Abstract

Solar radiation, traveling outside cloud water droplets, excites sharp resonances and surface waves by tunneling into the droplets. This effect contributes substantially to the total absorption (typically, of the order of 20%) and yields the major contribution to backscattering, producing the meteorological glory. Usual computational practices in atmospheric science misrepresent resonance contributions and cannot be relied on in the assessment of possible anomalies in cloud absorption.

© 2003 Optical Society of America

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References

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  1. I. Newton, Opticks, 4th ed. (Royal Society, London, 1730), Book III, Part I, Query 29.
  2. W. J. Wiscombe, “An absorbing mystery,” Nature (London) 376, 466–467 (1995), and references therein.
  3. J. T. Houghton, Y. Ding, D. J. Griggs, M. Noguer, P. J. van der Linden, X. Dai, K. Maskell, C. A. Johnson, eds., Climate Change 2001: The Scientific Basis (Cambridge U. Press, Cambridge, UK, 2001), p. 433.
  4. H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, UK, 1992).
    [CrossRef]
  5. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  6. J. B. Keller, “Geometrical theory of diffraction,” in Calculus of Variations and its Applications, L. M. Graves, ed. (McGraw-Hill, New York, 1958), pp. 27–52.
    [CrossRef]
  7. R. K. Chang, A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).
  8. L. G. Guimarães, H. M. Nussenzveig, “Uniform approximation to Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
    [CrossRef]
  9. S. C. Ching, H. M. Lai, K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am. B 4, 1995–2003 (1987).
    [CrossRef]
  10. C. A. A. de Carvalho, H. M. Nussenzveig, “Time delay,” Phys. Rep. 364, 83–174 (2002).
    [CrossRef]
  11. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  12. J. V. Dave, “Effect of the coarseness of the integration increment on the calculation of the radiation scattered by polydispersed aerosols,” Appl. Opt. 8, 1161–1167 (1969).
    [CrossRef] [PubMed]
  13. A. Slingo, H. M. Schrecker, “On the shortwave radiative properties of stratiform water clouds,” Q. J. R. Meteorol. Soc. 108, 407–426 (1982).
    [CrossRef]
  14. D. L. Mitchell, “Parameterization of the Mie extinction and absorption coefficients for water clouds,” J. Atmos. Sci. 57, 1311–1326 (2000).
    [CrossRef]
  15. P. Chylek, P. Damiano, N. Kalyaniwalla, E. P. Shettle, “Radiative properties of water clouds,” Atmos. Res. 35, 139–156 (1995).
    [CrossRef]
  16. R. Davies, W. L. Ridgway, K.-E. Kim, “Spectral absorption of solar radiation in cloudy atmospheres: a 20 cm-1 model,” J. Atmos. Sci. 41, 2126–2137 (1984).
    [CrossRef]
  17. D. M. Wieliczka, S. Weng, M. R. Querry, “Wedge shaped cell for highly absorbent liquids: infrared optical constants of water,” Appl. Opt. 28, 1714–1719 (1989).
    [CrossRef] [PubMed]
  18. D. J. Segelstein, “The complex refractive index of water,” M.S. thesis (Department of Physics, University of Missouri-Kansas City, Kansas City, Mo., 1981).
  19. J. C. Brandt, “An unusual observation of the glory,” Publ. Astron. Soc. Pac. 80, 25–28 (1968).
    [CrossRef]
  20. R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984).
  21. J. D. Klett, “Lidar inversion with variable backscatter/extinction ratios,” Appl. Opt. 24, 1638–1643 (1985).
    [CrossRef] [PubMed]
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    [CrossRef]
  23. V. Khare, H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
    [CrossRef]
  24. D. Ngo, R. G. Pinnick, “Suppression of scattering resonances in inhomogeneous microdroplets,” J. Opt. Soc. Am. A 11, 1352–1359 (1994).
    [CrossRef]
  25. V. A. Markel, “The effects of averaging on the enhancement factor for absorption of light by carbon particles in microdroplets of water,” J. Quant. Spectrosc. Radiat. Transfer 72, 765–774 (2002).
    [CrossRef]
  26. V. A. Markel, V. M. Shalaev, “Absorption of light by soot particles in micro-droplets of water,” J. Quant. Spectrosc. Radiat. Transfer 63, 321–339 (1999).
    [CrossRef]
  27. A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
    [CrossRef] [PubMed]
  28. J. P. Barton, “Effects of surface perturbations on the quality and focused-beam excitation of microsphere resonance,” J. Opt. Soc. Am. A 16, 1974–1980 (1999).
    [CrossRef]
  29. J. Wong, “Surface resonances in high-frequency scattering from a nearly-sharp three-dimensional well,” M.S. thesis (Department of Physics and Astronomy, University of New Mexico, Albuquerque, N.M., 1968).
  30. H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
    [CrossRef]
  31. H. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1980), Fig. 10–15.
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    [CrossRef] [PubMed]
  33. A. J. Baran, P. N. Francis, S. Havemann, P. Yang, “A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus,” J. Quant. Spectrosc. Radiat. Transfer 70, 505–518 (2001).
    [CrossRef]
  34. L. D. Landau, E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Butterworth-Heinemann, New York, 1997).

