Abstract

Many recently observed optical properties of dielectric microspheres arise from the fact that they behave as optical cavities with little leakage. The thermal spectrum and the density of states are evaluated for such cavitites as a first step toward quantizing the electromagnetic field. The density of states is shown to obey an asymptotic sum rule. The formalism resolves the apparent contradiction between dissipation (from leakage) and quantization.

© 1987 Optical Society of America

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  1. G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metaalosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908); M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969); J. F. Owen, P. W. Barber, B. J. Messinger, and R. K. Chang, “Determination of optical fiber diameter from resonances in the elastic scattering spectrum,” Opt. Lett. 6, 272–274 (1981).
    [Crossref] [PubMed]
  2. P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Am. Phys. (Leipzig) 30, 57 (1909); A. Ashkin and J. M. Dziedzic, “Observations of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
    [Crossref]
  3. R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigie and G. W. Stewart, eds., Soc. Photo-Opt. Instrum. Eng. Proc.573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
    [Crossref] [PubMed]
  4. J. B. Snow, S.-X. Qian, and R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985); S.-X. Qian, J. B. Snow, and R. K. Chang, “Coherent Raman mixing and coherent anti-Stokes Raman scattering from individual micrometer-size droplets,” Opt. Lett. 10, 499–501 (1985); S.-X. Qian and R. K. Chang, “Multiorder Stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
    [Crossref] [PubMed]
  5. H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Laser emission from individual droplets at wavelengths corresponding to morphology-dependent resonances,” Opt. Lett. 9, 499–501 (1984); S.-X. Qian, J. B. Snow, H. M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486–488 (1986).
    [Crossref] [PubMed]
  6. A. Einstein, “Zur Quantentheorie der Strahlung,” Phys. Z. 18, 121–128 (1917); R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1963), Vol. I.
  7. D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981); R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
    [Crossref] [PubMed]
  8. J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface: I, II,” Phys. Rev. A 30, 1185–1193 (1984); A 32, 2030–2043 (1985).
    [Crossref]
  9. P. Ullersma, “An exactly solvable model for Brownian motion I. Derivation of the Langevin equation,” Physica 32, 27–55 (1966); “An exactly solvable model for Brownian motion II. Derivation of the Fokker–Planck equation and the master equation,” Physica 32, 56–73 (1966); “An exactly solvable model for Brownian motion III. Motion of a heavy mass in a linear chain,” Physica 32, 74–89 (1966); “An exactly solvable model for Brownian motion IV. Susceptibility and Nyquist’s theorem,” Physica 32, 90–96 (1966); R. P. Feynman and F. L. Vernon, “The theory of a general quantum system interacting with a linear dissipative system,” Ann. Phys. 24, 118–173; (1963); P. S. Riseborough, P. Hanggi, and U. Weiss, “Exact results for a damped quantum-mechanical harmonic oscillator,” Phys. Rev. A 31, 471–478 (1985); H. Grabert, U. Weiss, and P. Talkner, “Quantum theory of damped harmonic oscillator,” Z. Phys. B 55, 87–94 (1984); A. O. Caldeira and A. J. Leggett, “Quantum tunneling in a dissipative system,” Ann. Phys. (N.Y.) 149, 374–456 (1983).
    [Crossref] [PubMed]
  10. R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow?” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling,” Phys. Rev. A 30, 1401–1406 (1984).
    [Crossref]
  11. A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
    [Crossref]
  12. H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A 119, 337–339 (1987).
    [Crossref]
  13. E. N. Economou, Green’s Function in Quantum Physics, 2nd ed. (Springer-Verlag, Berlin, 1983); P. W. Anderson, Basic Notions of Condensed Matter Physics (Benjamin, New York, 1984); B. Y. Tong, M. M. Pant, and B. Hede, “Localization in random systems,” J. Phys. C 13, 1221–1235 (1980).
    [Crossref]
  14. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  15. P. R. Conwell, P. W. Barber, and C. K. Rushforth, “Resonant spectra of dielectric spheres,” J. Opt. Soc. Am. A 1, 62–67 (1984).
    [Crossref]
  16. A. C. Tam and C. K. N. Patel, “Optical absorptions of light and heavy water by laser optoacoustic spectroscopy,” Appl. Opt. 18, 3348–3358 (1979).
    [Crossref] [PubMed]
  17. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, p. 766; H. Weyl, Gesammelte Abhandlungen, K. Chandrasekharan, ed. (Springer-Verlag, Berlin, 1968), Vol. 4, p. 636[English translation: The Spirit and the Uses of the Mathematical Sciences, T. L. Saaty and F. J. Weyl, eds. (McGraw-Hill, New York, 1969), p. 286]; M. Kac, “Can one hear the shape of a drum?” Am. Math. Monthly 73, Part II, 1–23 (1966); C. N. Yang, “Hermann Weyl’s contribution to physics, a Hermann Weyl 1885–1985 centenary lecture” (State University of New York, Stony Brook, N.Y., 1985; unpublished).
    [Crossref]
  18. S. C. Hill and R. E. Benner, “Morphology-dependent resonances associated with stimulated processes in microspheres,” J. Opt. Soc. Am. B 3, 1509–1514 (1986). These authors refer to dN/dx as “density of states,” but we call it the “density of resonances” in order to avoid confusion with our ρ.
    [Crossref]
  19. S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: Einstein A and B coefficients and level shift,” J. Opt. Soc. Am. B 4, 2004–2009 (1987).
    [Crossref]
  20. D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, and R. K. Chang, “Spatial distribution of the internal and near-field intensity of large cylindrical and spherical scatterers,” Appl. Opt. (to be published).

