Abstract

A new technique for the measurement of constant-curvature (bend) loss as a function of bend radius is described, and it is shown that the influence of transition (microbend) losses can be essentially eliminated. Based on this technique and via the application of curve-fitting procedures and the Newton-Raphson method for two variables, a sensible equivalent step index can be obtained if stress-induced changes in the bent fiber are taken into account. However, the prediction of bend losses at other wavelengths is coarse, and it is shown that, for our fiber, agreement between theory and experiment can be considerably improved via an empirically deduced stress-induced dependence that is far stronger than predicted by published theory.

© 1984 Optical Society of America

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References

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  1. D. Marcuse, “Gaussian Approximation of the fundamental Modes of Graded Index Fibers,” J. Opt. Soc. Am. 68, 103 (1978).
    [CrossRef]
  2. A. W. Snyder, P. A. Sammut, “Fundamental Modes of Graded Optical Fibers,” J. Opt. Soc. Am. 69, 1663 (1979).
    [CrossRef]
  3. H. Matsumura, T. Suganuma, “Normalization of Single-Mode Fibers Having an Arbitrary Index Profile,” Appl. Opt. 19, 3151 (1980).
    [CrossRef] [PubMed]
  4. E. Brinkmeyer, “Spot Size of Graded-Index Single-Mode Fibers: Profile-Independent Representation and New Determination Method,” Appl. Opt. 18, 932 (1979).
    [CrossRef] [PubMed]
  5. V. A. Bhagavatula, “Estimation of Single Mode Waveguide Dispersion Using an Equivalent-Step-Index Approach,” Electron. Lett. 18, 319 (1982).
    [CrossRef]
  6. C. A. Millar, “Direct Method for Determining Equivalent Step-Index Profiles for Monomode Fibers,” Electron. Lett. 17, 458 (1981).
    [CrossRef]
  7. K. Nagano, S. Kawakami, S. Nishida, “Change of the Refractive Index in an Optical Fiber due to External Forces,” Appl. Opt. 17, 2080 (1978).
    [CrossRef] [PubMed]
  8. L. Lewin, “Radiation from Curved Dielectric Slabs and Fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718 (1974).
    [CrossRef]
  9. E. F. Kuester, D. C. Chang, “Surface-Wave Radiation Loss from Curves Dielectric Slabs and Fibers,” IEEE J. Quantum Electron QE-11, 903 (1975).
    [CrossRef]
  10. D. Marcuse, “Curvature Loss Formula for Optical Fibers,” J. Opt. Soc. Am. 66, 216 (1976).
    [CrossRef]
  11. A. W. Snyder, I. White, D. J. Mitchell, “Radiation from Bent’ Optical Waveguides,” Electron. Lett. 11, 332 (1975).
    [CrossRef]
  12. A. B. Sharma, S. J. Halme, M. Lähteenoja, E. J. R. Hubach, “A Study of Multimode Fiber Attenuation Using a Precision Spectral Radiometer and the Near-Field Filtration Technique,” Opt. Quantum Electron. 15, 95 (1983).
    [CrossRef]
  13. Y. Murakami, H. Tsuchiya, “Bending Losses of Coated Single Mode Optical Fibers,” IEEE J. Quantum Electron QE-14, 495 (1978).
    [CrossRef]

1983 (1)

A. B. Sharma, S. J. Halme, M. Lähteenoja, E. J. R. Hubach, “A Study of Multimode Fiber Attenuation Using a Precision Spectral Radiometer and the Near-Field Filtration Technique,” Opt. Quantum Electron. 15, 95 (1983).
[CrossRef]

1982 (1)

V. A. Bhagavatula, “Estimation of Single Mode Waveguide Dispersion Using an Equivalent-Step-Index Approach,” Electron. Lett. 18, 319 (1982).
[CrossRef]

1981 (1)

C. A. Millar, “Direct Method for Determining Equivalent Step-Index Profiles for Monomode Fibers,” Electron. Lett. 17, 458 (1981).
[CrossRef]

1980 (1)

1979 (2)

1978 (3)

1976 (1)

1975 (2)

A. W. Snyder, I. White, D. J. Mitchell, “Radiation from Bent’ Optical Waveguides,” Electron. Lett. 11, 332 (1975).
[CrossRef]

E. F. Kuester, D. C. Chang, “Surface-Wave Radiation Loss from Curves Dielectric Slabs and Fibers,” IEEE J. Quantum Electron QE-11, 903 (1975).
[CrossRef]

1974 (1)

L. Lewin, “Radiation from Curved Dielectric Slabs and Fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718 (1974).
[CrossRef]

Bhagavatula, V. A.

