Abstract

Our main goal is to provide a comprehensive explanation of the existing differences in bending losses arising from having step-index multimode plastic optical fibers with different cladding thicknesses and under different types of conditions, namely, the variable bend radius R, the number of fiber turns, or the fiber diameter. For this purpose, both experimental and numerical results of bending losses are presented for different cladding thicknesses and conditions. For the measurements, two cladding thicknesses have been considered: one finite and another infinite. A fiber in air has a finite cladding thickness, and rays are reflected at the cladding-air interface, whereas a fiber covered by oil is equivalent to having an infinite cladding, since the very similar refractive index of oil prevents reflections from occurring at the cladding-oil interface. For the sake of comparison, numerical simulations based on ray tracing have been performed for finite-cladding step-index multimode waveguides. The numerical results reinforce the experimental data, and both the experimental measurements and the computational simulations turn out to be very useful to explain the behavior of refracting and tunneling rays along bent multimode waveguides and along finite-cladding fibers.

© 2003 Optical Society of America

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References

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  1. Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
    [CrossRef]
  2. Y. Koike, “Progress in GI-POF_Status of high speed plastic optical fiber and its future prospect,” in Proceedings of the Ninth International Conference on Plastic Optical Fibres and Applications-POF’00, Boston, Massachusetts, 2000 (Information Gatekeepers, Boston, Mass., 2000), pp. 1–5.
  3. T. Ishigure, E. Nihei, Y. Koike, “Optimum refractive index profile for graded-index polymer optical fibres, toward gigabit data links,” Appl. Opt. 35, 2048–2053 (1996).
    [CrossRef] [PubMed]
  4. M. Naritomi, “Model home project in Japan using GI-POF,” in Proceedings of the Ninth International Conference on Plastic Optical Fibres and Applications-POF’00, Boston, Massachusetts, 2000 (Information Gatekeepers, Boston, Mass., 2000), pp. 8–11.
  5. M. Naritomi, “CYTOP Amorphous Fluoropolymers for low loss POF,” in POF Asia Pacific Forum 1996, Tokyo, Japan, 1996 (POF Consortium, Tokyo, Japan, 1996), p. 23.
  6. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
  7. D. S. Jones, The Theory of Electromagnetism (Pergamon, New York, 1964).
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    [CrossRef]
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    [CrossRef] [PubMed]
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  11. J. D. Love, C. Winkler, “Power attenuation in bent multimode step-index slab and fiber waveguides,” Electron. Lett. 14, 32–34 (1978).
    [CrossRef]
  12. C. Winkler, J. D. Love, A. K. Ghatak, “Power attenuation in bent parabolic-index slab and fiber waveguides,” Electron. Lett. 14, 570–571 (1978).
    [CrossRef]
  13. A. W. Snyder, J. D. Love, “Reflection at a curved dielectric interface-electromagnetic tunnelling,” IEEE Trans. Microwave Theory Tech. MTT-23, 134–141 (1975).
    [CrossRef]
  14. D. Gloge, “Bending loss in multimode fibers with graded and ungraded core index,” Appl. Opt. 11, 2506–2513 (1972).
    [CrossRef] [PubMed]
  15. A. P. Boechat, D. Su, D. R. Hall, D. C. Jones, “Bend loss in large multimode optical fiber beam delivery system,” Appl. Opt. 30, 321–327 (1991).
    [CrossRef] [PubMed]
  16. “High performance plastic fiber optics, ESKA™,” technical leaflet, Mitsubishi Rayon Co., Tokyo, Japan.