1987 (2)

H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A 119, 337–339 (1987).
[Crossref]

S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: Einstein A and B coefficients and level shift,” J. Opt. Soc. Am. B 4, 2004–2009 (1987).
[Crossref]

1986 (1)

1985 (1)

1984 (3)

1981 (1)

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981); R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[Crossref] [PubMed]

1980 (1)

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigie and G. W. Stewart, eds., Soc. Photo-Opt. Instrum. Eng. Proc.573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
[Crossref] [PubMed]

1979 (1)

1973 (1)

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow?” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling,” Phys. Rev. A 30, 1401–1406 (1984).
[Crossref]

1966 (1)

P. Ullersma, “An exactly solvable model for Brownian motion I. Derivation of the Langevin equation,” Physica 32, 27–55 (1966); “An exactly solvable model for Brownian motion II. Derivation of the Fokker–Planck equation and the master equation,” Physica 32, 56–73 (1966); “An exactly solvable model for Brownian motion III. Motion of a heavy mass in a linear chain,” Physica 32, 74–89 (1966); “An exactly solvable model for Brownian motion IV. Susceptibility and Nyquist’s theorem,” Physica 32, 90–96 (1966); R. P. Feynman and F. L. Vernon, “The theory of a general quantum system interacting with a linear dissipative system,” Ann. Phys. 24, 118–173; (1963); P. S. Riseborough, P. Hanggi, and U. Weiss, “Exact results for a damped quantum-mechanical harmonic oscillator,” Phys. Rev. A 31, 471–478 (1985); H. Grabert, U. Weiss, and P. Talkner, “Quantum theory of damped harmonic oscillator,” Z. Phys. B 55, 87–94 (1984); A. O. Caldeira and A. J. Leggett, “Quantum tunneling in a dissipative system,” Ann. Phys. (N.Y.) 149, 374–456 (1983).
[Crossref] [PubMed]

1961 (1)

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

1917 (1)

A. Einstein, “Zur Quantentheorie der Strahlung,” Phys. Z. 18, 121–128 (1917); R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1963), Vol. I.