V. A. Bhagavatula, “Estimation of Single Mode Waveguide Dispersion Using an Equivalent-Step-Index Approach,” Electron. Lett. 18, 319 (1982).
[CrossRef]

Brinkmeyer, E.

Chang, D. C.

E. F. Kuester, D. C. Chang, “Surface-Wave Radiation Loss from Curves Dielectric Slabs and Fibers,” IEEE J. Quantum Electron QE-11, 903 (1975).
[CrossRef]

Halme, S. J.

A. B. Sharma, S. J. Halme, M. Lähteenoja, E. J. R. Hubach, “A Study of Multimode Fiber Attenuation Using a Precision Spectral Radiometer and the Near-Field Filtration Technique,” Opt. Quantum Electron. 15, 95 (1983).
[CrossRef]

Hubach, E. J. R.

A. B. Sharma, S. J. Halme, M. Lähteenoja, E. J. R. Hubach, “A Study of Multimode Fiber Attenuation Using a Precision Spectral Radiometer and the Near-Field Filtration Technique,” Opt. Quantum Electron. 15, 95 (1983).
[CrossRef]

Kawakami, S.

Kuester, E. F.

E. F. Kuester, D. C. Chang, “Surface-Wave Radiation Loss from Curves Dielectric Slabs and Fibers,” IEEE J. Quantum Electron QE-11, 903 (1975).
[CrossRef]

Lähteenoja, M.

A. B. Sharma, S. J. Halme, M. Lähteenoja, E. J. R. Hubach, “A Study of Multimode Fiber Attenuation Using a Precision Spectral Radiometer and the Near-Field Filtration Technique,” Opt. Quantum Electron. 15, 95 (1983).
[CrossRef]

Lewin, L.

L. Lewin, “Radiation from Curved Dielectric Slabs and Fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718 (1974).
[CrossRef]

Marcuse, D.

Matsumura, H.

Millar, C. A.

C. A. Millar, “Direct Method for Determining Equivalent Step-Index Profiles for Monomode Fibers,” Electron. Lett. 17, 458 (1981).
[CrossRef]

Mitchell, D. J.

A. W. Snyder, I. White, D. J. Mitchell, “Radiation from Bent’ Optical Waveguides,” Electron. Lett. 11, 332 (1975).
[CrossRef]

Murakami, Y.

Y. Murakami, H. Tsuchiya, “Bending Losses of Coated Single Mode Optical Fibers,” IEEE J. Quantum Electron QE-14, 495 (1978).
[CrossRef]

Nagano, K.

Nishida, S.

Sammut, P. A.

Sharma, A. B.

A. B. Sharma, S. J. Halme, M. Lähteenoja, E. J. R. Hubach, “A Study of Multimode Fiber Attenuation Using a Precision Spectral Radiometer and the Near-Field Filtration Technique,” Opt. Quantum Electron. 15, 95 (1983).
[CrossRef]

Snyder, A. W.

A. W. Snyder, P. A. Sammut, “Fundamental Modes of Graded Optical Fibers,” J. Opt. Soc. Am. 69, 1663 (1979).
[CrossRef]

A. W. Snyder, I. White, D. J. Mitchell, “Radiation from Bent’ Optical Waveguides,” Electron. Lett. 11, 332 (1975).
[CrossRef]

Suganuma, T.

Tsuchiya, H.

Y. Murakami, H. Tsuchiya, “Bending Losses of Coated Single Mode Optical Fibers,” IEEE J. Quantum Electron QE-14, 495 (1978).
[CrossRef]

White, I.

