Abstract

A theoretical expression is derived, based on a geometrical optics approach, with which to predict light-transmission losses in multimode plastic optical fibers for office or home lighting. Two types of optical ray arrangement, meridional ray and skew ray, are evaluated, and five loss mechanisms are identified and considered. The meridional arrangement results in a lower overall loss of light than the skew ray arrangement. The theoretical results were compared with experimental measurements taken for a 0.5-cm-diameter polymer optical fiber. For optical rays entering the fiber at incident angles of less than 20°, the theoretical results are in good agreement with the empirical results.

© 2005 Optical Society of America

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References

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  1. M. R. Cates, S. L. Jaiswal, L. C. Maxey, D. D. Earl, “Characterization of transmission properties of 3M LF120C plastic optical light guide,” in Proceedings of International Solar Energy Conference—ISEC, M. D. Thornbloom, S. A. Jones, eds. (American Society of Mechanical Engineers, New York, 2003), paper 44016.
  2. W. J. Cassarly, J. M. Davenport, “Advances in fiber optics: fiber applications move into the mainstream,” in Proceedings of 8th International Symposium on the Science and Technology of Light Sources LS-8 (Institute For Low Temperature Plasma Physics, Greifswald, Germany, 1998), pp. 61–69.
  3. J. Zubia, J. Arrue, “Plastic optical fibers: an introduction to their technological processes and applications,” Opt. Fiber Technol. 7, 101–140 (2001).
    [CrossRef]
  4. O. V. Kolninov, I. P. Shelukhov, E. R. Klinshpont, Z. N. Lavrova, A. M. Baran, V. M. Levin, “Effect of naphthalene additive on the radiation degradation of polymethylmethacrylate,” Radiat. Phys. Chem. 46, 843–846 (1995).
    [CrossRef]
  5. Y. Takezawa, N. Taketani, S. Tanno, S. Ohara, “Light absorption due to higher harmonics of molecular vibrations in transparent amorphous polymers for plastic optical fibers,” J. Polym. Sci. Part B Polym. Phys. 30, 879–885 (1992).
    [CrossRef]
  6. H. Liu, P. Yager, “Modeling of optical bending losses in multimode waveguides,” in Biomedical Optoelectronic Instrumentation, A. Katzir, J. A. Harrington, D. M. Harris, eds., Proc. SPIE2396, 120–129 (1995).
    [CrossRef]
  7. T. Kaino, “Plastic optical fibers,” in Polymers in Optics: Physics, Chemistry, and Applications, R. A. Lessard, W. F. Frank, eds., Vol. CR63 of SPIE Critical Reviews (SPIE, Bellingham, Wash., 1996), pp. 164–187.
  8. T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp systems by the fiber optic cables,” in 1998 SAE International Congress and Exposition, Detroit (Society of Automotive Engineers, Warrendale, PA, 1998), pp. 1827–1836.
  9. A. Biermann, N. Narendran, N. Maliyagoda, “How to report light loss values for optical fibers used in fiber-optic lighting applications,” in Illumination and Source Engineering, A. V. Arecchi, ed., Proc. SPIE3428, 62–72 (1998).
    [CrossRef]
  10. H. Nagata, “Effect of heating on jacketed optical fibers,” Opt. Fiber Technol. 6, 192–198 (2000).
    [CrossRef]
  11. Y. Takezawa, S. Tanno, N. Taketani, S. Ohara, H. Asano, “Analysis of thermal degradation for plastic optical fibers,” J. Appl. Polym. Sci. 42, 2811–2817 (1991).
    [CrossRef]
  12. S. Tsao, W. Cheng, “Simplified formula of bending loss for optical fiber sensors,” Fiber Integr. Opt. 21, 333–344 (2002).
    [CrossRef]
  13. J. T. Remillard, M. P. Everson, W. H. Weber, “Loss mechanisms in optical light pipes,” Appl. Opt. 31, 7232–7241 (1992).
    [CrossRef] [PubMed]
  14. T. Ishigure, M. Sato, A. Kondo, Y. Tsukimori, Y. Koike, “Graded-index polymer optical fiber with high temperature and high humidity stability,” J. Lightwave Technol. 20, 1818–1825 (2002).
    [CrossRef]
  15. T. Ishigure, H. Endo, K. Ohdoko, Y. Koike, “High-bandwidth plastic optical fiber with w-refractive index profile,” IEEE Photon. Technol. Lett. 16, 2081–2083 (2004).
    [CrossRef]
  16. Product specification web catalog at http://www.lumenyte.com/product/specs/Ffiber[1].HTM .
  17. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).
  18. J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw-Hill, New York, 1990).
  19. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (U.S. Government Printing Office, Washington, D.C., 1977).
  20. M. F. Modest, “Fundamentals of thermal radiation” and “Radiative properties of real surfaces,” in Radiative Heat Transfer, J. J. Corrigan, J. M. Morris, eds. (McGraw-Hill, New York, 1993), Chap. 1, p. 7;Radiative Heat TransferChap. 3, p. 88.
  21. G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
    [CrossRef]