1996

1995

Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
[CrossRef]

1991

A. P. Boechat, D. Su, D. R. Hall, D. C. Jones, “Bend loss in large multimode optical fiber beam delivery system,” Appl. Opt. 30, 321–327 (1991).
[CrossRef] [PubMed]

1988

1979

C. Winkler, J. D. Love, A. K. Ghatak, “Loss calculations in bent multimode optical waveguides,” Opt. Quantum Electron. 11, 173–183 (1979).
[CrossRef]

1978

J. D. Love, C. Winkler, “Power attenuation in bent multimode step-index slab and fiber waveguides,” Electron. Lett. 14, 32–34 (1978).
[CrossRef]

C. Winkler, J. D. Love, A. K. Ghatak, “Power attenuation in bent parabolic-index slab and fiber waveguides,” Electron. Lett. 14, 570–571 (1978).
[CrossRef]

1975

A. W. Snyder, J. D. Love, “Reflection at a curved dielectric interface-electromagnetic tunnelling,” IEEE Trans. Microwave Theory Tech. MTT-23, 134–141 (1975).
[CrossRef]

1974

A. W. Snyder, D. J. Mitchell, “Generalized Fresnel’s laws for determining radiation loss from optical waveguides and curved dielectric structures,” Optik (Stuttgart) 40, 438–459 (1974).

1972

D. Gloge, “Bending loss in multimode fibers with graded and ungraded core index,” Appl. Opt. 11, 2506–2513 (1972).
[CrossRef] [PubMed]

Boechat, A. P.

A. P. Boechat, D. Su, D. R. Hall, D. C. Jones, “Bend loss in large multimode optical fiber beam delivery system,” Appl. Opt. 30, 321–327 (1991).
[CrossRef] [PubMed]

Ghatak, A.

Ghatak, A. K.

C. Winkler, J. D. Love, A. K. Ghatak, “Loss calculations in bent multimode optical waveguides,” Opt. Quantum Electron. 11, 173–183 (1979).
[CrossRef]

C. Winkler, J. D. Love, A. K. Ghatak, “Power attenuation in bent parabolic-index slab and fiber waveguides,” Electron. Lett. 14, 570–571 (1978).
[CrossRef]

Gloge, D.

D. Gloge, “Bending loss in multimode fibers with graded and ungraded core index,” Appl. Opt. 11, 2506–2513 (1972).
[CrossRef] [PubMed]

Hall, D. R.

A. P. Boechat, D. Su, D. R. Hall, D. C. Jones, “Bend loss in large multimode optical fiber beam delivery system,” Appl. Opt. 30, 321–327 (1991).
[CrossRef] [PubMed]

Ishigure, T.

T. Ishigure, E. Nihei, Y. Koike, “Optimum refractive index profile for graded-index polymer optical fibres, toward gigabit data links,” Appl. Opt. 35, 2048–2053 (1996).
[CrossRef] [PubMed]

Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
[CrossRef]

Jones, D. C.

A. P. Boechat, D. Su, D. R. Hall, D. C. Jones, “Bend loss in large multimode optical fiber beam delivery system,” Appl. Opt. 30, 321–327 (1991).
[CrossRef] [PubMed]

Jones, D. S.

D. S. Jones, The Theory of Electromagnetism (Pergamon, New York, 1964).

Koike, Y.

T. Ishigure, E. Nihei, Y. Koike, “Optimum refractive index profile for graded-index polymer optical fibres, toward gigabit data links,” Appl. Opt. 35, 2048–2053 (1996).
[CrossRef] [PubMed]

Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
[CrossRef]

Y. Koike, “Progress in GI-POF_Status of high speed plastic optical fiber and its future prospect,” in Proceedings of the Ninth International Conference on Plastic Optical Fibres and Applications-POF’00, Boston, Massachusetts, 2000 (Information Gatekeepers, Boston, Mass., 2000), pp. 1–5.

Kompella, J.

Love, J. D.

C. Winkler, J. D. Love, A. K. Ghatak, “Loss calculations in bent multimode optical waveguides,” Opt. Quantum Electron. 11, 173–183 (1979).
[CrossRef]

C. Winkler, J. D. Love, A. K. Ghatak, “Power attenuation in bent parabolic-index slab and fiber waveguides,” Electron. Lett. 14, 570–571 (1978).
[CrossRef]

J. D. Love, C. Winkler, “Power attenuation in bent multimode step-index slab and fiber waveguides,” Electron. Lett. 14, 32–34 (1978).
[CrossRef]

A. W. Snyder, J. D. Love, “Reflection at a curved dielectric interface-electromagnetic tunnelling,” IEEE Trans. Microwave Theory Tech. MTT-23, 134–141 (1975).
[CrossRef]

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

Mitchell, D. J.

