Abstract

We present results of an experimental investigation of the optical losses produced by bending large core optical fibers, typical of those used in power beam delivery systems. Experiments have been conducted over a range of core diameters for both plastic clad silica and all-silica fibers as a function of bend radius. A theoretical model has been developed for predicting the magnitude of the bend loss, and agreement was obtained with the experimental results. The study thus yields design information for fiber beam delivery systems.

© 1991 Optical Society of America

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  1. L. Lewin, D. C. Chang, E. F. Kuester, Electromagnetic Waves and Curved Structures (Peter Peregrinus, London, 1977).
  2. D. Marcuse, “Steady State Losses of Optical Fibres and Fibre Resonators,” Bell Syst. Tech. J. 55, 1445–1462 (1976).
  3. C. M. de Blok, P. Mathiesse, “Core Alignment Monitor for Single-Mode Jointing,” Electron. lett. 20, 109–110 (1984).
    [CrossRef]
  4. J. N. Fields, C. K. Asawa, O. G. Ramer, M. K. Barnowski, “Fiber Optic Pressure Sensor,” J. Acoust. Soc. Am. 67, 816–818 (1980).
    [CrossRef]
  5. H. P. Weber, W. Hodel, “High Power Light Transmission in Optical Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 650, 102–108 (1986).
  6. D. Gloge, “Propagation Effects in Optical Fibers,” IEEE Trans. Microwave Theory Tech. MTT-23, 106–120 (1975).
    [CrossRef]
  7. D. Marcuse, “Curvature Loss Formula for Optical Fibers,” J. Opt. Soc. Am. 66, 216–220 (1976).
    [CrossRef]
  8. D. Marcuse, “Field Deformation and Loss Caused by Curvature of Optical Fibers,” J. Opt. Soc. Am. 66, 311–320 (1976).
    [CrossRef]
  9. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982).
  10. M. A. Miller, V. I. Talanow, “Electromagnetic Surface Waves Guided by a Boundary with Small Curvature,” Zh. Tekh. Fiz. 26, 2755–2773 (1956).
  11. E. A. J. Marcatili, “Bends in Optical Dielectric Guides,” Bell Syst. Tech. J. 48, 2013 (1968).
  12. L. Lewin, “Radiation from Curved Dielectric Slabs and Fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718–727 (1974).
    [CrossRef]
  13. J. A. Arnaud, “Transverse Coupling in Fiber Optics Part III: Bending Losses,” Bell Syst. Tech. J. 53, 1379–1324 (1974).
  14. A. W. Snyder, I. White, D. J. Mitchell, “Radiation Losses in Bent Wave Guides for Surface Waves,” Electron. Lett. 11, 332–333 (1975).
    [CrossRef]
  15. V. V. Shevchenko, “Radiation Losses in Bent Wave Guides for Surface Waves,” Radiophys. Quantum Electron. 14, 607–614 (1973).
    [CrossRef]
  16. D. C. Chang, E. F. Kuester, “Surface-Wave Radiation Loss from Curved Dielectric Slabs and Fibres,” IEEE J. Quantum Electron. QE-11, 903–907 (1975).
  17. E. A. J. Marcatili, S. E. Miller, “Improved Relations Describing Directional Control in Electromagnetic Wave Guidance,” Bell Syst. Tech. J. 48, 2161–2188 (1969).
  18. D. Gloge, “Bending Loss in Multimode Fibers with Graded and Ungraded Core Index,” Appl. Opt. 11, 2506–2513 (1972).
    [CrossRef] [PubMed]
  19. G. Cancellieri, P. Fantini, “Mode Coupling Effects in Optical Fibres: Perturbative Solution of the Time Dependent Power Flow Equation,” Opt. Quantum Electron. 15, 119–123 (1983).
    [CrossRef]
  20. A. J. Harris, P. F. Castle, “Bend Loss Measurements on High Numerical Aperture Single Mode Fibers as a Function of Wavelength and Bend Radius,” IEEE/OSA J. Lightwave Technol. LT-4, 34–40 (1986).
    [CrossRef]

1986

H. P. Weber, W. Hodel, “High Power Light Transmission in Optical Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 650, 102–108 (1986).

