Abstract

A geometrical optics approach is used to develop a theoretical model for analyzing loss mechanisms in optical light pipes. Five mechanisms are identified: intrinsic absorption, bulk scattering, losses that are due to roughness at the core–cladding interface, losses that are due to large-scale defects at the core–cladding interface, and losses that are due to absorption in the cladding material; and the effects of each of these on light-pipe transmission are considered. An approximate model appropriate for slightly rough surfaces is used to estimate the loss that is due to interface roughness. Optical experiments on commercially available light pipes are done to quantify the various loss processes. These experiments indicate that the interface effects play an important role in limiting the transmission in high-quality light pipes. From the optical measurements a rms interface roughness height in the 30–70-Å range is deduced, and these values are confirmed by direct surface profilometry with an atomic force microscope.

© 1992 Optical Society of America

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References

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  1. W. Wheeler, “Apparatus for lighting dwellings or other Structures,” U.S. Patent247,229 (20September1881).
  2. L. M. Fraas, W. R. Pyle, P. R. Ryason, “Concentrated and piped sunlight for indoor illumination,” Appl. Opt. 22, 578–582 (1983).
    [CrossRef] [PubMed]
  3. A. Zastrow, V. Wittwer, “Daylighting with fluorescent concentrators and highly reflective silver-coated plastic films: a new application for new materials,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion V, C. G. Granqvist, C. M. Lampert, J. Mason, V. Wittwer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.653, 93–100 (1986).
  4. A. Zastrow, V. Wittwer, “Daylighting with mirror light pipes and with fluorescent planar concentrators: first results from the demonstration project Stuttgart–Hohenheim,” in Materials and Optics for Solar Energy Conversion and Advanced Lighting Technology, C. M. Lampert, S. Holly, eds., Proc. Soc. Photo-Opt. Instrum. Eng.692, 227–234 (1986).
  5. C. Emslie, “Polymer optical fibers,” J. Mater. Sci. 23, 2281–2293 (1988); R. M. Glen, “Polymeric optical fiber,” Chemtronics 1, 98–106 (1986).
    [CrossRef]
  6. T. Kaino, M. Fujiki, S. Oikawa, S. Nara, “Low-loss plastic optical fibers,” Appl. Opt. 20, 2886–2888 (1981).
    [CrossRef] [PubMed]
  7. T. Kaino, M. Fujiki, S. Nara, “Low-loss polystyrene core-optical fibers,” J. Appl. Phys. 52, 7061–7063 (1981).
    [CrossRef]
  8. T. Kaino, K. Jingui, S. Nara, “Low loss poly(methyl methacrylate-d5) core optical fibers,” Appl. Phys. Lett. 41, 802–804 (1982).
    [CrossRef]
  9. T. Kaino, K. Jingui, S. Nara, “Low loss poly(methylmethacrylate-d8) core optical fibers,” Appl. Phys. Lett. 42, 567–569 (1983).
    [CrossRef]
  10. D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. DiDomenico, “Fundamental optical attenuation limits in the liquid and glassy state with application to fiber optical waveguide materials,” Appl. Phys. Lett. 22, 527–529 (1973).
    [CrossRef]
  11. R. G. Brown, B. N. Derick, “Plastic fiber optics: loss measurements and loss mechanisms,” Appl. Opt. 7, 1565–1569 (1968).
    [CrossRef] [PubMed]
  12. H. Blumenfeld, E. Gaillard, P. Rebourgeard, “Measurement of the reflection coefficient at the core–cladding interface in plastic scintillating fibers,” Nucl. Instrum. Methods A 309, 169–178 (1991).
    [CrossRef]
  13. G. Kettenring, “Measurement of the reflectivities and absorption lengths at different wavelengths of plastic scintillator and acrylglass,” Nucl. Instrum. Methods 131, 451–456 (1975).
    [CrossRef]
  14. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).
  15. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1987), pp. 109–121.
  16. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 10; P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics, E. Wolf, ed. (Pergamon, New York, 1967), Vol. 6, pp. 53–69.
    [CrossRef]
  17. Ref. 16, pp. 80–97.
  18. R. W. James, The Optical Principles of the Diffraction of X-rays (Bell, London, 1950), pp. 21–24.
  19. See, for example, G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
    [CrossRef]
  20. B. Crist, M. E. Marhic, G. Raviv, M. Epstein, “Optical absorption in polymer glasses by laser calorimetry,” J. Appl. Phys. 51, 1160–1162 (1980).
    [CrossRef]
  21. M. Haas, J. Davisson, H. Rosenstock, J. Babiskin, “Measurement of very low absorption coefficients by laser calorimetry,” Appl. Opt. 14, 1128–1130 (1975).
    [CrossRef]
  22. P. Avakian, W. Y. Hsu, P. Meakin, H. L. Snyder, “Optical absorption spectrum of PMMA via laser calorimetry,” J. Polym. Sci. 21, 647–655 (1983).
  23. D. A. Pinnow, T. C. Rich, “Development of a calorimetric method for making precision optical absorption measurements,” Appl. Opt. 12, 984–992 (1973).
    [CrossRef] [PubMed]
  24. D. Ruga, P. K. Hansma, “Atomic force microscopy,” Phys. Today 43, (10), 23–30 (1990); N. A. Burnham, R. J. Colton, H. M. Pollock, “Interpretation issues in force microscopy,” J. Vac. Sci. Technol. A 9, 2548–2556 (1991).
    [CrossRef]
  25. σ = FWHM/2.36.