2004

T. Ishigure, H. Endo, K. Ohdoko, Y. Koike, “High-bandwidth plastic optical fiber with w-refractive index profile,” IEEE Photon. Technol. Lett. 16, 2081–2083 (2004).
[CrossRef]

2002

2001

J. Zubia, J. Arrue, “Plastic optical fibers: an introduction to their technological processes and applications,” Opt. Fiber Technol. 7, 101–140 (2001).
[CrossRef]

2000

H. Nagata, “Effect of heating on jacketed optical fibers,” Opt. Fiber Technol. 6, 192–198 (2000).
[CrossRef]

1995

O. V. Kolninov, I. P. Shelukhov, E. R. Klinshpont, Z. N. Lavrova, A. M. Baran, V. M. Levin, “Effect of naphthalene additive on the radiation degradation of polymethylmethacrylate,” Radiat. Phys. Chem. 46, 843–846 (1995).
[CrossRef]

1992

Y. Takezawa, N. Taketani, S. Tanno, S. Ohara, “Light absorption due to higher harmonics of molecular vibrations in transparent amorphous polymers for plastic optical fibers,” J. Polym. Sci. Part B Polym. Phys. 30, 879–885 (1992).
[CrossRef]

J. T. Remillard, M. P. Everson, W. H. Weber, “Loss mechanisms in optical light pipes,” Appl. Opt. 31, 7232–7241 (1992).
[CrossRef] [PubMed]

1991

Y. Takezawa, S. Tanno, N. Taketani, S. Ohara, H. Asano, “Analysis of thermal degradation for plastic optical fibers,” J. Appl. Polym. Sci. 42, 2811–2817 (1991).
[CrossRef]

1984

G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Allen, G. R.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp systems by the fiber optic cables,” in 1998 SAE International Congress and Exposition, Detroit (Society of Automotive Engineers, Warrendale, PA, 1998), pp. 1827–1836.

Arrue, J.

J. Zubia, J. Arrue, “Plastic optical fibers: an introduction to their technological processes and applications,” Opt. Fiber Technol. 7, 101–140 (2001).
[CrossRef]

Asano, H.

Y. Takezawa, S. Tanno, N. Taketani, S. Ohara, H. Asano, “Analysis of thermal degradation for plastic optical fibers,” J. Appl. Polym. Sci. 42, 2811–2817 (1991).
[CrossRef]

Baran, A. M.

O. V. Kolninov, I. P. Shelukhov, E. R. Klinshpont, Z. N. Lavrova, A. M. Baran, V. M. Levin, “Effect of naphthalene additive on the radiation degradation of polymethylmethacrylate,” Radiat. Phys. Chem. 46, 843–846 (1995).
[CrossRef]

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

Biermann, A.

A. Biermann, N. Narendran, N. Maliyagoda, “How to report light loss values for optical fibers used in fiber-optic lighting applications,” in Illumination and Source Engineering, A. V. Arecchi, ed., Proc. SPIE3428, 62–72 (1998).
[CrossRef]

Buelow, R. F.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp systems by the fiber optic cables,” in 1998 SAE International Congress and Exposition, Detroit (Society of Automotive Engineers, Warrendale, PA, 1998), pp. 1827–1836.

Cassarly, W. J.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp systems by the fiber optic cables,” in 1998 SAE International Congress and Exposition, Detroit (Society of Automotive Engineers, Warrendale, PA, 1998), pp. 1827–1836.

