Abstract

The spectroscopy of the morphology-dependent resonances of a microdroplet has been studied at high precision. The line positions are shown to reveal optical dispersion and permit the refractive index to be determined with sufficient accuracy to provide an estimate of the droplet cooling that is due to evaporation. Comparison of the remaining discrepancies in mode positions for different radial modes indicates a small temperature gradient near the surface. Both the cooling and the temperature gradient are compatible with thermodynamic estimates. The mode quantum numbers are identified with high confidence, and the systematics of the line intensities permit an estimate of the extra radiative loss 1/QL over and above that predicted by Lorenz–Mie theory for a perfect homogeneous microsphere, for example, that which is due to internal scattering, with QL ≈ 2 × 108 for first-order modes.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metaalosungen,” Ann. Phys. (Leipzing) 25, 377–445 (1908); M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
    [Crossref]
  2. 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 variation of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., Proc. Soc. Photo-Opt. Instrum. Eng.573, 80–83 (1985).
    [Crossref]
  3. 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 and R. K. Chang, “Multi-order Stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56, 926–929 (1986); A. Biswas, H. Latifi, R. L. Armstrong, and R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989); J. Z. Zhang, G. Chen, and R. K. Chang, “Pumping of stimulated Raman scattering by stimulated Brillouin scattering within a single liquid droplet: input laser linewidth effects,” J. Opt. Soc. Am. B 7, 108–115 (1990).
    [Crossref] [PubMed]
  4. H.-B. Lin, A. L. Huston, J. D. Eversole, and A. J. Campillo, “Double-resonance stimulated Raman scattering in micrometer-sized droplets,” J. Opt. Soc. Am. B 7, 2079–2089 (1990).
    [Crossref]
  5. H.-B. Lin, J. D. Eversole, and A. J. Campillo, “Continuous-wave stimulated Raman scattering in microdroplets,” Opt. Lett. 17, 828–830 (1992).
    [Crossref] [PubMed]
  6. J. Z. Zhang and R. K. Chang, “Generation and suppression of stimulated Brillouin scattering in single liquid droplets,” J. Opt. Soc. Am. B 6, 151–153 (1989); S. C. Ching, P. T. Leung, and K. Young, “Spontaneous Brillouin scattering in a microdroplet,” Phys. Rev. A 41, 5026–5038 (1990); P. T. Leung and K. Young, “Doubly resonant stimulated Brillouin scattering in a microdroplet,” Phys. Rev. A 44, 593–607 (1991).
    [Crossref] [PubMed]
  7. 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); H.-B. Lin, A. L. Huston, B. L. Justus, and A. J. Campillo, “Some characteristics of a droplet whispering-gallery-mode laser,” Opt. Lett. 11, 614–616 (1986).
    [Crossref] [PubMed]
  8. H.-B. Lin, J. D. Eversole, and A. J. Campillo, “Spectral properties of lasing microdroplets,” J. Opt. Soc. Am. B 9, 43–50 (1992).
    [Crossref]
  9. S. Schiller and R. L. Byer, “High-resolution spectroscopy of whispering gallery modes in large dielectric spheres,” Opt. Lett. 16, 1138–1140 (1991); C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992).
    [Crossref] [PubMed]
  10. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1964); S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am. B 4, 1995–2003 (1987); “Dielectric microspheres as optical cavities: Einstein A and B coefficients and level shift,” J. Opt. Soc. Am. B 4, 2004–2009 (1987).
    [Crossref]
  11. 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); A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991); F. de Martini, M. Marrocco, P. Mataloni, and L. Crescentini, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991); H.-B. Lin, J. D. Eversole, C. D. Merritt, and A. J. Campillo, “Cavity-modified spontaneous-emission rates in liquid microdroplets,” Phys. Rev. A 45, 6756–6760 (1992).
    [Crossref] [PubMed]
  12. P. R. Conwell, C. K. Rushforth, R. E. Benner, and S. C. Hill, “Efficient automated algorithm for the sizing of dielectric microspheres using the resonance spectrum,” J. Opt. Soc. Am. A 1, 1181–1187 (1984); S. C. Hill, C. K. Rushforth, R. E. Benner, and 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); J. D. Eversole, H.-B. Lin, and A. J. Campillo, “Spherical cavity mode assignments of optical resonances in microdroplets using elastic scattering,” J. Opt. Soc. Am. A 7, 2159–2168 (1990).
    [Crossref] [PubMed]
  13. J. D. Eversole, H.-B. Lin, and A. J. Campillo, “Cavity-mode identification of fluorescence and lasing in dye-doped microdroplets,” Appl. Opt. 31, 1982–1991 (1992).
    [Crossref] [PubMed]
  14. G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, “Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1296–1271 (1991); J. C. Swindal, D. H. Leach, R. K. Chang, and K. Young, “Precession of morphology-dependent resonances in nonspherical droplets,” Opt. Lett. 18, 191–193 (1993).
    [Crossref]
  15. H.-B. Lin, J. D. Eversole, and A. J. Campillo, “Vibrating orifice droplet generator for precision optical studies,” Rev. Sci. Instrum. 61, 1018–1023 (1990).
    [Crossref]
  16. V. P. Froutasev and L. S. Shraiber, “Refractometric studies of some organic liquids,” Uch. Zap. Sarat. Gos. Univ. 69, 225 (1960).
  17. C. N. Davies, “Evaporation of airborne droplets,” in Fundamentals of Aerosol Science, D. T. Shaw, ed. (Wiley, New York, 1978), Chap. 3.
  18. B. B. Snavely, “Flashlamp-excited organic dye lasers,” Proc. IEEE 57, 1374–1390 (1969).
    [Crossref]
  19. P. Chylek, H.-B. Lin, J. D. Eversole, and A. J. Campillo, “Absorption effects on microdroplet resonant emission structure,” Opt. Lett. 16, 1723–1725 (1991).
    [Crossref] [PubMed]
  20. Higher orders in the asymptotic series have recently been obtained, e.g., “Asymptotic expansion of morphological resonance frequencies in Mie scattering,” by S. Schiller, Stanford University, Stanford, Calif. 94305 (personal communication), but these are relatively cumbersome, and the method described in Appendix A is in practice more suitable.

