Abstract

The spectral behavior of 15.3-μm-diameter Rhodamine 6G in water solution droplets was studied. Microdroplet lasing is known to occur simultaneously at many discrete wavelengths, each corresponding to one of many possible spherical cavity resonances. We show that lasing takes place on several mode orders at once. Modes of a given order were found to form a bell-shaped spectral cluster of typically 4–6 resonance lines having consecutive principal mode numbers. Clusters of different mode orders appear somewhat displaced spectrally from one another, with lowest-order clusters shifted to the red. This multiplicity of lasing modes is accounted for by spatial hole-burning effects. The relative lasing intensities of the differing mode orders are explained by an output coupling theory that considers the gain enhancement that is due to cavity quantum electrodynamic effects. An upper limit of 108 for the Q of a nondegenerate cavity mode was estimated from the data.

© 1992 Optical Society of America

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  1. 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).
    [CrossRef] [PubMed]
  2. 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).
    [CrossRef]
  3. S. C. Hill and R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988), Chap. 1, pp. 3–61.
  4. 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]
  5. 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]
  6. 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, 486–489 (1986).
    [CrossRef] [PubMed]
  7. A. Biswas, H. Latifi, R. L. Armstrong, and R. G. Pinnick, “Time-resolved spectroscopy of laser emission from dye-doped droplets,” Opt. Lett. 14, 214–216 (1989).
    [CrossRef] [PubMed]
  8. 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]
  9. J. D. Eversole, H-B. Lin, A. L. Huston, 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]
  10. P. Chylek, J. Kiehl, and M. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
    [CrossRef]
  11. G. E. Walraven, “Raman spectral studies of water structure,” J. Chem. Phys. 40, 3249–3256 (1964); “Raman spectral studies of the effects of temperature on water and electrolyte solutions,” J. Chem. Phys. 44, 1546–1558 (1966).
    [CrossRef]
  12. P. Laures, “Variation of the 6326 Å gas laser output power with mirror transmission,” Phys. Lett. 10, 61–62 (1964).
    [CrossRef]
  13. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), p. 186.
  14. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  15. B. B. Snavely, “Continuous-wave dye lasers,” in Dye Lasers, 3rd ed., Vol. 1 of Topics in Applied Physics, F. P. Schafer, ed. (Springer-Verlag, Berlin, 1989), pp. 91–137.
    [CrossRef]
  16. H. M. Lai, P. T. Leung, and K. Young, “Electromagnetic decay into a narrow resonance in an optical cavity,” Phys. Rev. A 37, 1597–1606 (1988).
    [CrossRef] [PubMed]
  17. H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
    [CrossRef] [PubMed]
  18. A. J. Campillo, J. D. Eversole, and H-B. Lin, “Cavity-enhanced emission in microdroplets,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper FGG4; “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437 (1991).
    [PubMed]
  19. L. M. Folan, S. Arnold, and S. D. Druger, “Enhanced energy transfer within a microparticle,” Chem. Phys. Lett. 118, 322–327 (1985).
    [CrossRef]
  20. P. T. Leung and K. Young, “Theory of enhanced energy transfer in an aerosol particle,” J. Chem. Phys. 89, 2894–2899 (1988).
    [CrossRef]
  21. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  22. 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]
  23. D. S. Benincasa, P. W. Barber, J-Z. Zhang, W-F. Hsieh, and 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]
  24. C. L. Tang, H. Statz, and G. deMars, “Spectral output and spiking behavior of solid-state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
    [CrossRef]
  25. F. P. Schäfer, “Principles of dye laser operation,” in Dye Lasers, 3rd ed., Vol. 1 of Topics in Applied Physics, F. P. Schäfer, ed. (Springer-Verlag, Berlin, 1989), pp. 1–89.
  26. J. D. Eversole, H-B. Lin, and A. J. Campillo, “Cavity mode identification of fluorescence and lasing in dye-doped microdroplets,” Appl. Opt. (to be published).
  27. J.-Z. Zhang and R. K. Chang, “Shape distortion of a single water droplet by laser-induced electrostriction,” Opt. Lett. 13, 916–918 (1988).
    [CrossRef] [PubMed]
  28. H. M. Lai, P. T. Leung, K. L. Poon, and K. Young, “Electrostrictive distortion of a micrometer-sized droplet by a laser pulse,” J. Opt. Soc. Am. B 6, 2430–2437 (1989).
    [CrossRef]
  29. J.-Z. Zhang, D. H. Leach, and R. K. Chang, “Photon lifetime within a droplet: temporal determination of elastic and stimulated scattering,” Opt. Lett. 13, 270–272 (1988).
    [CrossRef] [PubMed]
  30. S. Arnold and L. M. Folan, “Energy transfer and the photon lifetime within an aerosol particle,” Opt. Lett. 14, 387–389 (1989).
    [CrossRef] [PubMed]
  31. H. M. Lai, P. T. Leung, and K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent droplets,” Phys. Rev. A 41, 5199–5204 (1990).
    [CrossRef] [PubMed]
  32. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
    [CrossRef] [PubMed]
  33. A. L. Huston, H-B. Lin, J. D. Eversole, and A. J. Campillo, “Nonlinear Mie scattering: electrostrictive coupling of light to doplet acoustic modes,” Opt. Lett. 15, 1176–1178 (1990).
    [CrossRef] [PubMed]