W. J. Cassarly, J. M. Davenport, “Advances in fiber optics: fiber applications move into the mainstream,” in Proceedings of 8th International Symposium on the Science and Technology of Light Sources LS-8 (Institute For Low Temperature Plasma Physics, Greifswald, Germany, 1998), pp. 61–69.

Cates, M. R.

M. R. Cates, S. L. Jaiswal, L. C. Maxey, D. D. Earl, “Characterization of transmission properties of 3M LF120C plastic optical light guide,” in Proceedings of International Solar Energy Conference—ISEC, M. D. Thornbloom, S. A. Jones, eds. (American Society of Mechanical Engineers, New York, 2003), paper 44016.

Cheng, W.

S. Tsao, W. Cheng, “Simplified formula of bending loss for optical fiber sensors,” Fiber Integr. Opt. 21, 333–344 (2002).
[CrossRef]

Davenport, J. M.

W. J. Cassarly, J. M. Davenport, “Advances in fiber optics: fiber applications move into the mainstream,” in Proceedings of 8th International Symposium on the Science and Technology of Light Sources LS-8 (Institute For Low Temperature Plasma Physics, Greifswald, Germany, 1998), pp. 61–69.

Davenport, T. L.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp systems by the fiber optic cables,” in 1998 SAE International Congress and Exposition, Detroit (Society of Automotive Engineers, Warrendale, PA, 1998), pp. 1827–1836.

Earl, D. D.

M. R. Cates, S. L. Jaiswal, L. C. Maxey, D. D. Earl, “Characterization of transmission properties of 3M LF120C plastic optical light guide,” in Proceedings of International Solar Energy Conference—ISEC, M. D. Thornbloom, S. A. Jones, eds. (American Society of Mechanical Engineers, New York, 2003), paper 44016.

Endo, H.

T. Ishigure, H. Endo, K. Ohdoko, Y. Koike, “High-bandwidth plastic optical fiber with w-refractive index profile,” IEEE Photon. Technol. Lett. 16, 2081–2083 (2004).
[CrossRef]

Everson, M. P.

Ford, G. W.

G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (U.S. Government Printing Office, Washington, D.C., 1977).

Hansler, R. L.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp systems by the fiber optic cables,” in 1998 SAE International Congress and Exposition, Detroit (Society of Automotive Engineers, Warrendale, PA, 1998), pp. 1827–1836.

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (U.S. Government Printing Office, Washington, D.C., 1977).

Ishigure, T.

T. Ishigure, H. Endo, K. Ohdoko, Y. Koike, “High-bandwidth plastic optical fiber with w-refractive index profile,” IEEE Photon. Technol. Lett. 16, 2081–2083 (2004).
[CrossRef]

T. Ishigure, M. Sato, A. Kondo, Y. Tsukimori, Y. Koike, “Graded-index polymer optical fiber with high temperature and high humidity stability,” J. Lightwave Technol. 20, 1818–1825 (2002).
[CrossRef]

Jaiswal, S. L.

M. R. Cates, S. L. Jaiswal, L. C. Maxey, D. D. Earl, “Characterization of transmission properties of 3M LF120C plastic optical light guide,” in Proceedings of International Solar Energy Conference—ISEC, M. D. Thornbloom, S. A. Jones, eds. (American Society of Mechanical Engineers, New York, 2003), paper 44016.

Kaino, T.

T. Kaino, “Plastic optical fibers,” in Polymers in Optics: Physics, Chemistry, and Applications, R. A. Lessard, W. F. Frank, eds., Vol. CR63 of SPIE Critical Reviews (SPIE, Bellingham, Wash., 1996), pp. 164–187.

Klinshpont, E. R.

O. V. Kolninov, I. P. Shelukhov, E. R. Klinshpont, Z. N. Lavrova, A. M. Baran, V. M. Levin, “Effect of naphthalene additive on the radiation degradation of polymethylmethacrylate,” Radiat. Phys. Chem. 46, 843–846 (1995).
[CrossRef]

Koike, Y.

T. Ishigure, H. Endo, K. Ohdoko, Y. Koike, “High-bandwidth plastic optical fiber with w-refractive index profile,” IEEE Photon. Technol. Lett. 16, 2081–2083 (2004).
[CrossRef]

T. Ishigure, M. Sato, A. Kondo, Y. Tsukimori, Y. Koike, “Graded-index polymer optical fiber with high temperature and high humidity stability,” J. Lightwave Technol. 20, 1818–1825 (2002).
[CrossRef]

Kolninov, O. V.

