Abstract

The internal electric field of an illuminated liquid droplet is studied in detail with the use of both wave theory and ray theory. The internal field attains its maximum values on the caustics within the droplet. Ray theory is used to determine the equations of these caustics and the density of rays on them. The Debye-series expansion of the interior-field Mie amplitudes is used to calculate the wave-theory version of these caustics. The physical interpretation of the sources of stimulated Raman scattering and fluorescence emission within a liquid droplet is then given.

© 1991 Optical Society of America

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  1. J. R. Reitz, F. J. Milford, R. W. Christy, Foundations of Electromagnetic Theory, 3rd ed. (Addison-Wesley, Reading, Mass., 1979), Subsec. 18-2.
  2. M. Herzberger, Modern Geometrical Optics (Wiley Inter-scienceNew York, 1958), p. 156.
  3. T. Pearcy, “The structure of an electromagnetic field in the neighborhood of a cusp caustic,” Philos. Mag. 37, 311–317 (1946).
  4. D. G. Burkhard, D. L. Shealy, “Formula for the density of tangent rays over a caustic surface,” Appl. Opt. 21, 3299–3306 (1982).
    [CrossRef] [PubMed]
  5. P. W. Dusel, M. Kerker, D. D. Cooke, “Distribution of absorption centers within irradiated spheres,” J. Opt. Soc. Am. 69, 55–59 (1979).
    [CrossRef]
  6. W. M. Greene, R. E. Spjut, E. Bar-Ziv, A. F. Sarofim, J. P. Longwell, “Photophoresis of irradiated spheres: absorption centers,” J. Opt. Soc. Am. B 2, 998–1004 (1985).
    [CrossRef]
  7. C. C. Dobson, J. W. L. Lewis, “Survey of the Mie problem source function,” J. Opt. Soc. Am. A 6, 463–466 (1989).
    [CrossRef]
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    [CrossRef]
  9. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Subsec. 9.22.
  10. Ref. 1, Subsec. 18-5.
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    [CrossRef]
  12. H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. II. Theory of the rainbow and the glory,” J. Math. Phys. 10, 125–176 (1969).
    [CrossRef]
  13. J. A. Lock, “Cooperative effects among partial waves in Mie scattering,” J. Opt. Soc. Am. A 5, 2032–2044 (1988).
    [CrossRef]
  14. V. Khare, H. M. Nussenzveig, “Theory of the rainbow,” Phys. Rev. Lett. 33, 976–980 (1974).
    [CrossRef]
  15. V. Khare, H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
    [CrossRef]
  16. V. Khare, H. M. Nussenzveig, “The theory of the glory,” in Statistical Mechanics and Statistical Methods in Theory and Application,U. Landman, ed. (Plenum, New York, 1977), pp. 723–764.
    [CrossRef]
  17. H. M. Nussenzveig, “Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079; 1193–1194 (1979).
    [CrossRef]
  18. H. M. Nussenzveig, W. J. Wiscombe, “Forward optical glory,” Opt. Lett. 5, 455–457 (1980).
    [CrossRef] [PubMed]
  19. H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
    [CrossRef]
  20. H. M. Nussenzveig, W. J. Wiscombe, “Diffraction as tunneling,” Phys. Rev. Lett. 59, 1667–1670 (1987).
    [CrossRef] [PubMed]
  21. J. A. Lock, “Theory of the observations of high-order rainbows from a single water droplet,” Appl. Opt. 26, 5291–5298 (1987).
    [CrossRef] [PubMed]
  22. J. A. Lock, J. R. Woodruff, “Non-Debye enhancements in the Mie scattering of light from a single water droplet,” Appl. Opt. 28, 523–529 (1989).
    [CrossRef] [PubMed]
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  25. D. S. Langley, P. L. Marston, “Critical angle scattering of laser light from bubbles in water: measurements, models, and application to sizing of bubbles,” Appl. Opt. 23, 1044–1054 (1984).
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  26. W. P. Arnott, P. L. Marston, “Optical glory of small freely rising gas bubbles in water: observed and computed cross-polarized backscattering patterns,” J. Opt. Soc. Am. A 5, 496–506 (1988).
    [CrossRef]
  27. J. V. Dave, “Subroutines for computing the parameters of the electromagnetic radiation scattered by a sphere,” Rep. 320-3237 (IBM Scientific Center, Palo Alto, Calif., 1968).
  28. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