1909 (1)

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Am. Phys. (Leipzig) 30, 57 (1909); A. Ashkin and J. M. Dziedzic, “Observations of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[Crossref]

1908 (1)

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metaalosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908); M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969); J. F. Owen, P. W. Barber, B. J. Messinger, and R. K. Chang, “Determination of optical fiber diameter from resonances in the elastic scattering spectrum,” Opt. Lett. 6, 272–274 (1981).
[Crossref] [PubMed]

Barber, P. W.

P. R. Conwell, P. W. Barber, and C. K. Rushforth, “Resonant spectra of dielectric spheres,” J. Opt. Soc. Am. A 1, 62–67 (1984).
[Crossref]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigie and G. W. Stewart, eds., Soc. Photo-Opt. Instrum. Eng. Proc.573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
[Crossref] [PubMed]

D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, and R. K. Chang, “Spatial distribution of the internal and near-field intensity of large cylindrical and spherical scatterers,” Appl. Opt. (to be published).

Benincasa, D. S.

D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, and R. K. Chang, “Spatial distribution of the internal and near-field intensity of large cylindrical and spherical scatterers,” Appl. Opt. (to be published).

Benner, R. E.

S. C. Hill and R. E. Benner, “Morphology-dependent resonances associated with stimulated processes in microspheres,” J. Opt. Soc. Am. B 3, 1509–1514 (1986). These authors refer to dN/dx as “density of states,” but we call it the “density of resonances” in order to avoid confusion with our ρ.
[Crossref]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigie and G. W. Stewart, eds., Soc. Photo-Opt. Instrum. Eng. Proc.573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
[Crossref] [PubMed]

Chang, R. K.

J. B. Snow, S.-X. Qian, and R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985); S.-X. Qian, J. B. Snow, and R. K. Chang, “Coherent Raman mixing and coherent anti-Stokes Raman scattering from individual micrometer-size droplets,” Opt. Lett. 10, 499–501 (1985); S.-X. Qian and R. K. Chang, “Multiorder Stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
[Crossref] [PubMed]

H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Laser emission from individual droplets at wavelengths corresponding to morphology-dependent resonances,” Opt. Lett. 9, 499–501 (1984); S.-X. Qian, J. B. Snow, H. M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486–488 (1986).
[Crossref] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigie and G. W. Stewart, eds., Soc. Photo-Opt. Instrum. Eng. Proc.573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
[Crossref] [PubMed]

D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, and R. K. Chang, “Spatial distribution of the internal and near-field intensity of large cylindrical and spherical scatterers,” Appl. Opt. (to be published).

Ching, S. C.

Conwell, P. R.

Debye, P.

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Am. Phys. (Leipzig) 30, 57 (1909); A. Ashkin and J. M. Dziedzic, “Observations of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[Crossref]

Economou, E. N.

E. N. Economou, Green’s Function in Quantum Physics, 2nd ed. (Springer-Verlag, Berlin, 1983); P. W. Anderson, Basic Notions of Condensed Matter Physics (Benjamin, New York, 1984); B. Y. Tong, M. M. Pant, and B. Hede, “Localization in random systems,” J. Phys. C 13, 1221–1235 (1980).
[Crossref]

Einstein, A.

A. Einstein, “Zur Quantentheorie der Strahlung,” Phys. Z. 18, 121–128 (1917); R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1963), Vol. I.

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, p. 766; H. Weyl, Gesammelte Abhandlungen, K. Chandrasekharan, ed. (Springer-Verlag, Berlin, 1968), Vol. 4, p. 636[English translation: The Spirit and the Uses of the Mathematical Sciences, T. L. Saaty and F. J. Weyl, eds. (McGraw-Hill, New York, 1969), p. 286]; M. Kac, “Can one hear the shape of a drum?” Am. Math. Monthly 73, Part II, 1–23 (1966); C. N. Yang, “Hermann Weyl’s contribution to physics, a Hermann Weyl 1885–1985 centenary lecture” (State University of New York, Stony Brook, N.Y., 1985; unpublished).
[Crossref]

Fox, A. G.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

Hill, S. C.