A. W. Snyder, D. J. Mitchell, “Generalized Fresnel’s laws for determining radiation loss from optical waveguides and curved dielectric structures,” Optik (Stuttgart) 40, 438–459 (1974).

Naritomi, M.

M. Naritomi, “Model home project in Japan using GI-POF,” in Proceedings of the Ninth International Conference on Plastic Optical Fibres and Applications-POF’00, Boston, Massachusetts, 2000 (Information Gatekeepers, Boston, Mass., 2000), pp. 8–11.

M. Naritomi, “CYTOP Amorphous Fluoropolymers for low loss POF,” in POF Asia Pacific Forum 1996, Tokyo, Japan, 1996 (POF Consortium, Tokyo, Japan, 1996), p. 23.

Nihei, E.

T. Ishigure, E. Nihei, Y. Koike, “Optimum refractive index profile for graded-index polymer optical fibres, toward gigabit data links,” Appl. Opt. 35, 2048–2053 (1996).
[CrossRef] [PubMed]

Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
[CrossRef]

Sharma, E.

Snyder, A. W.

A. W. Snyder, J. D. Love, “Reflection at a curved dielectric interface-electromagnetic tunnelling,” IEEE Trans. Microwave Theory Tech. MTT-23, 134–141 (1975).
[CrossRef]

A. W. Snyder, D. J. Mitchell, “Generalized Fresnel’s laws for determining radiation loss from optical waveguides and curved dielectric structures,” Optik (Stuttgart) 40, 438–459 (1974).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

Su, D.

A. P. Boechat, D. Su, D. R. Hall, D. C. Jones, “Bend loss in large multimode optical fiber beam delivery system,” Appl. Opt. 30, 321–327 (1991).
[CrossRef] [PubMed]

Winkler, C.

C. Winkler, J. D. Love, A. K. Ghatak, “Loss calculations in bent multimode optical waveguides,” Opt. Quantum Electron. 11, 173–183 (1979).
[CrossRef]

J. D. Love, C. Winkler, “Power attenuation in bent multimode step-index slab and fiber waveguides,” Electron. Lett. 14, 32–34 (1978).
[CrossRef]

C. Winkler, J. D. Love, A. K. Ghatak, “Power attenuation in bent parabolic-index slab and fiber waveguides,” Electron. Lett. 14, 570–571 (1978).
[CrossRef]

Appl. Opt.

D. Gloge, “Bending loss in multimode fibers with graded and ungraded core index,” Appl. Opt. 11, 2506–2513 (1972).
[CrossRef] [PubMed]

A. P. Boechat, D. Su, D. R. Hall, D. C. Jones, “Bend loss in large multimode optical fiber beam delivery system,” Appl. Opt. 30, 321–327 (1991).
[CrossRef] [PubMed]

Appl. Opt.

Electron. Lett.

J. D. Love, C. Winkler, “Power attenuation in bent multimode step-index slab and fiber waveguides,” Electron. Lett. 14, 32–34 (1978).
[CrossRef]

C. Winkler, J. D. Love, A. K. Ghatak, “Power attenuation in bent parabolic-index slab and fiber waveguides,” Electron. Lett. 14, 570–571 (1978).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

A. W. Snyder, J. D. Love, “Reflection at a curved dielectric interface-electromagnetic tunnelling,” IEEE Trans. Microwave Theory Tech. MTT-23, 134–141 (1975).
[CrossRef]

J. Lightwave Technol.

Y. Koike, T. Ishigure, E. Nihei, “High-bandwidth graded index polymer optical fiber,” J. Lightwave Technol. 13, 1475–1489 (1995).
[CrossRef]

Opt. Quantum Electron.