A. J. Harris, P. F. Castle, “Bend Loss Measurements on High Numerical Aperture Single Mode Fibers as a Function of Wavelength and Bend Radius,” IEEE/OSA J. Lightwave Technol. LT-4, 34–40 (1986).
[CrossRef]

1984

C. M. de Blok, P. Mathiesse, “Core Alignment Monitor for Single-Mode Jointing,” Electron. lett. 20, 109–110 (1984).
[CrossRef]

1983

G. Cancellieri, P. Fantini, “Mode Coupling Effects in Optical Fibres: Perturbative Solution of the Time Dependent Power Flow Equation,” Opt. Quantum Electron. 15, 119–123 (1983).
[CrossRef]

1980

J. N. Fields, C. K. Asawa, O. G. Ramer, M. K. Barnowski, “Fiber Optic Pressure Sensor,” J. Acoust. Soc. Am. 67, 816–818 (1980).
[CrossRef]

1976

1975

D. Gloge, “Propagation Effects in Optical Fibers,” IEEE Trans. Microwave Theory Tech. MTT-23, 106–120 (1975).
[CrossRef]

D. C. Chang, E. F. Kuester, “Surface-Wave Radiation Loss from Curved Dielectric Slabs and Fibres,” IEEE J. Quantum Electron. QE-11, 903–907 (1975).

A. W. Snyder, I. White, D. J. Mitchell, “Radiation Losses in Bent Wave Guides for Surface Waves,” Electron. Lett. 11, 332–333 (1975).
[CrossRef]

1974

L. Lewin, “Radiation from Curved Dielectric Slabs and Fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718–727 (1974).
[CrossRef]

J. A. Arnaud, “Transverse Coupling in Fiber Optics Part III: Bending Losses,” Bell Syst. Tech. J. 53, 1379–1324 (1974).

1973

V. V. Shevchenko, “Radiation Losses in Bent Wave Guides for Surface Waves,” Radiophys. Quantum Electron. 14, 607–614 (1973).
[CrossRef]

1972

1969

E. A. J. Marcatili, S. E. Miller, “Improved Relations Describing Directional Control in Electromagnetic Wave Guidance,” Bell Syst. Tech. J. 48, 2161–2188 (1969).

1968

E. A. J. Marcatili, “Bends in Optical Dielectric Guides,” Bell Syst. Tech. J. 48, 2013 (1968).

1956

M. A. Miller, V. I. Talanow, “Electromagnetic Surface Waves Guided by a Boundary with Small Curvature,” Zh. Tekh. Fiz. 26, 2755–2773 (1956).

Arnaud, J. A.

J. A. Arnaud, “Transverse Coupling in Fiber Optics Part III: Bending Losses,” Bell Syst. Tech. J. 53, 1379–1324 (1974).

Asawa, C. K.

J. N. Fields, C. K. Asawa, O. G. Ramer, M. K. Barnowski, “Fiber Optic Pressure Sensor,” J. Acoust. Soc. Am. 67, 816–818 (1980).
[CrossRef]

Barnowski, M. K.

J. N. Fields, C. K. Asawa, O. G. Ramer, M. K. Barnowski, “Fiber Optic Pressure Sensor,” J. Acoust. Soc. Am. 67, 816–818 (1980).
[CrossRef]

Cancellieri, G.

G. Cancellieri, P. Fantini, “Mode Coupling Effects in Optical Fibres: Perturbative Solution of the Time Dependent Power Flow Equation,” Opt. Quantum Electron. 15, 119–123 (1983).
[CrossRef]

Castle, P. F.

A. J. Harris, P. F. Castle, “Bend Loss Measurements on High Numerical Aperture Single Mode Fibers as a Function of Wavelength and Bend Radius,” IEEE/OSA J. Lightwave Technol. LT-4, 34–40 (1986).
[CrossRef]

Chang, D. C.