    [CrossRef] [PubMed]
  29. G. J. Rosasco, H. S. Bennett, “Internal field resonance structure: implications for optical absorption and scattering by microscopic particles,” J. Opt. Soc. Am. 68, 1242–1250 (1978).
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  30. A. Bott, W. Zdunkowski, “Electromagnetic energy within dielectric spheres,” J. Opt. Soc. Am. A 4, 1361–1365 (1987).
    [CrossRef]
  31. C. C. Dobson, J. W. L. Lewis, “Survey of the Mie problem source function,” J. Opt. Soc. Am. A 6, 463–466 (1989).
    [CrossRef]
  32. S. Chang, “Internal electromagnetic energy within a dielectric sphere in a plane-polarized TEMoo laser beam,” J. Opt. Soc. Am. B 6, 1332–1338 (1989).
    [CrossRef]
  33. S. C. Hill, C. K. Rushforth, R. E. Benner, P. R. Conwell, “Sizing dielectric spheres and cylinders by aligning measured and computed resonance locations: algorithm for multiple orders,” Appl. Opt. 24, 2380–2390 (1985).
    [CrossRef] [PubMed]
  34. V. E. Cachorro, L. L. Salcedo, “New improvements for Mie scattering calculations,” J. Electron. Waves Appl. (to be published).
  35. D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 26, 1348–1356 (1987).
    [CrossRef] [PubMed]
  36. R. G. Pinnick, P. Chýlek, M. Jarzembski, E. Creegan, V. Srivastava, G. Fernandez, J. D. Pendleton, A. Biswas, “Aerosol-induced laser breakdown thresholds: wavelength dependence,” Appl. Opt. 27, 987–996 (1988).
    [CrossRef] [PubMed]
  37. C. F. Wood, D. H. Leach, J.-Z. Zhang, R. K. Chang, P. W. Barber, “Time-resolved shadowgraphs of large individual water and ethanol droplets vaporized by a pulsed CO2laser,” Appl. Opt. 27, 2279–2286 (1988).
    [CrossRef] [PubMed]
  38. A. B. Pluchino, “Surface waves and the radiative properties of micron-sized particles,” Appl. Opt. 20, 2986–2993 (1981).
    [CrossRef] [PubMed]
  39. P. Chýlek, J. D. Pendleton, R. G. Pinnick, “Internal and near-surface scattered field of a spherical particle at resonant conditions,” Appl. Opt. 24, 3940–3942 (1985).
    [CrossRef] [PubMed]
  40. P. Chýlek, M. A. Jarzembski, V. Srivastava, R. G. Pinnick, J. D. Pendleton, J. P. Cruncleton, “Effect of spherical particles on laser-induced breakdown in gases,” Appl. Opt. 26, 760–762 (1987).
    [CrossRef]
  41. J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
    [CrossRef]
  42. Ref. 5, Subsec. 13-24.
  43. M. V. Berry, C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” Prog. Opt. 18, 257–346 (1980).
    [CrossRef]
  44. M. Kerker, S. D. Druger, “Raman and fluorescent scattering by molecules embedded in spheres with radii up to several multiples of the wavelength,” Appl. Opt. 18, 1172–1179 (1979).
    [CrossRef] [PubMed]
  45. P. Chýlek, M. A. Jarzembski, N. Y. Chou, R. G. Pinnick, “The effect of size and material of liquid spherical particles on laser-induced breakdown,” Appl. Phys. Lett. 49, 1475–1477 (1986).
    [CrossRef]
  46. M. A. Jarzembski, V. Srivastava, “Electromagnetic field enhancement in small liquid droplets using geometric optics,” Appl. Opt. 28, 4962–4965 (1989).
    [CrossRef] [PubMed]
  47. P. Chýlek, “Partial wave resonances and the ripple structure in the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285–287 (1976).
    [CrossRef]
  48. A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
    [CrossRef]
  49. A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
    [CrossRef] [PubMed]
  50. H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
    [CrossRef]
  51. M. Kerker, P. J. McNulty, M. Sculley, H. Chew, D. D. Cooke, “Raman and fluorescent scattering by molecules embedded in small particles: numerical results for incoherent optical processes,” J. Opt. Soc. Am. 68, 1676–1686 (1978).
    [CrossRef]
  52. S. C. Hill, R. E. Benner, “Morphology-dependent resonances associated with stimulated processes in microspheres,” J. Opt. Soc. Am. B 3, 1509–1514 (1986).
    [CrossRef]
  53. P. Chýlek, Department of Physics, Dalhousie University, Halifax B3H 3 J5, Canada (personal communication).
  54. Y. Ji, K. Hongo, “Analysis of electromagnetic waves refracted by a spherical dielectric interface,” J. Opt. Soc. Am. A 8, 541–548 (1991).
    [CrossRef]