Hsieh, W.-F.

D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, and R. K. Chang, “Spatial distribution of the internal and near-field intensity of large cylindrical and spherical scatterers,” Appl. Opt. (to be published).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

Kleppner, D.

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981); R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[Crossref] [PubMed]

Lai, H. M.

H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A 119, 337–339 (1987).
[Crossref]

S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: Einstein A and B coefficients and level shift,” J. Opt. Soc. Am. B 4, 2004–2009 (1987).
[Crossref]

Lamb, W. E.

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow?” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling,” Phys. Rev. A 30, 1401–1406 (1984).
[Crossref]

Lang, R.

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow?” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling,” Phys. Rev. A 30, 1401–1406 (1984).
[Crossref]

Leung, P. T.

H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A 119, 337–339 (1987).
[Crossref]

Li, T.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

Long, M. B.

Mie, G.

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metaalosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908); M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969); J. F. Owen, P. W. Barber, B. J. Messinger, and R. K. Chang, “Determination of optical fiber diameter from resonances in the elastic scattering spectrum,” Opt. Lett. 6, 272–274 (1981).
[Crossref] [PubMed]

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, p. 766; H. Weyl, Gesammelte Abhandlungen, K. Chandrasekharan, ed. (Springer-Verlag, Berlin, 1968), Vol. 4, p. 636[English translation: The Spirit and the Uses of the Mathematical Sciences, T. L. Saaty and F. J. Weyl, eds. (McGraw-Hill, New York, 1969), p. 286]; M. Kac, “Can one hear the shape of a drum?” Am. Math. Monthly 73, Part II, 1–23 (1966); C. N. Yang, “Hermann Weyl’s contribution to physics, a Hermann Weyl 1885–1985 centenary lecture” (State University of New York, Stony Brook, N.Y., 1985; unpublished).
[Crossref]

Owen, J. F.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigie and G. W. Stewart, eds., Soc. Photo-Opt. Instrum. Eng. Proc.573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
[Crossref] [PubMed]

Patel, C. K. N.

Qian, S.-X.

Rushforth, C. K.

Scully, M. O.

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow?” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling,” Phys. Rev. A 30, 1401–1406 (1984).
[Crossref]

Sipe, J. E.

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface: I, II,” Phys. Rev. A 30, 1185–1193 (1984); A 32, 2030–2043 (1985).
[Crossref]

Snow, J. B.

Tam, A. C.

Tzeng, H.-M.

Ullersma, P.

P. Ullersma, “An exactly solvable model for Brownian motion I. Derivation of the Langevin equation,” Physica 32, 27–55 (1966); “An exactly solvable model for Brownian motion II. Derivation of the Fokker–Planck equation and the master equation,” Physica 32, 56–73 (1966); “An exactly solvable model for Brownian motion III. Motion of a heavy mass in a linear chain,” Physica 32, 74–89 (1966); “An exactly solvable model for Brownian motion IV. Susceptibility and Nyquist’s theorem,” Physica 32, 90–96 (1966); R. P. Feynman and F. L. Vernon, “The theory of a general quantum system interacting with a linear dissipative system,” Ann. Phys. 24, 118–173; (1963); P. S. Riseborough, P. Hanggi, and U. Weiss, “Exact results for a damped quantum-mechanical harmonic oscillator,” Phys. Rev. A 31, 471–478 (1985); H. Grabert, U. Weiss, and P. Talkner, “Quantum theory of damped harmonic oscillator,” Z. Phys. B 55, 87–94 (1984); A. O. Caldeira and A. J. Leggett, “Quantum tunneling in a dissipative system,” Ann. Phys. (N.Y.) 149, 374–456 (1983).
[Crossref] [PubMed]

Wall, K. F.

Wylie, J. M.

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface: I, II,” Phys. Rev. A 30, 1185–1193 (1984); A 32, 2030–2043 (1985).
[Crossref]

Young, K.