O. V. Kolninov, I. P. Shelukhov, E. R. Klinshpont, Z. N. Lavrova, A. M. Baran, V. M. Levin, “Effect of naphthalene additive on the radiation degradation of polymethylmethacrylate,” Radiat. Phys. Chem. 46, 843–846 (1995).
[CrossRef]

Kondo, A.

Lavrova, Z. N.

O. V. Kolninov, I. P. Shelukhov, E. R. Klinshpont, Z. N. Lavrova, A. M. Baran, V. M. Levin, “Effect of naphthalene additive on the radiation degradation of polymethylmethacrylate,” Radiat. Phys. Chem. 46, 843–846 (1995).
[CrossRef]

Levin, V. M.

O. V. Kolninov, I. P. Shelukhov, E. R. Klinshpont, Z. N. Lavrova, A. M. Baran, V. M. Levin, “Effect of naphthalene additive on the radiation degradation of polymethylmethacrylate,” Radiat. Phys. Chem. 46, 843–846 (1995).
[CrossRef]

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (U.S. Government Printing Office, Washington, D.C., 1977).

Liu, H.

H. Liu, P. Yager, “Modeling of optical bending losses in multimode waveguides,” in Biomedical Optoelectronic Instrumentation, A. Katzir, J. A. Harrington, D. M. Harris, eds., Proc. SPIE2396, 120–129 (1995).
[CrossRef]

Maliyagoda, N.

A. Biermann, N. Narendran, N. Maliyagoda, “How to report light loss values for optical fibers used in fiber-optic lighting applications,” in Illumination and Source Engineering, A. V. Arecchi, ed., Proc. SPIE3428, 62–72 (1998).
[CrossRef]

Maxey, L. C.

M. R. Cates, S. L. Jaiswal, L. C. Maxey, D. D. Earl, “Characterization of transmission properties of 3M LF120C plastic optical light guide,” in Proceedings of International Solar Energy Conference—ISEC, M. D. Thornbloom, S. A. Jones, eds. (American Society of Mechanical Engineers, New York, 2003), paper 44016.

Modest, M. F.

M. F. Modest, “Fundamentals of thermal radiation” and “Radiative properties of real surfaces,” in Radiative Heat Transfer, J. J. Corrigan, J. M. Morris, eds. (McGraw-Hill, New York, 1993), Chap. 1, p. 7;Radiative Heat TransferChap. 3, p. 88.

Nagata, H.

H. Nagata, “Effect of heating on jacketed optical fibers,” Opt. Fiber Technol. 6, 192–198 (2000).
[CrossRef]

Narendran, N.

A. Biermann, N. Narendran, N. Maliyagoda, “How to report light loss values for optical fibers used in fiber-optic lighting applications,” in Illumination and Source Engineering, A. V. Arecchi, ed., Proc. SPIE3428, 62–72 (1998).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (U.S. Government Printing Office, Washington, D.C., 1977).

Ohara, S.

Y. Takezawa, N. Taketani, S. Tanno, S. Ohara, “Light absorption due to higher harmonics of molecular vibrations in transparent amorphous polymers for plastic optical fibers,” J. Polym. Sci. Part B Polym. Phys. 30, 879–885 (1992).
[CrossRef]

Y. Takezawa, S. Tanno, N. Taketani, S. Ohara, H. Asano, “Analysis of thermal degradation for plastic optical fibers,” J. Appl. Polym. Sci. 42, 2811–2817 (1991).
[CrossRef]

Ohdoko, K.

T. Ishigure, H. Endo, K. Ohdoko, Y. Koike, “High-bandwidth plastic optical fiber with w-refractive index profile,” IEEE Photon. Technol. Lett. 16, 2081–2083 (2004).
[CrossRef]

Remillard, J. T.

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (U.S. Government Printing Office, Washington, D.C., 1977).

Sato, M.

Shelukhov, I. P.

O. V. Kolninov, I. P. Shelukhov, E. R. Klinshpont, Z. N. Lavrova, A. M. Baran, V. M. Levin, “Effect of naphthalene additive on the radiation degradation of polymethylmethacrylate,” Radiat. Phys. Chem. 46, 843–846 (1995).
[CrossRef]

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

Stenger, T. E.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp systems by the fiber optic cables,” in 1998 SAE International Congress and Exposition, Detroit (Society of Automotive Engineers, Warrendale, PA, 1998), pp. 1827–1836.