1992 (3)

1991 (3)

G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, “Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1296–1271 (1991); J. C. Swindal, D. H. Leach, R. K. Chang, and K. Young, “Precession of morphology-dependent resonances in nonspherical droplets,” Opt. Lett. 18, 191–193 (1993).
[Crossref]

P. Chylek, H.-B. Lin, J. D. Eversole, and A. J. Campillo, “Absorption effects on microdroplet resonant emission structure,” Opt. Lett. 16, 1723–1725 (1991).
[Crossref] [PubMed]

S. Schiller and R. L. Byer, “High-resolution spectroscopy of whispering gallery modes in large dielectric spheres,” Opt. Lett. 16, 1138–1140 (1991); C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992).
[Crossref] [PubMed]

1990 (2)

H.-B. Lin, A. L. Huston, J. D. Eversole, and A. J. Campillo, “Double-resonance stimulated Raman scattering in micrometer-sized droplets,” J. Opt. Soc. Am. B 7, 2079–2089 (1990).
[Crossref]

H.-B. Lin, J. D. Eversole, and A. J. Campillo, “Vibrating orifice droplet generator for precision optical studies,” Rev. Sci. Instrum. 61, 1018–1023 (1990).
[Crossref]

1989 (1)

1985 (1)

1984 (2)

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); A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991); F. de Martini, M. Marrocco, P. Mataloni, and L. Crescentini, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991); H.-B. Lin, J. D. Eversole, C. D. Merritt, and A. J. Campillo, “Cavity-modified spontaneous-emission rates in liquid microdroplets,” Phys. Rev. A 45, 6756–6760 (1992).
[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 variation of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., Proc. Soc. Photo-Opt. Instrum. Eng.573, 80–83 (1985).
[Crossref]

1969 (1)

B. B. Snavely, “Flashlamp-excited organic dye lasers,” Proc. IEEE 57, 1374–1390 (1969).
[Crossref]

1964 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1964); S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am. B 4, 1995–2003 (1987); “Dielectric microspheres as optical cavities: Einstein A and B coefficients and level shift,” J. Opt. Soc. Am. B 4, 2004–2009 (1987).
[Crossref]

1960 (1)

V. P. Froutasev and L. S. Shraiber, “Refractometric studies of some organic liquids,” Uch. Zap. Sarat. Gos. Univ. 69, 225 (1960).

1908 (1)

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metaalosungen,” Ann. Phys. (Leipzing) 25, 377–445 (1908); M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
[Crossref]

Barber, P. W.

G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, “Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1296–1271 (1991); J. C. Swindal, D. H. Leach, R. K. Chang, and K. Young, “Precession of morphology-dependent resonances in nonspherical droplets,” Opt. Lett. 18, 191–193 (1993).
[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 variation of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., Proc. Soc. Photo-Opt. Instrum. Eng.573, 80–83 (1985).
[Crossref]

Benner, R. E.