D. C. Chang, E. F. Kuester, “Surface-Wave Radiation Loss from Curved Dielectric Slabs and Fibres,” IEEE J. Quantum Electron. QE-11, 903–907 (1975).

L. Lewin, D. C. Chang, E. F. Kuester, Electromagnetic Waves and Curved Structures (Peter Peregrinus, London, 1977).

de Blok, C. M.

C. M. de Blok, P. Mathiesse, “Core Alignment Monitor for Single-Mode Jointing,” Electron. lett. 20, 109–110 (1984).
[CrossRef]

Fantini, P.

G. Cancellieri, P. Fantini, “Mode Coupling Effects in Optical Fibres: Perturbative Solution of the Time Dependent Power Flow Equation,” Opt. Quantum Electron. 15, 119–123 (1983).
[CrossRef]

Fields, J. N.

J. N. Fields, C. K. Asawa, O. G. Ramer, M. K. Barnowski, “Fiber Optic Pressure Sensor,” J. Acoust. Soc. Am. 67, 816–818 (1980).
[CrossRef]

Gloge, D.

D. Gloge, “Propagation Effects in Optical Fibers,” IEEE Trans. Microwave Theory Tech. MTT-23, 106–120 (1975).
[CrossRef]

D. Gloge, “Bending Loss in Multimode Fibers with Graded and Ungraded Core Index,” Appl. Opt. 11, 2506–2513 (1972).
[CrossRef] [PubMed]

Harris, A. J.

A. J. Harris, P. F. Castle, “Bend Loss Measurements on High Numerical Aperture Single Mode Fibers as a Function of Wavelength and Bend Radius,” IEEE/OSA J. Lightwave Technol. LT-4, 34–40 (1986).
[CrossRef]

Hodel, W.

H. P. Weber, W. Hodel, “High Power Light Transmission in Optical Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 650, 102–108 (1986).

Kuester, E. F.

D. C. Chang, E. F. Kuester, “Surface-Wave Radiation Loss from Curved Dielectric Slabs and Fibres,” IEEE J. Quantum Electron. QE-11, 903–907 (1975).

L. Lewin, D. C. Chang, E. F. Kuester, Electromagnetic Waves and Curved Structures (Peter Peregrinus, London, 1977).

Lewin, L.

L. Lewin, “Radiation from Curved Dielectric Slabs and Fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718–727 (1974).
[CrossRef]

L. Lewin, D. C. Chang, E. F. Kuester, Electromagnetic Waves and Curved Structures (Peter Peregrinus, London, 1977).

Marcatili, E. A. J.

E. A. J. Marcatili, S. E. Miller, “Improved Relations Describing Directional Control in Electromagnetic Wave Guidance,” Bell Syst. Tech. J. 48, 2161–2188 (1969).

E. A. J. Marcatili, “Bends in Optical Dielectric Guides,” Bell Syst. Tech. J. 48, 2013 (1968).

Marcuse, D.

D. Marcuse, “Curvature Loss Formula for Optical Fibers,” J. Opt. Soc. Am. 66, 216–220 (1976).
[CrossRef]

D. Marcuse, “Field Deformation and Loss Caused by Curvature of Optical Fibers,” J. Opt. Soc. Am. 66, 311–320 (1976).
[CrossRef]

D. Marcuse, “Steady State Losses of Optical Fibres and Fibre Resonators,” Bell Syst. Tech. J. 55, 1445–1462 (1976).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982).

Mathiesse, P.

C. M. de Blok, P. Mathiesse, “Core Alignment Monitor for Single-Mode Jointing,” Electron. lett. 20, 109–110 (1984).
[CrossRef]

Miller, M. A.

M. A. Miller, V. I. Talanow, “Electromagnetic Surface Waves Guided by a Boundary with Small Curvature,” Zh. Tekh. Fiz. 26, 2755–2773 (1956).