2002 (2)

C. A. A. de Carvalho, H. M. Nussenzveig, “Time delay,” Phys. Rep. 364, 83–174 (2002).
[CrossRef]

V. A. Markel, “The effects of averaging on the enhancement factor for absorption of light by carbon particles in microdroplets of water,” J. Quant. Spectrosc. Radiat. Transfer 72, 765–774 (2002).
[CrossRef]

2001 (1)

A. J. Baran, P. N. Francis, S. Havemann, P. Yang, “A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus,” J. Quant. Spectrosc. Radiat. Transfer 70, 505–518 (2001).
[CrossRef]

2000 (1)

D. L. Mitchell, “Parameterization of the Mie extinction and absorption coefficients for water clouds,” J. Atmos. Sci. 57, 1311–1326 (2000).
[CrossRef]

1999 (2)

V. A. Markel, V. M. Shalaev, “Absorption of light by soot particles in micro-droplets of water,” J. Quant. Spectrosc. Radiat. Transfer 63, 321–339 (1999).
[CrossRef]

J. P. Barton, “Effects of surface perturbations on the quality and focused-beam excitation of microsphere resonance,” J. Opt. Soc. Am. A 16, 1974–1980 (1999).
[CrossRef]

1995 (2)

P. Chylek, P. Damiano, N. Kalyaniwalla, E. P. Shettle, “Radiative properties of water clouds,” Atmos. Res. 35, 139–156 (1995).
[CrossRef]

W. J. Wiscombe, “An absorbing mystery,” Nature (London) 376, 466–467 (1995), and references therein.

1994 (2)

L. G. Guimarães, H. M. Nussenzveig, “Uniform approximation to Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
[CrossRef]

D. Ngo, R. G. Pinnick, “Suppression of scattering resonances in inhomogeneous microdroplets,” J. Opt. Soc. Am. A 11, 1352–1359 (1994).
[CrossRef]

1991 (1)

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[CrossRef]

1989 (1)

1987 (1)

1985 (1)

1984 (1)

R. Davies, W. L. Ridgway, K.-E. Kim, “Spectral absorption of solar radiation in cloudy atmospheres: a 20 cm-1 model,” J. Atmos. Sci. 41, 2126–2137 (1984).
[CrossRef]

1983 (1)

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and extinction in water clouds,” J. Geophys. Res. 88, 6787–6796 (1983).
[CrossRef]

1982 (1)

A. Slingo, H. M. Schrecker, “On the shortwave radiative properties of stratiform water clouds,” Q. J. R. Meteorol. Soc. 108, 407–426 (1982).
[CrossRef]

1980 (1)

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
[CrossRef] [PubMed]

1979 (1)

1977 (1)

V. Khare, H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[CrossRef]

1969 (1)

1968 (1)

J. C. Brandt, “An unusual observation of the glory,” Publ. Astron. Soc. Pac. 80, 25–28 (1968).
[CrossRef]

Asano, S.

Ashkin, A.

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
[CrossRef] [PubMed]

Baran, A. J.

A. J. Baran, P. N. Francis, S. Havemann, P. Yang, “A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus,” J. Quant. Spectrosc. Radiat. Transfer 70, 505–518 (2001).
[CrossRef]

Barton, J. P.

J. P. Barton, “Effects of surface perturbations on the quality and focused-beam excitation of microsphere resonance,” J. Opt. Soc. Am. A 16, 1974–1980 (1999).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Brandt, J. C.

J. C. Brandt, “An unusual observation of the glory,” Publ. Astron. Soc. Pac. 80, 25–28 (1968).
[CrossRef]

Ching, S. C.

Chylek, P.

P. Chylek, P. Damiano, N. Kalyaniwalla, E. P. Shettle, “Radiative properties of water clouds,” Atmos. Res. 35, 139–156 (1995).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and extinction in water clouds,” J. Geophys. Res. 88, 6787–6796 (1983).
[CrossRef]

Damiano, P.

