i + β i ) - cos θ i ] , v = ( 2 π ρ n / λ ) [ sin ( θ i + β i ) - sin θ i ] .
n sin ( θ i + β i ) = sin ( θ + β ) .
L = 37 ± 1 μ m ,             ρ = 2 , 5 ± 0.3 μ m .

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