Miller, S. E.

E. A. J. Marcatili, S. E. Miller, “Improved Relations Describing Directional Control in Electromagnetic Wave Guidance,” Bell Syst. Tech. J. 48, 2161–2188 (1969).

Mitchell, D. J.

A. W. Snyder, I. White, D. J. Mitchell, “Radiation Losses in Bent Wave Guides for Surface Waves,” Electron. Lett. 11, 332–333 (1975).
[CrossRef]

Ramer, O. G.

J. N. Fields, C. K. Asawa, O. G. Ramer, M. K. Barnowski, “Fiber Optic Pressure Sensor,” J. Acoust. Soc. Am. 67, 816–818 (1980).
[CrossRef]

Shevchenko, V. V.

V. V. Shevchenko, “Radiation Losses in Bent Wave Guides for Surface Waves,” Radiophys. Quantum Electron. 14, 607–614 (1973).
[CrossRef]

Snyder, A. W.

A. W. Snyder, I. White, D. J. Mitchell, “Radiation Losses in Bent Wave Guides for Surface Waves,” Electron. Lett. 11, 332–333 (1975).
[CrossRef]

Talanow, V. I.

M. A. Miller, V. I. Talanow, “Electromagnetic Surface Waves Guided by a Boundary with Small Curvature,” Zh. Tekh. Fiz. 26, 2755–2773 (1956).

Weber, H. P.

H. P. Weber, W. Hodel, “High Power Light Transmission in Optical Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 650, 102–108 (1986).

White, I.

A. W. Snyder, I. White, D. J. Mitchell, “Radiation Losses in Bent Wave Guides for Surface Waves,” Electron. Lett. 11, 332–333 (1975).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

D. Marcuse, “Steady State Losses of Optical Fibres and Fibre Resonators,” Bell Syst. Tech. J. 55, 1445–1462 (1976).

E. A. J. Marcatili, “Bends in Optical Dielectric Guides,” Bell Syst. Tech. J. 48, 2013 (1968).

J. A. Arnaud, “Transverse Coupling in Fiber Optics Part III: Bending Losses,” Bell Syst. Tech. J. 53, 1379–1324 (1974).

E. A. J. Marcatili, S. E. Miller, “Improved Relations Describing Directional Control in Electromagnetic Wave Guidance,” Bell Syst. Tech. J. 48, 2161–2188 (1969).

Electron. Lett.

A. W. Snyder, I. White, D. J. Mitchell, “Radiation Losses in Bent Wave Guides for Surface Waves,” Electron. Lett. 11, 332–333 (1975).
[CrossRef]

C. M. de Blok, P. Mathiesse, “Core Alignment Monitor for Single-Mode Jointing,” Electron. lett. 20, 109–110 (1984).
[CrossRef]

IEEE J. Quantum Electron.

D. C. Chang, E. F. Kuester, “Surface-Wave Radiation Loss from Curved Dielectric Slabs and Fibres,” IEEE J. Quantum Electron. QE-11, 903–907 (1975).

IEEE Trans. Microwave Theory Tech.

L. Lewin, “Radiation from Curved Dielectric Slabs and Fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718–727 (1974).
[CrossRef]

D. Gloge, “Propagation Effects in Optical Fibers,” IEEE Trans. Microwave Theory Tech. MTT-23, 106–120 (1975).
[CrossRef]

IEEE/OSA J. Lightwave Technol.

A. J. Harris, P. F. Castle, “Bend Loss Measurements on High Numerical Aperture Single Mode Fibers as a Function of Wavelength and Bend Radius,” IEEE/OSA J. Lightwave Technol. LT-4, 34–40 (1986).
[CrossRef]

J. Acoust. Soc. Am.

J. N. Fields, C. K. Asawa, O. G. Ramer, M. K. Barnowski, “Fiber Optic Pressure Sensor,” J. Acoust. Soc. Am. 67, 816–818 (1980).
[CrossRef]

J. Opt. Soc. Am.

Opt. Quantum Electron.