1991

1989

1988

1987

1986

P. Chýlek, M. A. Jarzembski, N. Y. Chou, R. G. Pinnick, “The effect of size and material of liquid spherical particles on laser-induced breakdown,” Appl. Phys. Lett. 49, 1475–1477 (1986).
[CrossRef]

S. C. Hill, R. E. Benner, “Morphology-dependent resonances associated with stimulated processes in microspheres,” J. Opt. Soc. Am. B 3, 1509–1514 (1986).
[CrossRef]

1985

1984

1982

1981

1980

M. V. Berry, C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” Prog. Opt. 18, 257–346 (1980).
[CrossRef]

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[CrossRef] [PubMed]

H. M. Nussenzveig, W. J. Wiscombe, “Forward optical glory,” Opt. Lett. 5, 455–457 (1980).
[CrossRef] [PubMed]

H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
[CrossRef]

1979

1978

1977

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

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

1976

P. Chýlek, “Partial wave resonances and the ripple structure in the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285–287 (1976).
[CrossRef]

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

1974

V. Khare, H. M. Nussenzveig, “Theory of the rainbow,” Phys. Rev. Lett. 33, 976–980 (1974).
[CrossRef]

1969

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. II. Theory of the rainbow and the glory,” J. Math. Phys. 10, 125–176 (1969).
[CrossRef]

1946

T. Pearcy, “The structure of an electromagnetic field in the neighborhood of a cusp caustic,” Philos. Mag. 37, 311–317 (1946).

Alexander, D. R.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

Arnott, W. P.

Ashkin, A.

A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

Barber, P. W.

Barton, J. P.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

Bar-Ziv, E.

Benincasa, D. S.

Benner, R. E.

Bennett, H. S.

Berry, M. V.

M. V. Berry, C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” Prog. Opt. 18, 257–346 (1980).
[CrossRef]

Biswas, A.

Bott, A.

Burkhard, D. G.

Cachorro, V. E.

V. E. Cachorro, L. L. Salcedo, “New improvements for Mie scattering calculations,” J. Electron. Waves Appl. (to be published).

Chang, R. K.

Chang, S.

Chew, H.

Chou, N. Y.

P. Chýlek, M. A. Jarzembski, N. Y. Chou, R. G. Pinnick, “The effect of size and material of liquid spherical particles on laser-induced breakdown,” Appl. Phys. Lett. 49, 1475–1477 (1986).
[CrossRef]

Christy, R. W.

J. R. Reitz, F. J. Milford, R. W. Christy, Foundations of Electromagnetic Theory, 3rd ed. (Addison-Wesley, Reading, Mass., 1979), Subsec. 18-2.

Chýlek, P.

Conwell, P. R.

Cooke, D. D.

Creegan, E.

Cruncleton, J. P.

Dave, J. V.

J. V. Dave, “Subroutines for computing the parameters of the electromagnetic radiation scattered by a sphere,” Rep. 320-3237 (IBM Scientific Center, Palo Alto, Calif., 1968).

Dobson, C. C.

Druger, S. D.

Dusel, P. W.

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

Fernandez, G.

Greene, W. M.

Herzberger, M.

M. Herzberger, Modern Geometrical Optics (Wiley Inter-scienceNew York, 1958), p. 156.

Hill, S. C.