Stover, J. C.

J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw-Hill, New York, 1990).

Taketani, N.

Y. Takezawa, N. Taketani, S. Tanno, S. Ohara, “Light absorption due to higher harmonics of molecular vibrations in transparent amorphous polymers for plastic optical fibers,” J. Polym. Sci. Part B Polym. Phys. 30, 879–885 (1992).
[CrossRef]

Y. Takezawa, S. Tanno, N. Taketani, S. Ohara, H. Asano, “Analysis of thermal degradation for plastic optical fibers,” J. Appl. Polym. Sci. 42, 2811–2817 (1991).
[CrossRef]

Takezawa, Y.

Y. Takezawa, N. Taketani, S. Tanno, S. Ohara, “Light absorption due to higher harmonics of molecular vibrations in transparent amorphous polymers for plastic optical fibers,” J. Polym. Sci. Part B Polym. Phys. 30, 879–885 (1992).
[CrossRef]

Y. Takezawa, S. Tanno, N. Taketani, S. Ohara, H. Asano, “Analysis of thermal degradation for plastic optical fibers,” J. Appl. Polym. Sci. 42, 2811–2817 (1991).
[CrossRef]

Tanno, S.

Y. Takezawa, N. Taketani, S. Tanno, S. Ohara, “Light absorption due to higher harmonics of molecular vibrations in transparent amorphous polymers for plastic optical fibers,” J. Polym. Sci. Part B Polym. Phys. 30, 879–885 (1992).
[CrossRef]

Y. Takezawa, S. Tanno, N. Taketani, S. Ohara, H. Asano, “Analysis of thermal degradation for plastic optical fibers,” J. Appl. Polym. Sci. 42, 2811–2817 (1991).
[CrossRef]

Tsao, S.

S. Tsao, W. Cheng, “Simplified formula of bending loss for optical fiber sensors,” Fiber Integr. Opt. 21, 333–344 (2002).
[CrossRef]

Tsukimori, Y.

Weber, W. H.

J. T. Remillard, M. P. Everson, W. H. Weber, “Loss mechanisms in optical light pipes,” Appl. Opt. 31, 7232–7241 (1992).
[CrossRef] [PubMed]

G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Yager, P.

H. Liu, P. Yager, “Modeling of optical bending losses in multimode waveguides,” in Biomedical Optoelectronic Instrumentation, A. Katzir, J. A. Harrington, D. M. Harris, eds., Proc. SPIE2396, 120–129 (1995).
[CrossRef]

Zubia, J.

J. Zubia, J. Arrue, “Plastic optical fibers: an introduction to their technological processes and applications,” Opt. Fiber Technol. 7, 101–140 (2001).
[CrossRef]

Appl. Opt.

Fiber Integr. Opt.

S. Tsao, W. Cheng, “Simplified formula of bending loss for optical fiber sensors,” Fiber Integr. Opt. 21, 333–344 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

T. Ishigure, H. Endo, K. Ohdoko, Y. Koike, “High-bandwidth plastic optical fiber with w-refractive index profile,” IEEE Photon. Technol. Lett. 16, 2081–2083 (2004).
[CrossRef]

J. Appl. Polym. Sci.

Y. Takezawa, S. Tanno, N. Taketani, S. Ohara, H. Asano, “Analysis of thermal degradation for plastic optical fibers,” J. Appl. Polym. Sci. 42, 2811–2817 (1991).
[CrossRef]

J. Lightwave Technol.

J. Polym. Sci. Part B Polym. Phys.

Y. Takezawa, N. Taketani, S. Tanno, S. Ohara, “Light absorption due to higher harmonics of molecular vibrations in transparent amorphous polymers for plastic optical fibers,” J. Polym. Sci. Part B Polym. Phys. 30, 879–885 (1992).
[CrossRef]

Opt. Fiber Technol.

J. Zubia, J. Arrue, “Plastic optical fibers: an introduction to their technological processes and applications,” Opt. Fiber Technol. 7, 101–140 (2001).
[CrossRef]

H. Nagata, “Effect of heating on jacketed optical fibers,” Opt. Fiber Technol. 6, 192–198 (2000).
[CrossRef]

Phys. Rep.