G. Cancellieri, P. Fantini, “Mode Coupling Effects in Optical Fibres: Perturbative Solution of the Time Dependent Power Flow Equation,” Opt. Quantum Electron. 15, 119–123 (1983).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

H. P. Weber, W. Hodel, “High Power Light Transmission in Optical Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 650, 102–108 (1986).

Radiophys. Quantum Electron.

V. V. Shevchenko, “Radiation Losses in Bent Wave Guides for Surface Waves,” Radiophys. Quantum Electron. 14, 607–614 (1973).
[CrossRef]

Zh. Tekh. Fiz.

M. A. Miller, V. I. Talanow, “Electromagnetic Surface Waves Guided by a Boundary with Small Curvature,” Zh. Tekh. Fiz. 26, 2755–2773 (1956).

Other

L. Lewin, D. C. Chang, E. F. Kuester, Electromagnetic Waves and Curved Structures (Peter Peregrinus, London, 1977).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982).

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Figures (10)

Fig. 1
Fig. 1

Curved Fiber: R, bend radius; a, core radius.

Fig. 2
Fig. 2

Diagram of the experiment setup: L, Nd:YAG laser; W, beam splitting wedge; D, adjustable aperture; l, launching lens; F, optical fiber; MS, mode stripper; PD1 and PD2, photodetectors; M, mandrel of radius RB.

Fig. 3
Fig. 3

(a) Far field intensity profile from an all-silica fiber with core diameter of 600 μm, numerical aperture of 0.22, and length of 50 cm, showing the trapezium fit, θi = 22% and θd = 95% of θc, where θc is calculated from the manufacturer’s specification for the numerical aperture. (b) Far field profile showing the fiber with mode stripper (----) and without mode stripper (—), in the conditions of (a). (c) Far field profile with a 6-m fiber length for the straight (—) and bent (----) fiber, in the same conditions as (a).

Fig. 4
Fig. 4

Theoretical and practical bending loss as a function of bend radius and core diameter. HCS fibers with N.A. of 0.37, 100% filling L = 6 m, and core diameters of 200, 400, 600 and 1000 μm.

Fig. 5
Fig. 5

Theoretical and practical bending loss for different fiber numerical apertures, fiber core diameter of 600 μm, L = 6 m, HCS N.A. = 0.37, and all-silica N.A. = 0.22.

Fig. 6
Fig. 6

Theoretical and practical bending loss variation with launching condition. HCS fiber with core diameter of 400 μm, L = 6 m. Input beam numerical apertures are 0.28, 0.32, and 0.37 (100% filling).

Fig. 7
Fig. 7

Theoretical bending loss as a function of fiber numerical aperture with fiber core diameter of 400 μm and bend radius of 50 mm.

Fig. 8
Fig. 8

Theoretical bending loss as a function of core radius with fiber numerical aperture of 0.3 and bend radius of 50 mm.

Fig. 9
Fig. 9

Theoretical bending loss variation with fiber filling condition with fiber numerical aperture of 0.3 and core radius of 400 μm.

Fig. 10
Fig. 10

Contour map of bending loss.

Equations (7)

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

α = 2 n 1 k ( θ c 2 θ 2 ) exp [ 2 3 n 1 k R ( θ c 2 θ 2 2 a R ) ] 3 / 2 ,
θ f = θ c ( 1 2 a R θ c 2 ) 1 / 2 ,
P ( θ ) = P 0 ( θ ) exp ( α l ) ,
P = 0 θ f P 0 ( θ ) exp ( α l ) d θ .
P r = [ 0 θ c P 0 ( θ ) d θ 0 θ f P 0 ( θ ) exp ( α l ) d θ ] / 0 θ c P 0 ( θ ) d θ .
P r = ( R 0 R 1 ) / R 0 .
P r θ f θ c P 0 ( θ ) d θ / 0 θ o P 0 ( θ ) d θ ,

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