P. Chylek, P. Damiano, N. Kalyaniwalla, E. P. Shettle, “Radiative properties of water clouds,” Atmos. Res. 35, 139–156 (1995).
[CrossRef]

Dave, J. V.

Davies, R.

R. Davies, W. L. Ridgway, K.-E. Kim, “Spectral absorption of solar radiation in cloudy atmospheres: a 20 cm-1 model,” J. Atmos. Sci. 41, 2126–2137 (1984).
[CrossRef]

de Carvalho, C. A. A.

C. A. A. de Carvalho, H. M. Nussenzveig, “Time delay,” Phys. Rep. 364, 83–174 (2002).
[CrossRef]

Francis, P. N.

A. J. Baran, P. N. Francis, S. Havemann, P. Yang, “A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus,” J. Quant. Spectrosc. Radiat. Transfer 70, 505–518 (2001).
[CrossRef]

Grandy, W. T.

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and extinction in water clouds,” J. Geophys. Res. 88, 6787–6796 (1983).
[CrossRef]

Guimarães, L. G.

L. G. Guimarães, H. M. Nussenzveig, “Uniform approximation to Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
[CrossRef]

Ham, C.

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and extinction in water clouds,” J. Geophys. Res. 88, 6787–6796 (1983).
[CrossRef]

Havemann, S.

A. J. Baran, P. N. Francis, S. Havemann, P. Yang, “A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus,” J. Quant. Spectrosc. Radiat. Transfer 70, 505–518 (2001).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Jennings, S. G.

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and extinction in water clouds,” J. Geophys. Res. 88, 6787–6796 (1983).
[CrossRef]

Kalyaniwalla, N.

P. Chylek, P. Damiano, N. Kalyaniwalla, E. P. Shettle, “Radiative properties of water clouds,” Atmos. Res. 35, 139–156 (1995).
[CrossRef]

Keller, J. B.

J. B. Keller, “Geometrical theory of diffraction,” in Calculus of Variations and its Applications, L. M. Graves, ed. (McGraw-Hill, New York, 1958), pp. 27–52.
[CrossRef]

Khare, V.

V. Khare, H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[CrossRef]

Kim, K.-E.

R. Davies, W. L. Ridgway, K.-E. Kim, “Spectral absorption of solar radiation in cloudy atmospheres: a 20 cm-1 model,” J. Atmos. Sci. 41, 2126–2137 (1984).
[CrossRef]

Klett, J. D.

J. D. Klett, “Lidar inversion with variable backscatter/extinction ratios,” Appl. Opt. 24, 1638–1643 (1985).
[CrossRef] [PubMed]

H. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1980), Fig. 10–15.

Lai, H. M.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[CrossRef]

S. C. Ching, H. M. Lai, K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am. B 4, 1995–2003 (1987).
[CrossRef]

Lam, C. C.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Butterworth-Heinemann, New York, 1997).

Leung, P. T.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[CrossRef]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Butterworth-Heinemann, New York, 1997).

Markel, V. A.

V. A. Markel, “The effects of averaging on the enhancement factor for absorption of light by carbon particles in microdroplets of water,” J. Quant. Spectrosc. Radiat. Transfer 72, 765–774 (2002).
[CrossRef]

V. A. Markel, V. M. Shalaev, “Absorption of light by soot particles in micro-droplets of water,” J. Quant. Spectrosc. Radiat. Transfer 63, 321–339 (1999).
[CrossRef]

Measures, R. M.

R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984).

Mitchell, D. L.

D. L. Mitchell, “Parameterization of the Mie extinction and absorption coefficients for water clouds,” J. Atmos. Sci. 57, 1311–1326 (2000).
[CrossRef]

Newton, I.

I. Newton, Opticks, 4th ed. (Royal Society, London, 1730), Book III, Part I, Query 29.

Ngo, D.

Nussenzveig, H. M.

C. A. A. de Carvalho, H. M. Nussenzveig, “Time delay,” Phys. Rep. 364, 83–174 (2002).
[CrossRef]

L. G. Guimarães, H. M. Nussenzveig, “Uniform approximation to Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
[CrossRef]

V. Khare, H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[CrossRef]

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, UK, 1992).
[CrossRef]

Pinnick, R. G.