1990 (6)

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]

J. D. Eversole, H-B. Lin, A. L. Huston, 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]

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. M. Lai, P. T. Leung, and K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent droplets,” Phys. Rev. A 41, 5199–5204 (1990).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

A. L. Huston, H-B. Lin, J. D. Eversole, and A. J. Campillo, “Nonlinear Mie scattering: electrostrictive coupling of light to doplet acoustic modes,” Opt. Lett. 15, 1176–1178 (1990).
[CrossRef] [PubMed]

1989 (3)

1988 (5)

J.-Z. Zhang and R. K. Chang, “Shape distortion of a single water droplet by laser-induced electrostriction,” Opt. Lett. 13, 916–918 (1988).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, and K. Young, “Electromagnetic decay into a narrow resonance in an optical cavity,” Phys. Rev. A 37, 1597–1606 (1988).
[CrossRef] [PubMed]

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[CrossRef] [PubMed]

P. T. Leung and K. Young, “Theory of enhanced energy transfer in an aerosol particle,” J. Chem. Phys. 89, 2894–2899 (1988).
[CrossRef]

J.-Z. Zhang, D. H. Leach, and R. K. Chang, “Photon lifetime within a droplet: temporal determination of elastic and stimulated scattering,” Opt. Lett. 13, 270–272 (1988).
[CrossRef] [PubMed]

1987 (2)

1986 (3)

1985 (1)

L. M. Folan, S. Arnold, and S. D. Druger, “Enhanced energy transfer within a microparticle,” Chem. Phys. Lett. 118, 322–327 (1985).
[CrossRef]

1984 (1)

1978 (1)

P. Chylek, J. Kiehl, and M. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

1964 (2)

G. E. Walraven, “Raman spectral studies of water structure,” J. Chem. Phys. 40, 3249–3256 (1964); “Raman spectral studies of the effects of temperature on water and electrolyte solutions,” J. Chem. Phys. 44, 1546–1558 (1966).
[CrossRef]

P. Laures, “Variation of the 6326 Å gas laser output power with mirror transmission,” Phys. Lett. 10, 61–62 (1964).
[CrossRef]

1963 (1)

C. L. Tang, H. Statz, and G. deMars, “Spectral output and spiking behavior of solid-state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[CrossRef]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Armstrong, R. L.

Arnold, S.

S. Arnold and L. M. Folan, “Energy transfer and the photon lifetime within an aerosol particle,” Opt. Lett. 14, 387–389 (1989).
[CrossRef] [PubMed]

L. M. Folan, S. Arnold, and S. D. Druger, “Enhanced energy transfer within a microparticle,” Chem. Phys. Lett. 118, 322–327 (1985).
[CrossRef]

Barber, P. W.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[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 intensities of large cylindrical and spherical scatterers,” Appl. Opt. 26, 1348–1356 (1987).
[CrossRef] [PubMed]

Benincasa, D. S.

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).
[CrossRef]

S. C. Hill and R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988), Chap. 1, pp. 3–61.

Biswas, A.

Campillo, A. J.

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]

J. D. Eversole, H-B. Lin, A. L. Huston, 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]

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]

A. L. Huston, H-B. Lin, J. D. Eversole, and A. J. Campillo, “Nonlinear Mie scattering: electrostrictive coupling of light to doplet acoustic modes,” Opt. Lett. 15, 1176–1178 (1990).
[CrossRef] [PubMed]

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. D. Eversole, H-B. Lin, and A. J. Campillo, “Cavity mode identification of fluorescence and lasing in dye-doped microdroplets,” Appl. Opt. (to be published).

A. J. Campillo, J. D. Eversole, and H-B. Lin, “Cavity-enhanced emission in microdroplets,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper FGG4; “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437 (1991).
[PubMed]

Chang, R. K.

Chew, H.

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[CrossRef] [PubMed]

Ching, S. C.

Chylek, P.

P. Chylek, J. Kiehl, and M. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

deMars, G.