P. R. Conwell, C. K. Rushforth, R. E. Benner, and S. C. Hill, “Efficient automated algorithm for the sizing of dielectric microspheres using the resonance spectrum,” J. Opt. Soc. Am. A 1, 1181–1187 (1984); S. C. Hill, C. K. Rushforth, R. E. Benner, and 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); J. D. Eversole, H.-B. Lin, and A. J. Campillo, “Spherical cavity mode assignments of optical resonances in microdroplets using elastic scattering,” J. Opt. Soc. Am. A 7, 2159–2168 (1990).
[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 variation of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., Proc. Soc. Photo-Opt. Instrum. Eng.573, 80–83 (1985).
[Crossref]

Byer, R. L.

Campillo, A. J.

Chang, R. K.

G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, “Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1296–1271 (1991); J. C. Swindal, D. H. Leach, R. K. Chang, and K. Young, “Precession of morphology-dependent resonances in nonspherical droplets,” Opt. Lett. 18, 191–193 (1993).
[Crossref]

J. Z. Zhang and R. K. Chang, “Generation and suppression of stimulated Brillouin scattering in single liquid droplets,” J. Opt. Soc. Am. B 6, 151–153 (1989); S. C. Ching, P. T. Leung, and K. Young, “Spontaneous Brillouin scattering in a microdroplet,” Phys. Rev. A 41, 5026–5038 (1990); P. T. Leung and K. Young, “Doubly resonant stimulated Brillouin scattering in a microdroplet,” Phys. Rev. A 44, 593–607 (1991).
[Crossref] [PubMed]

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 and R. K. Chang, “Multi-order Stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56, 926–929 (1986); A. Biswas, H. Latifi, R. L. Armstrong, and R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989); J. Z. Zhang, G. Chen, and R. K. Chang, “Pumping of stimulated Raman scattering by stimulated Brillouin scattering within a single liquid droplet: input laser linewidth effects,” J. Opt. Soc. Am. B 7, 108–115 (1990).
[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); H.-B. Lin, A. L. Huston, B. L. Justus, and A. J. Campillo, “Some characteristics of a droplet whispering-gallery-mode laser,” Opt. Lett. 11, 614–616 (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 variation of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., Proc. Soc. Photo-Opt. Instrum. Eng.573, 80–83 (1985).
[Crossref]

Chen, G.

G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, “Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1296–1271 (1991); J. C. Swindal, D. H. Leach, R. K. Chang, and K. Young, “Precession of morphology-dependent resonances in nonspherical droplets,” Opt. Lett. 18, 191–193 (1993).
[Crossref]

Chylek, P.

Conwell, P. R.

Davies, C. N.

C. N. Davies, “Evaporation of airborne droplets,” in Fundamentals of Aerosol Science, D. T. Shaw, ed. (Wiley, New York, 1978), Chap. 3.

Eversole, J. D.

Froutasev, V. P.

V. P. Froutasev and L. S. Shraiber, “Refractometric studies of some organic liquids,” Uch. Zap. Sarat. Gos. Univ. 69, 225 (1960).

Hill, S. C.

Huston, A. L.

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); A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991); F. de Martini, M. Marrocco, P. Mataloni, and L. Crescentini, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991); H.-B. Lin, J. D. Eversole, C. D. Merritt, and A. J. Campillo, “Cavity-modified spontaneous-emission rates in liquid microdroplets,” Phys. Rev. A 45, 6756–6760 (1992).
[Crossref] [PubMed]

Lin, H.-B.

Long, M. B.

Mie, G.

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metaalosungen,” Ann. Phys. (Leipzing) 25, 377–445 (1908); M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
[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 variation of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., Proc. Soc. Photo-Opt. Instrum. Eng.573, 80–83 (1985).
[Crossref]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1964); S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am. B 4, 1995–2003 (1987); “Dielectric microspheres as optical cavities: Einstein A and B coefficients and level shift,” J. Opt. Soc. Am. B 4, 2004–2009 (1987).
[Crossref]

Qian, S. X.

Rushforth, C. K.

Schiller, S.

S. Schiller and R. L. Byer, “High-resolution spectroscopy of whispering gallery modes in large dielectric spheres,” Opt. Lett. 16, 1138–1140 (1991); C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992).
[Crossref] [PubMed]

Higher orders in the asymptotic series have recently been obtained, e.g., “Asymptotic expansion of morphological resonance frequencies in Mie scattering,” by S. Schiller, Stanford University, Stanford, Calif. 94305 (personal communication), but these are relatively cumbersome, and the method described in Appendix A is in practice more suitable.