A. W. Snyder, I. White, D. J. Mitchell, “Radiation from Bent’ Optical Waveguides,” Electron. Lett. 11, 332 (1975).
[CrossRef]

Appl. Opt. (3)

Electron. Lett. (3)

V. A. Bhagavatula, “Estimation of Single Mode Waveguide Dispersion Using an Equivalent-Step-Index Approach,” Electron. Lett. 18, 319 (1982).
[CrossRef]

C. A. Millar, “Direct Method for Determining Equivalent Step-Index Profiles for Monomode Fibers,” Electron. Lett. 17, 458 (1981).
[CrossRef]

A. W. Snyder, I. White, D. J. Mitchell, “Radiation from Bent’ Optical Waveguides,” Electron. Lett. 11, 332 (1975).
[CrossRef]

IEEE J. Quantum Electron (2)

E. F. Kuester, D. C. Chang, “Surface-Wave Radiation Loss from Curves Dielectric Slabs and Fibers,” IEEE J. Quantum Electron QE-11, 903 (1975).
[CrossRef]

Y. Murakami, H. Tsuchiya, “Bending Losses of Coated Single Mode Optical Fibers,” IEEE J. Quantum Electron QE-14, 495 (1978).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

L. Lewin, “Radiation from Curved Dielectric Slabs and Fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718 (1974).
[CrossRef]

J. Opt. Soc. Am. (3)

Opt. Quantum Electron. (1)

A. B. Sharma, S. J. Halme, M. Lähteenoja, E. J. R. Hubach, “A Study of Multimode Fiber Attenuation Using a Precision Spectral Radiometer and the Near-Field Filtration Technique,” Opt. Quantum Electron. 15, 95 (1983).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of the winding equipment used for the measurement of constant-curvature loss.

Fig. 2
Fig. 2

Logarithmic plot of output power as a function of the bifilar turns unwound from the cylinder in Fig. 1. The figure shows the validity of the homogeneity condition at several cylinder diameters (in millimeters) and wavelengths for an arbitrarily selected high-quality fiber.

Fig. 3
Fig. 3

Logarithmic plot of the bend loss (Np/m) as a function of bend radius for the fiber whose results are reported in this paper.

Fig. 4
Fig. 4

Behavior of the ratio of A and B [from Eq. (1)] for typical fibers and operating conditions.

Fig. 5
Fig. 5

Bend loss vs bend radius: solid lines show the loss predicted via ESI parameters obtained at 1550 nm. Experimentally determined data points are according to the inset legends.

Fig. 6
Fig. 6

Behavior of the empirically deduced radius-correction factor.

Fig. 7
Fig. 7

Presentation of the data in Fig. 5 after correction according to Fig. 6.

Tables (1)

Tables Icon

Table I ESI Parameters at Different Wavelengths Based on a Radius-Correction Factor of 1.31

Equations (12)

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

α = ( A / R ) exp ( - B R ) ,
A = 1 2 π / ( a W 3 ) · [ U / V K 1 ( W ) ] 2
B = 4 Δ W 3 / ( 3 a V 2 ) .
V 2 = U 2 + W 2 ,
U 2 = a 2 ( k 0 2 n 1 2 - β 2 ) ,
W 2 = a 2 ( β 2 - k 0 2 n 2 2 ) ,
v i = ln A - 1 2 ln R i - B R i - ln α i
A = exp [ 1 2 N Σ i ln ( α i 2 R i ) + B N Σ i R i ] ,
B = - Σ i ( R i - Σ k R k / N ) ln ( α i 2 R i ) 2 Σ i ( R i - Σ k R k / N ) 2 ,
A = 1 a ( - 18.7835 + 33.0168 V - 19.142 V 2 + 4.281 V 3 ) ,
B = Δ a ( 0.7783 - 1.838 V + 1.1944 V 2 - 0.1455 V 3 ) .
P ( z ) = P ( 0 ) exp ( - α 2 π ϕ n ) ,

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