C. L. Tang, H. Statz, and G. deMars, “Spectral output and spiking behavior of solid-state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[CrossRef]

Druger, S. D.

L. M. Folan, S. Arnold, and S. D. Druger, “Enhanced energy transfer within a microparticle,” Chem. Phys. Lett. 118, 322–327 (1985).
[CrossRef]

Eversole, J. D.

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]

J. D. Eversole, H-B. Lin, A. L. Huston, 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]

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]

A. L. Huston, H-B. Lin, J. D. Eversole, and A. J. Campillo, “Nonlinear Mie scattering: electrostrictive coupling of light to doplet acoustic modes,” Opt. Lett. 15, 1176–1178 (1990).
[CrossRef] [PubMed]

J. D. Eversole, H-B. Lin, and A. J. Campillo, “Cavity mode identification of fluorescence and lasing in dye-doped microdroplets,” Appl. Opt. (to be published).

A. J. Campillo, J. D. Eversole, and H-B. Lin, “Cavity-enhanced emission in microdroplets,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper FGG4; “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437 (1991).
[PubMed]

Folan, L. M.

S. Arnold and L. M. Folan, “Energy transfer and the photon lifetime within an aerosol particle,” Opt. Lett. 14, 387–389 (1989).
[CrossRef] [PubMed]

L. M. Folan, S. Arnold, and S. D. Druger, “Enhanced energy transfer within a microparticle,” Chem. Phys. Lett. 118, 322–327 (1985).
[CrossRef]

Hill, S. C.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

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).
[CrossRef]

S. C. Hill and R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988), Chap. 1, pp. 3–61.

Hsieh, W-F.

Huston, A. L.

Justus, B. L.

Kiehl, J.

P. Chylek, J. Kiehl, and M. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

Ko, M.

P. Chylek, J. Kiehl, and M. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

Lai, H. M.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, and K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent droplets,” Phys. Rev. A 41, 5199–5204 (1990).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. L. Poon, and K. Young, “Electrostrictive distortion of a micrometer-sized droplet by a laser pulse,” J. Opt. Soc. Am. B 6, 2430–2437 (1989).
[CrossRef]

H. M. Lai, P. T. Leung, and K. Young, “Electromagnetic decay into a narrow resonance in an optical cavity,” Phys. Rev. A 37, 1597–1606 (1988).
[CrossRef] [PubMed]

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]

Latifi, H.

Laures, P.

P. Laures, “Variation of the 6326 Å gas laser output power with mirror transmission,” Phys. Lett. 10, 61–62 (1964).
[CrossRef]

Leach, D. H.

Leung, P. T.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, and K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent droplets,” Phys. Rev. A 41, 5199–5204 (1990).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. L. Poon, and K. Young, “Electrostrictive distortion of a micrometer-sized droplet by a laser pulse,” J. Opt. Soc. Am. B 6, 2430–2437 (1989).
[CrossRef]

H. M. Lai, P. T. Leung, and K. Young, “Electromagnetic decay into a narrow resonance in an optical cavity,” Phys. Rev. A 37, 1597–1606 (1988).
[CrossRef] [PubMed]

P. T. Leung and K. Young, “Theory of enhanced energy transfer in an aerosol particle,” J. Chem. Phys. 89, 2894–2899 (1988).
[CrossRef]

Lin, H-B.

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]

J. D. Eversole, H-B. Lin, A. L. Huston, 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]

A. L. Huston, H-B. Lin, J. D. Eversole, and A. J. Campillo, “Nonlinear Mie scattering: electrostrictive coupling of light to doplet acoustic modes,” Opt. Lett. 15, 1176–1178 (1990).
[CrossRef] [PubMed]

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]

A. J. Campillo, J. D. Eversole, and H-B. Lin, “Cavity-enhanced emission in microdroplets,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper FGG4; “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437 (1991).
[PubMed]

J. D. Eversole, H-B. Lin, and A. J. Campillo, “Cavity mode identification of fluorescence and lasing in dye-doped microdroplets,” Appl. Opt. (to be published).

Long, M. B.

Pinnick, R. G.

Poon, K. L.

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Qian, S.-X.

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, 486–489 (1986).
[CrossRef] [PubMed]

Schäfer, F. P.

F. P. Schäfer, “Principles of dye laser operation,” in Dye Lasers, 3rd ed., Vol. 1 of Topics in Applied Physics, F. P. Schäfer, ed. (Springer-Verlag, Berlin, 1989), pp. 1–89.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Snavely, B. B.

B. B. Snavely, “Continuous-wave dye lasers,” in Dye Lasers, 3rd ed., Vol. 1 of Topics in Applied Physics, F. P. Schafer, ed. (Springer-Verlag, Berlin, 1989), pp. 91–137.
[CrossRef]

Snow, J. B.