Shraiber, L. S.

V. P. Froutasev and L. S. Shraiber, “Refractometric studies of some organic liquids,” Uch. Zap. Sarat. Gos. Univ. 69, 225 (1960).

Snavely, B. B.

B. B. Snavely, “Flashlamp-excited organic dye lasers,” Proc. IEEE 57, 1374–1390 (1969).
[Crossref]

Snow, J. B.

Tzeng, H. M.

Wall, K. F.

Zhang, J. Z.

Ann. Phys. (Leipzing) (1)

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metaalosungen,” Ann. Phys. (Leipzing) 25, 377–445 (1908); M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
[Crossref]

Appl. Opt. (1)

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

J. Opt. Soc. Am. B (3)

Opt. Lett. (6)

S. Schiller and R. L. Byer, “High-resolution spectroscopy of whispering gallery modes in large dielectric spheres,” Opt. Lett. 16, 1138–1140 (1991); C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992).
[Crossref] [PubMed]

H.-B. Lin, J. D. Eversole, and A. J. Campillo, “Continuous-wave stimulated Raman scattering in microdroplets,” Opt. Lett. 17, 828–830 (1992).
[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); H.-B. Lin, A. L. Huston, B. L. Justus, and A. J. Campillo, “Some characteristics of a droplet whispering-gallery-mode laser,” Opt. Lett. 11, 614–616 (1986).
[Crossref] [PubMed]

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 and R. K. Chang, “Multi-order Stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56, 926–929 (1986); A. Biswas, H. Latifi, R. L. Armstrong, and R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989); J. Z. Zhang, G. Chen, and R. K. Chang, “Pumping of stimulated Raman scattering by stimulated Brillouin scattering within a single liquid droplet: input laser linewidth effects,” J. Opt. Soc. Am. B 7, 108–115 (1990).
[Crossref] [PubMed]

G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, “Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1296–1271 (1991); J. C. Swindal, D. H. Leach, R. K. Chang, and K. Young, “Precession of morphology-dependent resonances in nonspherical droplets,” Opt. Lett. 18, 191–193 (1993).
[Crossref]

P. Chylek, H.-B. Lin, J. D. Eversole, and A. J. Campillo, “Absorption effects on microdroplet resonant emission structure,” Opt. Lett. 16, 1723–1725 (1991).
[Crossref] [PubMed]

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1964); S. C. Ching, H. M. Lai, and K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am. B 4, 1995–2003 (1987); “Dielectric microspheres as optical cavities: Einstein A and B coefficients and level shift,” J. Opt. Soc. Am. B 4, 2004–2009 (1987).
[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); A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991); F. de Martini, M. Marrocco, P. Mataloni, and L. Crescentini, “Spontaneous emission in the optical microscopic cavity,” Phys. Rev. A 43, 2480–2497 (1991); H.-B. Lin, J. D. Eversole, C. D. Merritt, and A. J. Campillo, “Cavity-modified spontaneous-emission rates in liquid microdroplets,” Phys. Rev. A 45, 6756–6760 (1992).
[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 variation of liquid droplets deduced from morphology-dependent resonances in fluorescence spectra,” in Particle Sizing and Spray Analysis, N. Chigier and G. W. Stewart, eds., Proc. Soc. Photo-Opt. Instrum. Eng.573, 80–83 (1985).
[Crossref]

Proc. IEEE (1)

B. B. Snavely, “Flashlamp-excited organic dye lasers,” Proc. IEEE 57, 1374–1390 (1969).
[Crossref]

Rev. Sci. Instrum. (1)

H.-B. Lin, J. D. Eversole, and A. J. Campillo, “Vibrating orifice droplet generator for precision optical studies,” Rev. Sci. Instrum. 61, 1018–1023 (1990).
[Crossref]

Uch. Zap. Sarat. Gos. Univ. (1)

V. P. Froutasev and L. S. Shraiber, “Refractometric studies of some organic liquids,” Uch. Zap. Sarat. Gos. Univ. 69, 225 (1960).

Other (2)

C. N. Davies, “Evaporation of airborne droplets,” in Fundamentals of Aerosol Science, D. T. Shaw, ed. (Wiley, New York, 1978), Chap. 3.