Hongo, K.

Hsieh, W.-F.

Jarzembski, M.

Jarzembski, M. A.

Ji, Y.

Kerker, M.

Khare, V.

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

V. Khare, H. M. Nussenzveig, “Theory of the rainbow,” Phys. Rev. Lett. 33, 976–980 (1974).
[CrossRef]

V. Khare, H. M. Nussenzveig, “The theory of the glory,” in Statistical Mechanics and Statistical Methods in Theory and Application,U. Landman, ed. (Plenum, New York, 1977), pp. 723–764.
[CrossRef]

Kingsbury, D. L.

Langley, D. S.

Leach, D. H.

Lewis, J. W. L.

Lock, J. A.

Longwell, J. P.

Marston, P. L.

Martson, P. L.

McNulty, P. J.

Milford, F. J.

J. R. Reitz, F. J. Milford, R. W. Christy, Foundations of Electromagnetic Theory, 3rd ed. (Addison-Wesley, Reading, Mass., 1979), Subsec. 18-2.

Nussenzveig, H. M.

H. M. Nussenzveig, W. J. Wiscombe, “Diffraction as tunneling,” Phys. Rev. Lett. 59, 1667–1670 (1987).
[CrossRef] [PubMed]

H. M. Nussenzveig, W. J. Wiscombe, “Forward optical glory,” Opt. Lett. 5, 455–457 (1980).
[CrossRef] [PubMed]

H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
[CrossRef]

H. M. Nussenzveig, “Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079; 1193–1194 (1979).
[CrossRef]

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

V. Khare, H. M. Nussenzveig, “Theory of the rainbow,” Phys. Rev. Lett. 33, 976–980 (1974).
[CrossRef]

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. II. Theory of the rainbow and the glory,” J. Math. Phys. 10, 125–176 (1969).
[CrossRef]

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

V. Khare, H. M. Nussenzveig, “The theory of the glory,” in Statistical Mechanics and Statistical Methods in Theory and Application,U. Landman, ed. (Plenum, New York, 1977), pp. 723–764.
[CrossRef]

Pearcy, T.

T. Pearcy, “The structure of an electromagnetic field in the neighborhood of a cusp caustic,” Philos. Mag. 37, 311–317 (1946).

Pendleton, J. D.

Pinnick, R. G.

Pluchino, A. B.

Reitz, J. R.

J. R. Reitz, F. J. Milford, R. W. Christy, Foundations of Electromagnetic Theory, 3rd ed. (Addison-Wesley, Reading, Mass., 1979), Subsec. 18-2.

Rosasco, G. J.

Rushforth, C. K.

Salcedo, L. L.

V. E. Cachorro, L. L. Salcedo, “New improvements for Mie scattering calculations,” J. Electron. Waves Appl. (to be published).

Sarofim, A. F.

Schaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

Sculley, M.

Shealy, D. L.

Spjut, R. E.

Srivastava, V.

Upstill, C.

M. V. Berry, C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” Prog. Opt. 18, 257–346 (1980).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Subsec. 9.22.

Wiscombe, W. J.

H. M. Nussenzveig, W. J. Wiscombe, “Diffraction as tunneling,” Phys. Rev. Lett. 59, 1667–1670 (1987).
[CrossRef] [PubMed]

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[CrossRef] [PubMed]

H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
[CrossRef]

H. M. Nussenzveig, W. J. Wiscombe, “Forward optical glory,” Opt. Lett. 5, 455–457 (1980).
[CrossRef] [PubMed]

Wood, C. F.

Woodruff, J. R.

Zdunkowski, W.

Zhang, J.-Z.

Appl. Opt.