1991 (1)

H. Blumenfeld, E. Gaillard, P. Rebourgeard, “Measurement of the reflection coefficient at the core–cladding interface in plastic scintillating fibers,” Nucl. Instrum. Methods A 309, 169–178 (1991).
[CrossRef]

1990 (1)

D. Ruga, P. K. Hansma, “Atomic force microscopy,” Phys. Today 43, (10), 23–30 (1990); N. A. Burnham, R. J. Colton, H. M. Pollock, “Interpretation issues in force microscopy,” J. Vac. Sci. Technol. A 9, 2548–2556 (1991).
[CrossRef]

1988 (1)

C. Emslie, “Polymer optical fibers,” J. Mater. Sci. 23, 2281–2293 (1988); R. M. Glen, “Polymeric optical fiber,” Chemtronics 1, 98–106 (1986).
[CrossRef]

1984 (1)

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

1983 (3)

T. Kaino, K. Jingui, S. Nara, “Low loss poly(methylmethacrylate-d8) core optical fibers,” Appl. Phys. Lett. 42, 567–569 (1983).
[CrossRef]

P. Avakian, W. Y. Hsu, P. Meakin, H. L. Snyder, “Optical absorption spectrum of PMMA via laser calorimetry,” J. Polym. Sci. 21, 647–655 (1983).

L. M. Fraas, W. R. Pyle, P. R. Ryason, “Concentrated and piped sunlight for indoor illumination,” Appl. Opt. 22, 578–582 (1983).
[CrossRef] [PubMed]

1982 (1)

T. Kaino, K. Jingui, S. Nara, “Low loss poly(methyl methacrylate-d5) core optical fibers,” Appl. Phys. Lett. 41, 802–804 (1982).
[CrossRef]

1981 (2)

T. Kaino, M. Fujiki, S. Nara, “Low-loss polystyrene core-optical fibers,” J. Appl. Phys. 52, 7061–7063 (1981).
[CrossRef]

T. Kaino, M. Fujiki, S. Oikawa, S. Nara, “Low-loss plastic optical fibers,” Appl. Opt. 20, 2886–2888 (1981).
[CrossRef] [PubMed]

1980 (1)

B. Crist, M. E. Marhic, G. Raviv, M. Epstein, “Optical absorption in polymer glasses by laser calorimetry,” J. Appl. Phys. 51, 1160–1162 (1980).
[CrossRef]

1975 (2)

G. Kettenring, “Measurement of the reflectivities and absorption lengths at different wavelengths of plastic scintillator and acrylglass,” Nucl. Instrum. Methods 131, 451–456 (1975).
[CrossRef]

M. Haas, J. Davisson, H. Rosenstock, J. Babiskin, “Measurement of very low absorption coefficients by laser calorimetry,” Appl. Opt. 14, 1128–1130 (1975).
[CrossRef]

1973 (2)

D. A. Pinnow, T. C. Rich, “Development of a calorimetric method for making precision optical absorption measurements,” Appl. Opt. 12, 984–992 (1973).
[CrossRef] [PubMed]

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. DiDomenico, “Fundamental optical attenuation limits in the liquid and glassy state with application to fiber optical waveguide materials,” Appl. Phys. Lett. 22, 527–529 (1973).
[CrossRef]

1968 (1)

Avakian, P.