C. Winkler, J. D. Love, A. K. Ghatak, “Loss calculations in bent multimode optical waveguides,” Opt. Quantum Electron. 11, 173–183 (1979).
[CrossRef]

Optik (Stuttgart)

A. W. Snyder, D. J. Mitchell, “Generalized Fresnel’s laws for determining radiation loss from optical waveguides and curved dielectric structures,” Optik (Stuttgart) 40, 438–459 (1974).

Other

M. Naritomi, “Model home project in Japan using GI-POF,” in Proceedings of the Ninth International Conference on Plastic Optical Fibres and Applications-POF’00, Boston, Massachusetts, 2000 (Information Gatekeepers, Boston, Mass., 2000), pp. 8–11.

M. Naritomi, “CYTOP Amorphous Fluoropolymers for low loss POF,” in POF Asia Pacific Forum 1996, Tokyo, Japan, 1996 (POF Consortium, Tokyo, Japan, 1996), p. 23.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

D. S. Jones, The Theory of Electromagnetism (Pergamon, New York, 1964).

Y. Koike, “Progress in GI-POF_Status of high speed plastic optical fiber and its future prospect,” in Proceedings of the Ninth International Conference on Plastic Optical Fibres and Applications-POF’00, Boston, Massachusetts, 2000 (Information Gatekeepers, Boston, Mass., 2000), pp. 1–5.

“High performance plastic fiber optics, ESKA™,” technical leaflet, Mitsubishi Rayon Co., Tokyo, Japan.

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Figures (9)

Fig. 1
Fig. 1

Diagram showing the experimental setup. L, white light source; M, monochromator; CS, convergent lens; O, object lens; POF, plastic optical fiber; R, cylinder with radius R; OH, optical head; LM, lightwave multimeter; C, computer.

Fig. 2
Fig. 2

Typical ray path in a bent fiber of finite cladding thickness. The classical path in the core is shown with a thick line. The other ray paths represent guided rays as a consequence of the finite cladding thickness.

Fig. 3
Fig. 3

Output power in decibels relative to the unbent POF as a function of wavelength for a different number of full turns around the cylinder of radius R = 5.1 mm. Fiber diameter considered: d POF = 1 mm.

Fig. 4
Fig. 4

Measured relative output power as a function of the number of full turns. Different curves correspond to different bend radii. The case of ten fiber turns dipped in oil is also included.

Fig. 5
Fig. 5

Detected relative output power as a function of the wavelength for n = 2 and n = 10 fiber turns, with and without oil.

Fig. 6
Fig. 6

Representation of the power difference P 2 - P 1 at the fiber output for different bend radii R and for n = 2 and n = 10 fiber turns. P 1, power received when the bent section of the fiber is dipped in oil; P 2, power received when the entire fiber is left in air. Experimental as well as computational results are presented for a fixed value of the wavelength (λ = 540 nm).

Fig. 7
Fig. 7

Power difference P 2 - P 1 at the POF exit for different bending radii and n = 2 fiber full turns. Experimental as well as computational results are presented for three fiber diameters: d 1 = 1.00, d 2 = 0.75, and d 3 = 0.50 mm.

Fig. 8
Fig. 8

Simulated values of the relative output power for different cladding thicknesses when the fiber is covered by air (squares) and by oil (triangles). As the cladding thickness increases, the curve corresponding to the air-covered POF converges to the straight line that corresponds to the fiber dipped in oil (congruent to the infinite cladding thickness).

Fig. 9
Fig. 9

Numerical simulation showing the power received at the waveguide output as a function of the number of waveguide turns around a cylinder of radius R = 8.00 mm. The waveguide is covered by air. Waveguide core diameter, 980 μm; cladding thickness, 10 μm; n core = 1.492; n cladding = 1.402.

Equations (2)

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T r = 4   sin   θ i sin 2   θ i - sin 2   θ c 1 / 2 sin   θ i + sin 2   θ i - sin 2   θ c 1 / 2 2 ,
T t = 4   sin   θ i sin   θ c 1 - sin 2   θ i sin 2   θ c 1 / 2   exp - 2 / 3 n co k × R + ρ θ c 2 - θ i 2 3 / 2 ,

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