D. Ngo, R. G. Pinnick, “Suppression of scattering resonances in inhomogeneous microdroplets,” J. Opt. Soc. Am. A 11, 1352–1359 (1994).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and extinction in water clouds,” J. Geophys. Res. 88, 6787–6796 (1983).
[CrossRef]

Pruppacher, H.

H. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1980), Fig. 10–15.

Querry, M. R.

Ridgway, W. L.

R. Davies, W. L. Ridgway, K.-E. Kim, “Spectral absorption of solar radiation in cloudy atmospheres: a 20 cm-1 model,” J. Atmos. Sci. 41, 2126–2137 (1984).
[CrossRef]

Schrecker, H. M.

A. Slingo, H. M. Schrecker, “On the shortwave radiative properties of stratiform water clouds,” Q. J. R. Meteorol. Soc. 108, 407–426 (1982).
[CrossRef]

Segelstein, D. J.

D. J. Segelstein, “The complex refractive index of water,” M.S. thesis (Department of Physics, University of Missouri-Kansas City, Kansas City, Mo., 1981).

Shalaev, V. M.

V. A. Markel, V. M. Shalaev, “Absorption of light by soot particles in micro-droplets of water,” J. Quant. Spectrosc. Radiat. Transfer 63, 321–339 (1999).
[CrossRef]

Shettle, E. P.

P. Chylek, P. Damiano, N. Kalyaniwalla, E. P. Shettle, “Radiative properties of water clouds,” Atmos. Res. 35, 139–156 (1995).
[CrossRef]

Slingo, A.

A. Slingo, H. M. Schrecker, “On the shortwave radiative properties of stratiform water clouds,” Q. J. R. Meteorol. Soc. 108, 407–426 (1982).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Weng, S.

Wieliczka, D. M.

Wiscombe, W. J.

W. J. Wiscombe, “An absorbing mystery,” Nature (London) 376, 466–467 (1995), and references therein.

Wong, J.

J. Wong, “Surface resonances in high-frequency scattering from a nearly-sharp three-dimensional well,” M.S. thesis (Department of Physics and Astronomy, University of New Mexico, Albuquerque, N.M., 1968).

Yang, P.

A. J. Baran, P. N. Francis, S. Havemann, P. Yang, “A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus,” J. Quant. Spectrosc. Radiat. Transfer 70, 505–518 (2001).
[CrossRef]

Young, K.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[CrossRef]

S. C. Ching, H. M. Lai, K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am. B 4, 1995–2003 (1987).
[CrossRef]

Appl. Opt. (4)

Atmos. Res. (1)

P. Chylek, P. Damiano, N. Kalyaniwalla, E. P. Shettle, “Radiative properties of water clouds,” Atmos. Res. 35, 139–156 (1995).
[CrossRef]

J. Atmos. Sci. (1)

R. Davies, W. L. Ridgway, K.-E. Kim, “Spectral absorption of solar radiation in cloudy atmospheres: a 20 cm-1 model,” J. Atmos. Sci. 41, 2126–2137 (1984).
[CrossRef]

J. Atmos. Sci. (1)

D. L. Mitchell, “Parameterization of the Mie extinction and absorption coefficients for water clouds,” J. Atmos. Sci. 57, 1311–1326 (2000).
[CrossRef]

J. Geophys. Res. (1)

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and extinction in water clouds,” J. Geophys. Res. 88, 6787–6796 (1983).
[CrossRef]

J. Mod. Opt. (1)

L. G. Guimarães, H. M. Nussenzveig, “Uniform approximation to Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. P. Barton, “Effects of surface perturbations on the quality and focused-beam excitation of microsphere resonance,” J. Opt. Soc. Am. A 16, 1974–1980 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

A. J. Baran, P. N. Francis, S. Havemann, P. Yang, “A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus,” J. Quant. Spectrosc. Radiat. Transfer 70, 505–518 (2001).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

V. A. Markel, V. M. Shalaev, “Absorption of light by soot particles in micro-droplets of water,” J. Quant. Spectrosc. Radiat. Transfer 63, 321–339 (1999).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

V. A. Markel, “The effects of averaging on the enhancement factor for absorption of light by carbon particles in microdroplets of water,” J. Quant. Spectrosc. Radiat. Transfer 72, 765–774 (2002).
[CrossRef]

Nature (London) (1)

W. J. Wiscombe, “An absorbing mystery,” Nature (London) 376, 466–467 (1995), and references therein.

Phys. Rep. (1)

C. A. A. de Carvalho, H. M. Nussenzveig, “Time delay,” Phys. Rep. 364, 83–174 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