P. Avakian, W. Y. Hsu, P. Meakin, H. L. Snyder, “Optical absorption spectrum of PMMA via laser calorimetry,” J. Polym. Sci. 21, 647–655 (1983).

Babiskin, J.

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 10; P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics, E. Wolf, ed. (Pergamon, New York, 1967), Vol. 6, pp. 53–69.
[CrossRef]

Blumenfeld, H.

H. Blumenfeld, E. Gaillard, P. Rebourgeard, “Measurement of the reflection coefficient at the core–cladding interface in plastic scintillating fibers,” Nucl. Instrum. Methods A 309, 169–178 (1991).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1987), pp. 109–121.

Brown, R. G.

Crist, B.

B. Crist, M. E. Marhic, G. Raviv, M. Epstein, “Optical absorption in polymer glasses by laser calorimetry,” J. Appl. Phys. 51, 1160–1162 (1980).
[CrossRef]

Davisson, J.

Derick, B. N.

DiDomenico, M.

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. DiDomenico, “Fundamental optical attenuation limits in the liquid and glassy state with application to fiber optical waveguide materials,” Appl. Phys. Lett. 22, 527–529 (1973).
[CrossRef]

Emslie, C.

C. Emslie, “Polymer optical fibers,” J. Mater. Sci. 23, 2281–2293 (1988); R. M. Glen, “Polymeric optical fiber,” Chemtronics 1, 98–106 (1986).
[CrossRef]

Epstein, M.

B. Crist, M. E. Marhic, G. Raviv, M. Epstein, “Optical absorption in polymer glasses by laser calorimetry,” J. Appl. Phys. 51, 1160–1162 (1980).
[CrossRef]

Ford, G. W.

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

Fraas, L. M.

Fujiki, M.

T. Kaino, M. Fujiki, S. Oikawa, S. Nara, “Low-loss plastic optical fibers,” Appl. Opt. 20, 2886–2888 (1981).
[CrossRef] [PubMed]

T. Kaino, M. Fujiki, S. Nara, “Low-loss polystyrene core-optical fibers,” J. Appl. Phys. 52, 7061–7063 (1981).
[CrossRef]

Gaillard, E.

H. Blumenfeld, E. Gaillard, P. Rebourgeard, “Measurement of the reflection coefficient at the core–cladding interface in plastic scintillating fibers,” Nucl. Instrum. Methods A 309, 169–178 (1991).
[CrossRef]

Haas, M.

Hansma, P. K.

D. Ruga, P. K. Hansma, “Atomic force microscopy,” Phys. Today 43, (10), 23–30 (1990); N. A. Burnham, R. J. Colton, H. M. Pollock, “Interpretation issues in force microscopy,” J. Vac. Sci. Technol. A 9, 2548–2556 (1991).
[CrossRef]

Hsu, W. Y.

P. Avakian, W. Y. Hsu, P. Meakin, H. L. Snyder, “Optical absorption spectrum of PMMA via laser calorimetry,” J. Polym. Sci. 21, 647–655 (1983).

James, R. W.

R. W. James, The Optical Principles of the Diffraction of X-rays (Bell, London, 1950), pp. 21–24.

Jingui, K.

T. Kaino, K. Jingui, S. Nara, “Low loss poly(methylmethacrylate-d8) core optical fibers,” Appl. Phys. Lett. 42, 567–569 (1983).
[CrossRef]

T. Kaino, K. Jingui, S. Nara, “Low loss poly(methyl methacrylate-d5) core optical fibers,” Appl. Phys. Lett. 41, 802–804 (1982).
[CrossRef]

Kaino, T.

T. Kaino, K. Jingui, S. Nara, “Low loss poly(methylmethacrylate-d8) core optical fibers,” Appl. Phys. Lett. 42, 567–569 (1983).
[CrossRef]

T. Kaino, K. Jingui, S. Nara, “Low loss poly(methyl methacrylate-d5) core optical fibers,” Appl. Phys. Lett. 41, 802–804 (1982).
[CrossRef]

T. Kaino, M. Fujiki, S. Oikawa, S. Nara, “Low-loss plastic optical fibers,” Appl. Opt. 20, 2886–2888 (1981).
[CrossRef] [PubMed]

T. Kaino, M. Fujiki, S. Nara, “Low-loss polystyrene core-optical fibers,” J. Appl. Phys. 52, 7061–7063 (1981).
[CrossRef]

Kettenring, G.