D. G. Burkhard, D. L. Shealy, “Formula for the density of tangent rays over a caustic surface,” Appl. Opt. 21, 3299–3306 (1982).
[CrossRef] [PubMed]

J. A. Lock, “Theory of the observations of high-order rainbows from a single water droplet,” Appl. Opt. 26, 5291–5298 (1987).
[CrossRef] [PubMed]

J. A. Lock, J. R. Woodruff, “Non-Debye enhancements in the Mie scattering of light from a single water droplet,” Appl. Opt. 28, 523–529 (1989).
[CrossRef] [PubMed]

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[CrossRef] [PubMed]

D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 26, 1348–1356 (1987).
[CrossRef] [PubMed]

R. G. Pinnick, P. Chýlek, M. Jarzembski, E. Creegan, V. Srivastava, G. Fernandez, J. D. Pendleton, A. Biswas, “Aerosol-induced laser breakdown thresholds: wavelength dependence,” Appl. Opt. 27, 987–996 (1988).
[CrossRef] [PubMed]

C. F. Wood, D. H. Leach, J.-Z. Zhang, R. K. Chang, P. W. Barber, “Time-resolved shadowgraphs of large individual water and ethanol droplets vaporized by a pulsed CO2laser,” Appl. Opt. 27, 2279–2286 (1988).
[CrossRef] [PubMed]

A. B. Pluchino, “Surface waves and the radiative properties of micron-sized particles,” Appl. Opt. 20, 2986–2993 (1981).
[CrossRef] [PubMed]

P. Chýlek, J. D. Pendleton, R. G. Pinnick, “Internal and near-surface scattered field of a spherical particle at resonant conditions,” Appl. Opt. 24, 3940–3942 (1985).
[CrossRef] [PubMed]

P. Chýlek, M. A. Jarzembski, V. Srivastava, R. G. Pinnick, J. D. Pendleton, J. P. Cruncleton, “Effect of spherical particles on laser-induced breakdown in gases,” Appl. Opt. 26, 760–762 (1987).
[CrossRef]

D. S. Langley, P. L. Marston, “Critical angle scattering of laser light from bubbles in water: measurements, models, and application to sizing of bubbles,” Appl. Opt. 23, 1044–1054 (1984).
[CrossRef] [PubMed]

S. C. Hill, C. K. Rushforth, R. E. Benner, P. R. Conwell, “Sizing dielectric spheres and cylinders by aligning measured and computed resonance locations: algorithm for multiple orders,” Appl. Opt. 24, 2380–2390 (1985).
[CrossRef] [PubMed]

M. Kerker, S. D. Druger, “Raman and fluorescent scattering by molecules embedded in spheres with radii up to several multiples of the wavelength,” Appl. Opt. 18, 1172–1179 (1979).
[CrossRef] [PubMed]

M. A. Jarzembski, V. Srivastava, “Electromagnetic field enhancement in small liquid droplets using geometric optics,” Appl. Opt. 28, 4962–4965 (1989).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
[CrossRef] [PubMed]

Appl. Phys. Lett.

P. Chýlek, M. A. Jarzembski, N. Y. Chou, R. G. Pinnick, “The effect of size and material of liquid spherical particles on laser-induced breakdown,” Appl. Phys. Lett. 49, 1475–1477 (1986).
[CrossRef]

J. Appl. Phys.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

J. Math. Phys.

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. II. Theory of the rainbow and the glory,” J. Math. Phys. 10, 125–176 (1969).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Lett.

Philos. Mag.

T. Pearcy, “The structure of an electromagnetic field in the neighborhood of a cusp caustic,” Philos. Mag. 37, 311–317 (1946).

Phys. Rev. A

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

Phys. Rev. Lett.

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
[CrossRef]

H. M. Nussenzveig, W. J. Wiscombe, “Diffraction as tunneling,” Phys. Rev. Lett. 59, 1667–1670 (1987).
[CrossRef] [PubMed]

V. Khare, H. M. Nussenzveig, “Theory of the rainbow,” Phys. Rev. Lett. 33, 976–980 (1974).
[CrossRef]

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

Prog. Opt.

M. V. Berry, C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” Prog. Opt. 18, 257–346 (1980).
[CrossRef]

Other

J. V. Dave, “Subroutines for computing the parameters of the electromagnetic radiation scattered by a sphere,” Rep. 320-3237 (IBM Scientific Center, Palo Alto, Calif., 1968).

V. E. Cachorro, L. L. Salcedo, “New improvements for Mie scattering calculations,” J. Electron. Waves Appl. (to be published).