V. Khare, H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

J. C. Brandt, “An unusual observation of the glory,” Publ. Astron. Soc. Pac. 80, 25–28 (1968).
[CrossRef]

Q. J. R. Meteorol. Soc. (1)

A. Slingo, H. M. Schrecker, “On the shortwave radiative properties of stratiform water clouds,” Q. J. R. Meteorol. Soc. 108, 407–426 (1982).
[CrossRef]

Science (1)

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
[CrossRef] [PubMed]

Other (12)

J. Wong, “Surface resonances in high-frequency scattering from a nearly-sharp three-dimensional well,” M.S. thesis (Department of Physics and Astronomy, University of New Mexico, Albuquerque, N.M., 1968).

R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984).

D. J. Segelstein, “The complex refractive index of water,” M.S. thesis (Department of Physics, University of Missouri-Kansas City, Kansas City, Mo., 1981).

I. Newton, Opticks, 4th ed. (Royal Society, London, 1730), Book III, Part I, Query 29.

J. T. Houghton, Y. Ding, D. J. Griggs, M. Noguer, P. J. van der Linden, X. Dai, K. Maskell, C. A. Johnson, eds., Climate Change 2001: The Scientific Basis (Cambridge U. Press, Cambridge, UK, 2001), p. 433.

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, UK, 1992).
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

J. B. Keller, “Geometrical theory of diffraction,” in Calculus of Variations and its Applications, L. M. Graves, ed. (McGraw-Hill, New York, 1958), pp. 27–52.
[CrossRef]

R. K. Chang, A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).

L. D. Landau, E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Butterworth-Heinemann, New York, 1997).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

H. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1980), Fig. 10–15.

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Figures (5)

Fig. 1
Fig. 1

Average spectral absorption efficiency of a 10-μm-radius water droplet in the near infrared. Black curve, Mie result (log scale); red curve, percentage that is due to tunneling (resonances); blue curve, percentage error when plotted at 0.1 steps in size parameter.

Fig. 2
Fig. 2

Example of the aliasing effect of 0.1 step plotting for N = 1.317 + 1.155 × 10-5 i. Solid black curve, Mie result; solid purple curve, 0.1 step result; dashed blue curve, pure resonance contribution; solid gold curve, nonresonant (background); dashed red curve, Lorentzian plus nonresonant (background) fit; dashed green curve, geometrical-optics approximation.

Fig. 3
Fig. 3

Glory, photographed on clouds at the Haleakala crater in Maui. The estimated average droplet radius is near 9 μm (reproduced from Ref. 19 with permission by John C. Brandt, Institute for Astrophysics, University of New Mexico).

Fig. 4
Fig. 4

Average backscattering gain factor of a transparent water droplet, with N = 1.33007, in the size parameter range 5–150. Shown are black curve, Mie result; purple dashed curve, above-edge; solid blue curve, below-edge; dashed-dotted red curve, geometrical-optics (go); solid red curve, CAM approximation to nonresonant (nr) contributions.

Fig. 5
Fig. 5

(a) Effective radial potential U λ(r), λ ≡ l + 1/2, for a transparent sphere with N > 1 and angular momentum l. Narrow resonances arise in the domain between the top T and the bottom B of the potential pocket. Resonant wave functions with mode orders n = 0, 1 are sketched. (b) Associated ray picture according to the localization principle. The above-edge ray with impact parameter b corresponds to the narrowest resonance, n = 0.

Equations (10)

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Q abs , go = 8 3   m 2 1 - R κ x ,   κ x     1 ,
Q abs , res Q abs , go = 3 4 arctan   μ m 3 - μ 3 μ arctan   μ 2 - 1 .
2 π / π + 2 - 4 m - μ + arccos 1 / m ,
Q abs , l , n x = 2 l + 1 x 2 γ l , n γ inel x - x l , n 2 + γ l , n + γ inel 2 ,
Δ Q abs , l , n = π peak   value total   width = 2 π 2 l + 1 x l , n 2   γ , l , n ,
1 γ , l , n 1 γ l , n + 1 γ inel .
Δ Q abs , l , n Q abs , go 3 π 4 2 l + 1 m 3 - μ 3 x l , n 2 .
Q abs , res Q abs , go 3 π 2 1 m 3 - μ 3 x 2 l 2 l + 1 ,
Δ l l x   Δ x μ arctan   μ π μ = π arctan   μ .
l 2 l + 1 = l max 2 - l min 2 2 Δ l arctan   μ 2 π μ arctan   μ 2 - 1 x 2 ,

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