G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Radiat. Phys. Chem.

O. V. Kolninov, I. P. Shelukhov, E. R. Klinshpont, Z. N. Lavrova, A. M. Baran, V. M. Levin, “Effect of naphthalene additive on the radiation degradation of polymethylmethacrylate,” Radiat. Phys. Chem. 46, 843–846 (1995).
[CrossRef]

Other

M. R. Cates, S. L. Jaiswal, L. C. Maxey, D. D. Earl, “Characterization of transmission properties of 3M LF120C plastic optical light guide,” in Proceedings of International Solar Energy Conference—ISEC, M. D. Thornbloom, S. A. Jones, eds. (American Society of Mechanical Engineers, New York, 2003), paper 44016.

W. J. Cassarly, J. M. Davenport, “Advances in fiber optics: fiber applications move into the mainstream,” in Proceedings of 8th International Symposium on the Science and Technology of Light Sources LS-8 (Institute For Low Temperature Plasma Physics, Greifswald, Germany, 1998), pp. 61–69.

H. Liu, P. Yager, “Modeling of optical bending losses in multimode waveguides,” in Biomedical Optoelectronic Instrumentation, A. Katzir, J. A. Harrington, D. M. Harris, eds., Proc. SPIE2396, 120–129 (1995).
[CrossRef]

T. Kaino, “Plastic optical fibers,” in Polymers in Optics: Physics, Chemistry, and Applications, R. A. Lessard, W. F. Frank, eds., Vol. CR63 of SPIE Critical Reviews (SPIE, Bellingham, Wash., 1996), pp. 164–187.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp systems by the fiber optic cables,” in 1998 SAE International Congress and Exposition, Detroit (Society of Automotive Engineers, Warrendale, PA, 1998), pp. 1827–1836.

A. Biermann, N. Narendran, N. Maliyagoda, “How to report light loss values for optical fibers used in fiber-optic lighting applications,” in Illumination and Source Engineering, A. V. Arecchi, ed., Proc. SPIE3428, 62–72 (1998).
[CrossRef]

Product specification web catalog at http://www.lumenyte.com/product/specs/Ffiber[1].HTM .

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw-Hill, New York, 1990).

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (U.S. Government Printing Office, Washington, D.C., 1977).

M. F. Modest, “Fundamentals of thermal radiation” and “Radiative properties of real surfaces,” in Radiative Heat Transfer, J. J. Corrigan, J. M. Morris, eds. (McGraw-Hill, New York, 1993), Chap. 1, p. 7;Radiative Heat TransferChap. 3, p. 88.

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Figures (8)

Fig. 1
Fig. 1

Geometry of the ray path, indicated by bold arrows of length l. r is the pipe radius, the z axis is the pipe axis, and the x axis is chosen to lie along d. (a) skew ray, (b) meridional ray.

Fig. 2
Fig. 2

Cross sections of the fiber, showing the propagation of rays: (a) skew rays, (b) meridional rays.

Fig. 3
Fig. 3

Path-length difference in a pair of rays reflected from two places on a rough surface whose height difference is h.

Fig. 4
Fig. 4

Attenuation coefficients calculated for various rays in a 1.2-cm-diameter light pipe (αabs + αscatt = 10−3 cm−1 and σ = 5 nm). (a) Skew ray arrangement with Eq. (15), (b) meridional ray arrangement with Eq. (23).

Fig. 5
Fig. 5

Calculated α-versus-φ curves for rays that pass through the pipe axis (d = 0). (a) The skew ray from Eq. (22), (b) the meridional ray from Eq. (25). Solid curves, cladding loss; dashed curves, interface roughness. The remaining parameters are the same as those in Fig. 4.

Fig. 6
Fig. 6

Attenuation coefficient for 0.5-cm-diameter Lumenyte for skew or meridional arrangement of rays. The solid and dashed curves were calculated from Eqs. (17) and (24), respectively, with the dashed curve’s contribution coming from first and third terms only.

Fig. 7
Fig. 7

Attenuation coefficient for a 0.6-cm-diameter Lumenyte optical fiber. (a) Skew ray arrangement with Eq. (17), (b) meridional ray arrangement with Eq. (24).