P. Chýlek, Department of Physics, Dalhousie University, Halifax B3H 3 J5, Canada (personal communication).

V. Khare, H. M. Nussenzveig, “The theory of the glory,” in Statistical Mechanics and Statistical Methods in Theory and Application,U. Landman, ed. (Plenum, New York, 1977), pp. 723–764.
[CrossRef]

J. R. Reitz, F. J. Milford, R. W. Christy, Foundations of Electromagnetic Theory, 3rd ed. (Addison-Wesley, Reading, Mass., 1979), Subsec. 18-2.

M. Herzberger, Modern Geometrical Optics (Wiley Inter-scienceNew York, 1958), p. 156.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Subsec. 9.22.

Ref. 1, Subsec. 18-5.

Ref. 5, Subsec. 13-24.

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Figures (9)

Fig. 1
Fig. 1

Geometrical light ray with an angle of incidence θi, entering and internally reflecting within a liquid droplet of radius a.

Fig. 2
Fig. 2

Gray-level plots (left-hand side) of the p term of the Debye-series interior source function for x = 100 and n = 1.36 for unpolarized incident light. Line drawings (right-hand side) of the geometrical p-ray family within the droplet for n = 1.36.

Fig. 3
Fig. 3

18.4-cm thin-walled water-filled spherical glass globe: (a) the p = 1 caustic ring, (b) the p = 2 cusp caustic of revolution, (c) the p = 2 axial caustic.

Fig. 4
Fig. 4

Formation of the p = 5 axial caustic for various incident ray angles θi. Turning points occur at the locations where the p = 5 cusp caustic intersects itself on the Z axis. The arrows below the figure show the progression of the axial caustic for the rays A‐H and I‐P.

Fig. 5
Fig. 5

Interior source function in Mie theory for a sphere with x = 100, n = 1.36, and for unpolarized incident light shown (a) as a carpet plot, (b) as a gray-level plot, and (c) along the Z axis of the droplet.

Fig. 6
Fig. 6

The p = 2 Debye-series contribution to the interior source function showing the p = 2 cusp point and the interior portion of the first-order rainbow and supernumerary rainbows.

Fig. 7
Fig. 7

Contribution of the p term of the Debye series to the interior source function on the droplet axis for p = 2 to p = 10 (curves) and the density of geometrical rays on the axial caustic from Eq. (9) (points).

Fig. 8
Fig. 8

Apparent position of a light source on the droplet axis as a function of the actual position for the geometric-optics model of Appendix C and n = 1.333. The filled-circle data points are the measured positions of grid marks on a scale fitted along the diameter of an 18.4-cm thin-walled glass globe when empty (actual positions) and filled with water (apparent positions).

Fig. 9
Fig. 9

(a) Light ray leaving a source at the coordinate zs on the axis of a spherical droplet, (b) Three such rays leaving source S and imaged by a lens. The virtual source of rays A, B, and C is S′. (c) Imaging of the spherical droplet by a lens. The image of the topmost portion of droplet T is T ¯. The image of the lower-most portion of droplet L is L ¯. The image of source S is S ¯.

Tables (1)

Tables Icon

Table 1 Experimentally Observed Locations of the Sources of Stimulated Raman cattering and Fluorescence Emission in Liquid Droplets

Equations (47)