H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A 119, 337–339 (1987).
[Crossref]

S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: Einstein A and B coefficients and level shift,” J. Opt. Soc. Am. B 4, 2004–2009 (1987).
[Crossref]

Zhang, J.-Z.

D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, and R. K. Chang, “Spatial distribution of the internal and near-field intensity of large cylindrical and spherical scatterers,” Appl. Opt. (to be published).

Am. Phys. (Leipzig) (1)

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Am. Phys. (Leipzig) 30, 57 (1909); A. Ashkin and J. M. Dziedzic, “Observations of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[Crossref]

Ann. Phys. (Leipzig) (1)

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metaalosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908); M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969); J. F. Owen, P. W. Barber, B. J. Messinger, and R. K. Chang, “Determination of optical fiber diameter from resonances in the elastic scattering spectrum,” Opt. Lett. 6, 272–274 (1981).
[Crossref] [PubMed]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

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

J. Opt. Soc. Am. B (2)

Opt. Lett. (2)

Phys. Lett. A (1)

H. M. Lai, P. T. Leung, and K. Young, “Thermal spectrum in leaky cavities: a string model,” Phys. Lett. A 119, 337–339 (1987).
[Crossref]

Phys. Rev. A (2)

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow?” Phys. Rev. A 7, 1788–1797 (1973); J. C. Penaforte and B. Baseia, “Quantum theory of a one-dimensional laser with output coupling,” Phys. Rev. A 30, 1401–1406 (1984).
[Crossref]

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface: I, II,” Phys. Rev. A 30, 1185–1193 (1984); A 32, 2030–2043 (1985).
[Crossref]

Phys. Rev. Lett. (2)

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981); R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[Crossref] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980); H.-M. Tzeng, M. B. Long, and R. K. Chang, “Size and shape variations of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigie and G. W. Stewart, eds., Soc. Photo-Opt. Instrum. Eng. Proc.573, 80–83 (1985); H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Evaporation and condensation rates of liquid droplets deduced from structure resonances in the fluorescence spectra,” Opt. Lett. 9, 273–275 (1984).
[Crossref] [PubMed]

Phys. Z. (1)

A. Einstein, “Zur Quantentheorie der Strahlung,” Phys. Z. 18, 121–128 (1917); R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1963), Vol. I.

Physica (1)

P. Ullersma, “An exactly solvable model for Brownian motion I. Derivation of the Langevin equation,” Physica 32, 27–55 (1966); “An exactly solvable model for Brownian motion II. Derivation of the Fokker–Planck equation and the master equation,” Physica 32, 56–73 (1966); “An exactly solvable model for Brownian motion III. Motion of a heavy mass in a linear chain,” Physica 32, 74–89 (1966); “An exactly solvable model for Brownian motion IV. Susceptibility and Nyquist’s theorem,” Physica 32, 90–96 (1966); R. P. Feynman and F. L. Vernon, “The theory of a general quantum system interacting with a linear dissipative system,” Ann. Phys. 24, 118–173; (1963); P. S. Riseborough, P. Hanggi, and U. Weiss, “Exact results for a damped quantum-mechanical harmonic oscillator,” Phys. Rev. A 31, 471–478 (1985); H. Grabert, U. Weiss, and P. Talkner, “Quantum theory of damped harmonic oscillator,” Z. Phys. B 55, 87–94 (1984); A. O. Caldeira and A. J. Leggett, “Quantum tunneling in a dissipative system,” Ann. Phys. (N.Y.) 149, 374–456 (1983).
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[Crossref]

E. N. Economou, Green’s Function in Quantum Physics, 2nd ed. (Springer-Verlag, Berlin, 1983); P. W. Anderson, Basic Notions of Condensed Matter Physics (Benjamin, New York, 1984); B. Y. Tong, M. M. Pant, and B. Hede, “Localization in random systems,” J. Phys. C 13, 1221–1235 (1980).
[Crossref]

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D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, and R. K. Chang, “Spatial distribution of the internal and near-field intensity of large cylindrical and spherical scatterers,” Appl. Opt. (to be published).