G. Kettenring, “Measurement of the reflectivities and absorption lengths at different wavelengths of plastic scintillator and acrylglass,” Nucl. Instrum. Methods 131, 451–456 (1975).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

Marhic, M. E.

B. Crist, M. E. Marhic, G. Raviv, M. Epstein, “Optical absorption in polymer glasses by laser calorimetry,” J. Appl. Phys. 51, 1160–1162 (1980).
[CrossRef]

Meakin, P.

P. Avakian, W. Y. Hsu, P. Meakin, H. L. Snyder, “Optical absorption spectrum of PMMA via laser calorimetry,” J. Polym. Sci. 21, 647–655 (1983).

Nara, S.

T. Kaino, K. Jingui, S. Nara, “Low loss poly(methylmethacrylate-d8) core optical fibers,” Appl. Phys. Lett. 42, 567–569 (1983).
[CrossRef]

T. Kaino, K. Jingui, S. Nara, “Low loss poly(methyl methacrylate-d5) core optical fibers,” Appl. Phys. Lett. 41, 802–804 (1982).
[CrossRef]

T. Kaino, M. Fujiki, S. Oikawa, S. Nara, “Low-loss plastic optical fibers,” Appl. Opt. 20, 2886–2888 (1981).
[CrossRef] [PubMed]

T. Kaino, M. Fujiki, S. Nara, “Low-loss polystyrene core-optical fibers,” J. Appl. Phys. 52, 7061–7063 (1981).
[CrossRef]

Oikawa, S.

Ostermayer, F. W.

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. DiDomenico, “Fundamental optical attenuation limits in the liquid and glassy state with application to fiber optical waveguide materials,” Appl. Phys. Lett. 22, 527–529 (1973).
[CrossRef]

Pinnow, D. A.

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. DiDomenico, “Fundamental optical attenuation limits in the liquid and glassy state with application to fiber optical waveguide materials,” Appl. Phys. Lett. 22, 527–529 (1973).
[CrossRef]

D. A. Pinnow, T. C. Rich, “Development of a calorimetric method for making precision optical absorption measurements,” Appl. Opt. 12, 984–992 (1973).
[CrossRef] [PubMed]

Pyle, W. R.

Raviv, G.

B. Crist, M. E. Marhic, G. Raviv, M. Epstein, “Optical absorption in polymer glasses by laser calorimetry,” J. Appl. Phys. 51, 1160–1162 (1980).
[CrossRef]

Rebourgeard, P.

H. Blumenfeld, E. Gaillard, P. Rebourgeard, “Measurement of the reflection coefficient at the core–cladding interface in plastic scintillating fibers,” Nucl. Instrum. Methods A 309, 169–178 (1991).
[CrossRef]

Rich, T. C.

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. DiDomenico, “Fundamental optical attenuation limits in the liquid and glassy state with application to fiber optical waveguide materials,” Appl. Phys. Lett. 22, 527–529 (1973).
[CrossRef]

D. A. Pinnow, T. C. Rich, “Development of a calorimetric method for making precision optical absorption measurements,” Appl. Opt. 12, 984–992 (1973).
[CrossRef] [PubMed]

Rosenstock, H.

Ruga, D.

D. Ruga, P. K. Hansma, “Atomic force microscopy,” Phys. Today 43, (10), 23–30 (1990); N. A. Burnham, R. J. Colton, H. M. Pollock, “Interpretation issues in force microscopy,” J. Vac. Sci. Technol. A 9, 2548–2556 (1991).
[CrossRef]

Ryason, P. R.

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

Snyder, H. L.

P. Avakian, W. Y. Hsu, P. Meakin, H. L. Snyder, “Optical absorption spectrum of PMMA via laser calorimetry,” J. Polym. Sci. 21, 647–655 (1983).

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 10; P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics, E. Wolf, ed. (Pergamon, New York, 1967), Vol. 6, pp. 53–69.
[CrossRef]

Weber, W. H.

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

Wheeler, W.

W. Wheeler, “Apparatus for lighting dwellings or other Structures,” U.S. Patent247,229 (20September1881).

Wittwer, V.

A. Zastrow, V. Wittwer, “Daylighting with fluorescent concentrators and highly reflective silver-coated plastic films: a new application for new materials,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion V, C. G. Granqvist, C. M. Lampert, J. Mason, V. Wittwer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.653, 93–100 (1986).