Fig. 8
Fig. 8

Attenuation coefficient for 0.5-cm-diameter Lumenyte as a function of d for fixed φ. The dashed curves were calculated without the interface-defect loss term. (a) Skew ray with Eq. (17), (b) meridional ray with Eq. (24).

Tables (1)

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Table 1 Results of the Parametric Sensitivity Analysis

Equations (27)

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α a [ dB / m ] = 10 lm / m log [ exp ( α 100 cm ) ] ,
θ cr = sin 1 ( n cl / n co ) ,
f 1 = l l = 1 cos φ .
cos θ = sin φ [ 1 ( d / r ) 2 ] 1 / 2 .
1 2 l = tan φ 2 ( r 2 d 2 ) 1 / 2 ,
α ( φ , d ) = ( α abs + α scatt ) cos φ + ( 1 R ) tan φ 2 ( r 2 d 2 ) 1 / 2 .
Δ Φ = 4 π h n co cos θ λ = 2 k h ,
Δ Φ = 4 π h n co cos θ λ 1 ,
ρ = ρ 0 exp ( i Δ Φ )
ρ = ρ 0 exp ( i 2 k h ) = ρ 0 + p ( h ) exp ( i 2 k h ) d h ,
p ( h ) = 1 σ ( 2 π ) 1 / 2 exp [ h 2 / ( 2 σ 2 ) ] ,
ρ = ρ 0 exp [ ( 1 / 2 ) ( 2 k σ ) 2 ] .
R = | ρ | 2 = R 0 exp [ ( 2 k σ ) 2 ] ,
1 R = 1 exp [ ( 4 π σ n co cos θ λ ) 2 ] .
α ( φ , d , λ ) = ( α abs + α scatt ) cos φ + { 1 exp [ ( 2 k σ ) 2 ] } tan φ 2 ( r 2 d 2 ) 1 / 2 .
α ( φ , d , λ ) = ( α abs + α scatt ) cos φ + { 1 exp [ ( 2 k σ ) 2 ] + D } tan θ 2 ( r 2 d 2 ) 1 / 2 .
α ( φ , d , λ ) = ( α abs + α scatt ) cos φ + { 1 exp [ ( 2 k σ ) 2 ] } tan φ 2 ( r 2 d 2 ) 1 / 2 + D tan φ 2 ( r 2 d 2 ) 1 / 2 .
r s = [ ( n 1 cos θ 1 p ) 2 + q 2 ( n 1 cos θ 1 + p ) 2 + q 2 ] 1 / 2 ,
r p = [ ( p n 1 sin θ 1 tan θ 1 ) 2 + q 2 ( p + n 1 sin θ 1 tan θ 1 ) 2 + q 2 ] 1 / 2 r s ,
p 2 = 1 2 { [ ( n 2 2 κ 2 2 n 1 2 sin 2 θ 1 ) 2 + 4 n 2 2 κ 2 2 ] 1 / 2 + ( n 2 2 κ 2 2 n 1 2 sin 2 θ 1 ) 2 } ,
q 2 = 1 2 { [ ( n 2 2 κ 2 2 n 1 2 sin 2 θ 1 ) 2 + 4 n 2 2 κ 2 2 ] 1 / 2 ( n 2 2 κ 2 2 n 1 2 sin 2 θ 1 ) 2 } ,
R 0 = 1 / 2 ( | r s | 2 + | r p | 2 ) ,
α ( φ , d , λ ) = ( α abs + α scatt ) cos φ + { 1 R 0 exp [ ( 2 k σ ) 2 ] } tan φ 2 ( r 2 d 2 ) 1 / 2 + D tan φ 2 ( r 2 d 2 ) 1 / 2 .
α ( φ , d , λ ) = ( α abs + α scatt ) cos φ + { 1 exp [ ( 2 k σ ) 2 ] } tan φ 2 ( r + d ) ,
α ( φ , d , λ ) = ( α abs + α scatt ) cos φ + { 1 exp [ ( 2 k σ ) 2 ] } tan φ 2 ( r + d ) + D tan φ 2 ( r + d ) ,
α ( φ , d , λ ) = ( α abs + α scatt ) cos φ + { 1 R 0 exp [ ( 2 k σ ) 2 ] } tan φ 2 ( r + d ) + D tan φ 2 ( r + d ) ,
cos θ = sin φ , k = 2 π n co λ cos θ

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