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Figures (5)

Fig. 1
Fig. 1

(a) Normalized density of states GC and (b) scattering efficiency Qsc versus size parameter x for a dielectric microsphere with n = 1.4. Peaks are labeled by μ, l, ν ¯.

Fig. 2
Fig. 2

One peak of Fig. 1(a) shown in detail.

Fig. 3
Fig. 3

Deviations of HC(x)/x2 from the fitted straight line; data shown only in steps of 0.2. Inset shows a segment enlarged.

Fig. 4
Fig. 4

Normalized local density of states g (solid line) and normalized electric- and magnetic-field fluctuations (dashed lines) versus position parameter ξ = r/a for n = 1.4 and (a) x = 31.7892 (resonance peak) and (b) x = 31.9000 (nonresonant).

Fig. 5
Fig. 5

Normalized local density of states g (solid line) and normalized electric- and magnetic-field fluctuations (dashed lines) at fixed ξ = 0.94 versus size parameter x for (a) range of x as in Fig. 1 and for (b) range of x as in Fig. 2.

Tables (1)

Tables Icon

Table 1 Position of Peak (x0), Angular Momentum (l), and the Fractions f1 and f2 for the Four Peaks in Fig. 1

Equations (50)

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x = 2 π a / λ ,
S C ( T , ω ) = ρ C ( ω ) ω N ( ω / k B T ) ,
S C ( T , ω ) = C d 3 r S ( T , ω , r ) , ρ C ( ω ) = C d 3 r ρ ( ω , r ) .
ρ vac ( ω ) = ω 2 / π 2 c 3 ,
ρ vac C ( ω ) = V ρ vac ( ω ) ,
E = s ω s - 1 d α ( s , t ) / d t e ( s , r ) , B = s α ( s , t ) b ( s , r ) ,
× e ( s , r ) = - ( ω s / c ) b ( s , r ) .
× [ × e ( s , r ) ] = ( ω s 2 / c 2 ) n 2 ( r ) e ( s , r ) ,
d 2 α ( s , t ) / d t 2 = - ω s 2 α ( s , t ) .
I ( 1 ) ( s , s ) = ( 1 / 4 π ) R d 3 r n 2 ( r ) e ( s , r ) · e ( s , r ) , I ( 2 ) ( s , s ) = ( 1 / 4 π ) R d 3 r b ( s , r ) · b ( s , r )
I ( 1 ) ( s , s ) = I ( 2 ) ( s , s ) = ω s δ s s
R d 3 r U ( r ) = R d 3 r ( 1 / 8 π ) [ n 2 ( r ) E ( r ) 2 + B ( r ) 2 ] = R d 3 r s N s u s ( r ) ,
u s ( r ) = ( 1 / 8 π ) [ n 2 ( r ) e ( s , r ) 2 + b ( s , r ) 2 ]
N s = 1 2 { 1 ω s 2 [ d α ( s , t ) d t ] 2 + α ( s , t ) 2 } ,
ρ ( ω , r ) = ( 1 / ω ) s δ ( ω - ω s ) u s ( r ) ,
E i j ( ω , r ) = ( 1 / 4 π ω ) s δ ( ω - ω s ) e i ( s , r ) e j ( s , r ) , B i j ( ω , r ) = ( 1 / 4 π ω ) s δ ( ω - ω s ) b i ( s , r ) b j ( s , r )
E ( ω , r ) = i E i i ( ω , r ) ,             B ( ω , r ) = i B i i ( ω , r ) .