A. Zastrow, V. Wittwer, “Daylighting with mirror light pipes and with fluorescent planar concentrators: first results from the demonstration project Stuttgart–Hohenheim,” in Materials and Optics for Solar Energy Conversion and Advanced Lighting Technology, C. M. Lampert, S. Holly, eds., Proc. Soc. Photo-Opt. Instrum. Eng.692, 227–234 (1986).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1987), pp. 109–121.

Zastrow, A.

A. Zastrow, V. Wittwer, “Daylighting with mirror light pipes and with fluorescent planar concentrators: first results from the demonstration project Stuttgart–Hohenheim,” in Materials and Optics for Solar Energy Conversion and Advanced Lighting Technology, C. M. Lampert, S. Holly, eds., Proc. Soc. Photo-Opt. Instrum. Eng.692, 227–234 (1986).

A. Zastrow, V. Wittwer, “Daylighting with fluorescent concentrators and highly reflective silver-coated plastic films: a new application for new materials,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion V, C. G. Granqvist, C. M. Lampert, J. Mason, V. Wittwer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.653, 93–100 (1986).

Appl. Opt. (5)

Appl. Phys. Lett. (3)

T. Kaino, K. Jingui, S. Nara, “Low loss poly(methyl methacrylate-d5) core optical fibers,” Appl. Phys. Lett. 41, 802–804 (1982).
[CrossRef]

T. Kaino, K. Jingui, S. Nara, “Low loss poly(methylmethacrylate-d8) core optical fibers,” Appl. Phys. Lett. 42, 567–569 (1983).
[CrossRef]

D. A. Pinnow, T. C. Rich, F. W. Ostermayer, M. DiDomenico, “Fundamental optical attenuation limits in the liquid and glassy state with application to fiber optical waveguide materials,” Appl. Phys. Lett. 22, 527–529 (1973).
[CrossRef]

J. Appl. Phys. (2)

T. Kaino, M. Fujiki, S. Nara, “Low-loss polystyrene core-optical fibers,” J. Appl. Phys. 52, 7061–7063 (1981).
[CrossRef]

B. Crist, M. E. Marhic, G. Raviv, M. Epstein, “Optical absorption in polymer glasses by laser calorimetry,” J. Appl. Phys. 51, 1160–1162 (1980).
[CrossRef]

J. Mater. Sci. (1)

C. Emslie, “Polymer optical fibers,” J. Mater. Sci. 23, 2281–2293 (1988); R. M. Glen, “Polymeric optical fiber,” Chemtronics 1, 98–106 (1986).
[CrossRef]

J. Polym. Sci. (1)

P. Avakian, W. Y. Hsu, P. Meakin, H. L. Snyder, “Optical absorption spectrum of PMMA via laser calorimetry,” J. Polym. Sci. 21, 647–655 (1983).

Nucl. Instrum. Methods (1)

G. Kettenring, “Measurement of the reflectivities and absorption lengths at different wavelengths of plastic scintillator and acrylglass,” Nucl. Instrum. Methods 131, 451–456 (1975).
[CrossRef]

Nucl. Instrum. Methods A (1)

H. Blumenfeld, E. Gaillard, P. Rebourgeard, “Measurement of the reflection coefficient at the core–cladding interface in plastic scintillating fibers,” Nucl. Instrum. Methods A 309, 169–178 (1991).
[CrossRef]

Phys. Rep. (1)

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

Phys. Today (1)

D. Ruga, P. K. Hansma, “Atomic force microscopy,” Phys. Today 43, (10), 23–30 (1990); N. A. Burnham, R. J. Colton, H. M. Pollock, “Interpretation issues in force microscopy,” J. Vac. Sci. Technol. A 9, 2548–2556 (1991).
[CrossRef]

Other (9)

σ = FWHM/2.36.

W. Wheeler, “Apparatus for lighting dwellings or other Structures,” U.S. Patent247,229 (20September1881).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1987), pp. 109–121.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 10; P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics, E. Wolf, ed. (Pergamon, New York, 1967), Vol. 6, pp. 53–69.
[CrossRef]

Ref. 16, pp. 80–97.

R. W. James, The Optical Principles of the Diffraction of X-rays (Bell, London, 1950), pp. 21–24.

A. Zastrow, V. Wittwer, “Daylighting with fluorescent concentrators and highly reflective silver-coated plastic films: a new application for new materials,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion V, C. G. Granqvist, C. M. Lampert, J. Mason, V. Wittwer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.653, 93–100 (1986).