Higher orders in the asymptotic series have recently been obtained, e.g., “Asymptotic expansion of morphological resonance frequencies in Mie scattering,” by S. Schiller, Stanford University, Stanford, Calif. 94305 (personal communication), but these are relatively cumbersome, and the method described in Appendix A is in practice more suitable.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Two typical fluorescence spectra from 7.652-μm-radius R6G-doped ethanol droplets. The spectra were obtained with slightly different laser pump intensities and are vertically offset, showing that MDR peaks are consistently reproduced.

Fig. 2
Fig. 2

Correlation C[n, a*(n)] versus refractive index n for the fit without dispersion or offset: (a) spectrum A, (b) spectrum B.

Fig. 3
Fig. 3

Correlation versus (a) n0, (b) n1, and (c) a, with the other two variables fixed at the optimized values.

Fig. 4
Fig. 4

Dispersion curves implied by the fitted values of n0 and n1 for spectrum A (higher line) and spectrum B (lower line). The points are the literature data for ethanol at various temperatures: ■, 25°C; ▸, 23°C; ●, 20°C.

Fig. 5
Fig. 5

Total wavelength integrated fluorescence from R6G-doped ethanol droplets as a function of droplet size (orifice vibration frequency of the aerosol generator). Plots were obtained at vertical fall distances (a) 0.25, (b) 0.51, (c) 0.76, (d) 1.02, and (e) 1.64 nm from the orifice. Small shifts in the characteristic patterns reflect evaporation of the droplets as they fall.

Fig. 6
Fig. 6

Difference Δν between the experimental peak positions and the corresponding theoretical positions versus the wave number for (a) spectrum A and (b) spectrum B. Radial orders: ■, i = 1; ▸, i = 2; ●, i = 3; *, i = 4.

Fig. 7
Fig. 7

Comparison of the theoretical peaks and the experimental peaks of (a) spectrum A and (b) spectrum B. In each figure the top trace shows the positions and heights of the experimental peaks. The middle trace shows all theoretical peaks with i ≤ 4 that have been matched with experimental peaks, drawn with heights proportional to 5 − i. The bottom trace shows all the theoretical peaks with i ≤ 4 that are not matched with experimental peaks.

Fig. 8
Fig. 8

Experimental peak heights of spectrum A versus wave number (points). The curve is the emission spectrum of R6G.

Fig. 9
Fig. 9

Experimental peak heights segregated into groups of the same polarization and radial order. (a) TE polarization and (b) TM polarization. Radial orders: ■, i = 1; ▸, i = 2; ●, i = 3; *, i = 4.

Fig. 10
Fig. 10

Experimental peak heights (points) and the theoretical intensities (curves) calculated from Eq. (9): (a) TEl1, (b) TEl2, (c) TEl3, (d) TMl1, (e) TMl2, (f) TMl3. The solid curves are the theoretical curves with C and γL chosen for a best fit, whereas the dashed curves show the case for γL = 0. For i = 3 the best fit appears to be γL = 0, so only a single curve is shown.

Fig. 11
Fig. 11

Absorption spectrum of R6G obtained from direct measurement in a bulk sample.

Tables (6)

Tables Icon

Table 1 Experimental Peak Positions, Heights, and Widths for Spectrum A and the Results of Mode Identification for the Polarization μ Mode Number l and Radial Order ia

Tables Icon

Table 2 Experimental Peak Positions for Spectrum B and the Results of Mode Indentification for the Polarization μ Mode Number l and Radial Order ia

Tables Icon

Table 3 Results of Fit without Dispersion or Offset

Tables Icon

Table 4 Results of Fit without Dispersion but with Offset

Tables Icon

Table 5 Results of Fit with Dispersion

Tables Icon

Table 6 Fitted Values of γL for Different Mode Orders and Polarizations

Equations (10)

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

d ( n , a ; j ) = Min μ l i | ν E ( j ) ν T ( n , a ; μ , l , i ) | .
s ( n , a ; j ) = { 1 if d ( n , a ; j ) Δ 0 if d ( n , a ; j ) > Δ .
S ( n , a ) = j s ( n , a ; j ) ,
C ( n , a ) = 1 J j c ( n , a ; j ) ,
c ( n , a ; j ) = 1 1 + [ d ( n , a ; j ) / Δ ] 2 ,
n = n 0 + n 1 ( ν ν 0 ) ,
Δ T = ρ Le M K a d a d t ,
γ A = ( a / n ) α ( ν ) ,
I = C E ( ν ) γ M + γ L γ M + γ L + γ A ,
M ( x ) = { n l ( x ) n l ( x ) n j l ( n x ) j l ( n x ) for TE n l ( x ) n l ( x ) 1 n j l ( n x ) j l ( n x ) + 1 n 2 x for TM ,

Metrics