ρ ( ω , r ) = ( 1 / 2 ) [ n 2 ( r ) E ( ω , r ) + B ( ω , r ) ] .
ρ vac ( ω , r ) = E vac ( ω , r ) = B vac ( ω , r ) .
s = ( μ , l , m , ν ) ,
e ( s , r ) = e ( μ , l , m , ν ; r ) , α ( s , t ) = α ( μ , l , m , ν ; t ) ,
TE             e ( E , l , m , ν ; r ) = { β E ( l , m ) j l ( n k r ) L Y l m ( θ , ϕ ) ,             r < a [ γ E ( 1 ) ( l , m ) h l ( 1 ) ( k r ) + γ E ( 2 ) ( l , m ) h l ( 2 ) ( k r ) ] L Y l m ( θ , ϕ ) ,             r > a , b ( E , l , m , ν ; r ) = - ( 1 / k ) × e ( E , l , m , ν ; r ) ; TM             b ( M , l , m , ν ; r ) = { β M ( l , m ) j l ( n k r ) L Y l m ( θ , ϕ ) ,             r < a [ γ M ( 1 ) ( l , m ) h l ( 1 ) ( k r ) + γ M ( 2 ) ( l , m ) h l ( 2 ) ( k r ) ] L Y l m ( θ , ϕ ) ,             r > a , e ( M , l , m , ν ; r ) = - [ 1 / n 2 ( r ) k ] × b ( M , l , m , ν ; r ) ,
exp [ 2 i δ E ( l ) ] = γ E ( 1 ) ( l , m ) / γ E ( 2 ) ( l , m )
tan δ μ ( l ) = W μ ( j ˜ l , j l ) / W μ ( j ˜ l , n l ) ,
W E ( f , g ) = f g - f g , W M ( f , g ) = f g - n - 2 f g + ( 1 - n - 2 ) f g / x .
β μ ( l , m ) / γ μ ( 1 ) ( l , m ) = - 2 i / x 2 W μ ( j ˜ l , h l ( 2 ) ) .
ω s = ( ν + l 2 ) π c Λ - c Λ δ E ( l ) ,             ν = 0 , 1 , 2 , ,
γ μ ( 1 , 2 ) 2 = 4 π c l ( l + 1 ) k 3 Λ .
s = μ l , m ν ,
ν Λ π c d ω s .
ρ ( ω , r ) = μ , l ρ μ l ( ω , r ) ,
ρ E l = 2 l + 1 4 π 2 c 1 x 4 C l ( r ) / r 2 W E ( j ˜ l h l ( 2 ) ) 2 ,
C l ( r ) = 2 n 2 y 2 j ˜ l ( y ) 2 + d d y { y j ˜ l ( y ) d d y [ y j ˜ l ( y ) ] } ,
Q sc = μ l Q μ l
Q μ l = ( 2 / x 2 ) ( 2 l + 1 ) sin 2 δ μ ( l )
G C = ρ C ( ω ) / ρ vac C ( ω ) ,
Q μ l 2 ( 2 l + 1 ) / x 2 .
f 1 1 2 l + 1 peak ρ C ( ω ) d ω ~ 1 .
f 2 l / x = O ( 1 ) ,
f 3 ω 1 peaks ω 2 ρ C ( ω ) d ω / ω 1 ω 2 ρ C ( ω ) d ω .
0 ω ρ C ( ω ) d ω = C 1 ( ω ) V + C 2 ( ω ) A + ,
C 1 ( ω ) = n 3 ω 3 / 3 π 2 c 3 .
H C ( x ) 0 x G C ( x ) x 2 d x = ( n 3 / 3 ) x 3 + O ( x 2 ) .
Δ ω ρ C ( ω ) d ω = f 3 - 1 Δ ω peaks ρ C ( ω ) d ω = f 3 - 1 ( d N d x Δ x ) ( 2 f 1 f 2 x ) ,
d N d x = ( 2 3 π f 3 f 1 f 2 n 3 ) x α x .
g ( x , ξ ) = ρ ( ω , r ) / ρ vac ( ω ) ,
ξ = r / a = y / x ,
h E = n 2 E / ρ vac ,             h B = B / ρ vac ,
g = ( h E + h B ) / 2
N s ( a s + a s + a s a s + ) / 2 ,

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