A. Zastrow, V. Wittwer, “Daylighting with mirror light pipes and with fluorescent planar concentrators: first results from the demonstration project Stuttgart–Hohenheim,” in Materials and Optics for Solar Energy Conversion and Advanced Lighting Technology, C. M. Lampert, S. Holly, eds., Proc. Soc. Photo-Opt. Instrum. Eng.692, 227–234 (1986).

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Figures (8)

Fig. 1
Fig. 1

Geometry for the ray path indicated by the bold arrow 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.

Fig. 2
Fig. 2

k-Space plot of the trapped rays (shaded region) in a cylindrical light pipe with nco = 1.48 and ncl = 1.33.

Fig. 3
Fig. 3

Attenuation coefficients calculated for various rays in a 5-mm-diameter light pipe by using Eqs. (1) and (9) with αabs + αscatt = 1.4 × 10−3 cm−1 and α = 72 Å.

Fig. 4
Fig. 4

Calculated α-versus-φ curves for rays that pass through the pipe axis (d = 0): solid curves, cladding loss; dashed curve, interface roughness. The remaining parameters are the same as those in Fig. 3.

Fig. 5
Fig. 5

Temperature versus time of Lumenyte illuminated with 1.34-W (circles) and 0.67-W (triangles) laser beams.

Fig. 6
Fig. 6

Attenuation coefficient for 5-mm-diameter Lumenyte. The solid curve was calculated with αabs + αscatt + D/2r = 7.45 × 10−4 cm−1, d = 0, r = 0.25 cm, and σ = 30 Å. The dashed curve is the contribution due to the first and third terms in Eq. (11).

Fig. 7
Fig. 7

Attenuation coefficient for 5-mm-diameter Lumenyte as a function of d for fixed φ. The solid curves were calculated by using Eqs. (9) and (11) with αabs + αscatt = 8.41 × 10−4 cm−1, D = 5.85 × 10−5, and σ = 39 Å. The dashed curves were calculated without the interface defect loss term and with αabs + αscatt = 9.58 × 10−4 cm−1.

Fig. 8
Fig. 8

Representative AFM image of Teflon cladding surface of a Lumenyte light pipe; units are in nanometers. Note that the vertical axis scale is enhanced by approximately a factor of 4 over the lateral scale to make the feature shapes more evident.

Equations (16)

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

α ( φ , d ) = ( α abs + α scatt ) cos φ + ( 1 - R ) tan φ 2 ( r 2 - d 2 ) 1 / 2 ,
θ = cos - 1 [ sin φ ( 1 - d 2 / r 2 ) 1 / 2 ] .
4 π h cos θ λ 1 ,
Δ Φ = 4 π h cos θ λ = 2 k h ,
ρ = ρ 0 exp ( i 2 k h ) = ρ 0 - d h p ( h ) exp ( i 2 k h ) ,
p ( h ) = 1 σ ( 2 π ) 1 / 2 exp ( - h 2 / 2 σ 2 ) ,
ρ = ρ 0 exp [ - ½ ( 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 ) = ( α abs + α scatt ) cos φ + ( 1 - exp [ - ( 2 k σ ) 2 ] + D / cos θ ) tan φ 2 ( r 2 - d 2 ) 1 / 2 ,
α ( φ , d ) = ( α abs + α scatt ) cos φ + { 1 - exp [ - ( 2 k σ ) 2 ] } tan φ 2 ( r 2 - d 2 ) 1 / 2 + D r 2 ( r 2 - d 2 ) cos φ .
r s = q 1 - q 2 q 1 + q 2 ,             r p = 2 q 1 - 1 q 2 2 q 1 + 1 q 2 ,
R 0 = ( r s 2 + r p 2 ) / 2 ,
α ( φ , d ) = ( α abs + α scatt ) cos φ + { 1 - ½ ( r s 2 + r p 2 ) exp [ - ( 2 k σ ) 2 ] } tan φ 2 ( r 2 - d 2 ) 1 / 2 + D r 2 ( r 2 - d 2 ) cos φ .
d ( Δ T ) d t = α P L M C p - b ( Δ T ) ,
Δ T ( t ) = ( 1 / b ) ( α P L / M C p ) [ 1 - exp ( - b t ) ] .

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