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z = [ sin ( γ ) sin ( θ r ) + κ cos ( γ ) cos ( θ r ) ] a , ρ = [ cos ( γ ) sin ( θ r ) κ sin ( γ ) cos ( θ r ) ] a ,
n sin ( θ r ) = sin ( θ i ) ,
γ = θ i + p π ( 2 p 1 ) θ r ,
κ = [ 2 p 1 n cos ( θ r ) cos ( θ i ) ] 1 .
z c = ( 1 ) p 2 p 1 n a , ρ c = 0
( z z c ) / a = W ( p / a ) 2 / 3 ,
W = ( 1 ) p 2 × { 9 [ ( 2 p 1 n ) 3 ( 2 p 1 n ) + n ( n 2 1 ) ] ( 2 p 1 n ) 4 } 1 / 3 .
z = a sin ( θ r ) sin ( γ ) , ρ = 0 ,
d F p d z = | 2 π a 2 n κ T ( θ i ) R p 1 ( θ i ) sin ( θ r ) cos ( θ r ) sin 2 ( γ ) cos ( γ ) sin ( θ r ) + κ sin ( γ ) cos ( θ r ) | ,
[ a l b l ] = 1 2 ( 1 R l 22 T l 21 T l 12 1 R l 11 ) = 1 2 [ 1 R l 22 p = 1 T l 21 ( R l 11 ) p 1 T l 12 ] ,
[ c l d l ] = T l 21 1 R l 11 = p = 1 T l 21 ( R l 11 ) p 1 .
T l 21 = 2 i / x 2 ( t l 1 t l 2 ) + i ( t l 3 t l 4 ) ,
R l 11 = ( t l 1 t l 2 ) i ( t l 3 + t l 4 ) ( t l 1 + t l 2 ) + i ( t l 3 t l 4 ) .
t l 1 = x y { j l ( x ) j l 1 ( y ) n j l 1 ( x ) j l ( y ) + [ l ( n 2 1 ) / y ] j l ( x ) j l ( y ) } , t l 2 = x y { n l ( x ) n l 1 ( y ) n n l 1 ( x ) n l ( y ) + [ l ( n 2 1 ) / y ] n l ( x ) n l ( y ) } , t l 3 = x y { n l ( x ) j l 1 ( y ) n n l 1 ( x ) j l ( y ) + [ l ( n 2 1 ) / y ] n l ( x ) j l ( y ) } , t l 4 = x y { j l ( x ) n l 1 ( y ) n j l 1 ( x ) n l ( y ) + [ l ( n 2 1 ) / y ] j l ( x ) n l ( y ) } ,
t l 1 = x y [ n j l ( x ) j l 1 ( y ) j l 1 ( x ) j l ( y ) ] , t l 2 = x y [ n n l ( x ) n l 1 ( y ) n l 1 ( x ) n l ( y ) ] , t l 3 = x y [ n n l ( x ) j l 1 ( y ) n l 1 ( x ) j l ( y ) ] , t l 4 = x y [ n j l ( x ) n l 1 ( y ) j l 1 ( x ) n l ( y ) ] ,
x = 2 π a / λ ,
y = n x
| R l 22 | = | R l 11 | ,
T l 12 = T l 21 / n ,
| T l 22 | 2 / n + | R l 11 | 2 = 1.
T l 21 1.
R l 11 1 ( 2 / 2 n ) .
c l d l ,
a l b l 2 ,
l max = x + 7 x 1 / 3 + 2
S ( r ) = [ E * ( r ) · E ( r ) ] / E 0 2 ,
x = 100.0
n = 1.36
z i = a cos ( θ i ) , ρ i = + a sin ( θ i ) .
z p 1 = a cos [ θ i + 2 ( p 1 ) ϕ ] , ρ p 1 = + a sin [ θ i + 2 ( p 1 ) ϕ ] ,
z p = a cos ( θ i + 2 p ϕ ) , ρ p = + a sin ( θ i + 2 p ϕ ) ,
ϕ = ( π / 2 ) θ r
ρ = ρ p 1 [ tan ( γ ) ] ( z z p 1 ) ,
δ cos ( θ i ) n cos ( θ r )
z = z p 1 + ρ p 1 tan ( γ ) .
d F inc = 2 π a 2 sin ( θ i ) cos ( θ i ) d θ i .
d F p = d F inc T ( θ i ) R p 1 ( θ i ) .
d F p d z = ( d F p d θ i ) / ( d z d θ i ) .
z s = w a ,
z out = u a ,
u = w + [ w 2 + 1 2 w cos ( β ) ] 1 / 2 cos ( β + θ i ) ,
sin ( θ i ) = w sin ( β ) [ w 2 + 1 2 w cos ( β ) ] 1 / 2 .
ξ = β + θ r ,
sin ( θ r ) = n w sin ( β ) [ w 2 + 1 2 w cos ( β ) ] 1 / 2 .
ξ = ( π / 2 ) + arctan ( z out / d ) .
cos ( β ) = sin ( θ r )
w 2 + 1 2 w cos ( β ) = n 2 w 2 tan 2 ( β ) .

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