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, 486–489 (1986).
[CrossRef] [PubMed]

Statz, H.

C. L. Tang, H. Statz, and G. deMars, “Spectral output and spiking behavior of solid-state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[CrossRef]

Tang, C. L.

C. L. Tang, H. Statz, and G. deMars, “Spectral output and spiking behavior of solid-state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[CrossRef]

Tzeng, H-M.

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, 486–489 (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).
[CrossRef] [PubMed]

Wall, K. F.

Walraven, G. E.

G. E. Walraven, “Raman spectral studies of water structure,” J. Chem. Phys. 40, 3249–3256 (1964); “Raman spectral studies of the effects of temperature on water and electrolyte solutions,” J. Chem. Phys. 44, 1546–1558 (1966).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), p. 186.

Young, K.

H. M. Lai, P. T. Leung, and K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent droplets,” Phys. Rev. A 41, 5199–5204 (1990).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. L. Poon, and K. Young, “Electrostrictive distortion of a micrometer-sized droplet by a laser pulse,” J. Opt. Soc. Am. B 6, 2430–2437 (1989).
[CrossRef]

H. M. Lai, P. T. Leung, and K. Young, “Electromagnetic decay into a narrow resonance in an optical cavity,” Phys. Rev. A 37, 1597–1606 (1988).
[CrossRef] [PubMed]

P. T. Leung and K. Young, “Theory of enhanced energy transfer in an aerosol particle,” J. Chem. Phys. 89, 2894–2899 (1988).
[CrossRef]

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]

Zhang, J.-Z.

Zhang, J-Z.

Appl. Opt. (1)

Chem. Phys. Lett. (1)

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Figures (8)

Fig. 1
Fig. 1

0.5-nm-resolution spectrum of 15.3-μm-diameter Rhodamine 6G in water solution droplets pumped by a Q-switched 532-nm laser. An intensity dip between two principal mode clusters is evident.

Fig. 2
Fig. 2

0.1-nm-resolution spectrum of lasing droplets obtained from the same droplets as in Fig. 1. The higher resolution shows that the narrowest features have intensities comparable with those of the broader features. Alignment of mode combs as discussed in the text shows that at least five types of mode (therefore at least three orders) are lasing simultaneously.

Fig. 3
Fig. 3

Plot of normalized emitted and output power versus gain-normalized output coupling for various ratios of gain-normalized droplet loss. The dashed and solid curves are the normalized emitted power for the L/κg0 = 0.1 and L/κg0 = 0 cases, respectively. The dotted and two dotted–dashed curves are normalized output powers for the cases in which L/κg0 is 0.1, 10−2, and 10−3, respectively.

Fig. 4
Fig. 4

Cavity Q’s as a function of size parameter calculated from Lorenz–Mie theory. Here a lossless sphere was assumed with a = 6.82 μm and m = 1.363. Triangles, circles, and diamonds refer to second-, third-, and fourth-order modes, respectively. First- and second-order modes are assumed to be constrained to an upper value of 107 by perturbations in size and index of refraction. Solid triangles, circles, and diamonds correspond to TE modes, while open triangles, circles, and diamonds correspond to TM modes.

Fig. 5
Fig. 5

Illustration of the standing-wave spatial hole-burning effect for modes of the same order but having different mode numbers n [n = 6 (solid curve) and n = 7 (dashed curve)]. The plot shows hypothetical intensity versus azimuthal angular dependence.

Fig. 6
Fig. 6

Calculated plots of the radial intensity distribution of the first four order TE modes for a droplet having a radius of 7.34 μm and an index of refraction of 1.363. Note that the order number corresponds to the number of peaks in the radial field distribution. The higher-order modes peak progressively closer to the center of the droplet. This difference in radial extent accounts for spatial hole burning in the droplet owing to modes of differing l number.

Fig. 7
Fig. 7

Phenomenological picture illustrating the origin of the cluster effect resulting from spatial hole burning: (a), (c), and (e) correspond to first-order modes and (b), (d), and (f) correspond to second-order modes. (a) and (b) show spatial regions of highest intensity (shaded) for the respective mode orders. Plotted in (c) and (d) are the relative shapes of the laser gain G and the singlet absorption loss L. The vertical lines represent the relative magnitude of the cavity Q’s of MDR’s of each order. In (d) the cavity Q’s are approximately a factor of 100 less than in (c). This order can lase because the shaded region of (b) is not saturated by first-order modes. In (e) and (f) standing-wave hole burning permits several modes of each order to lase, forming a cluster. The wavelength of the first-order cluster occurs to the red of the second-order cluster because the requirement for mode visibility, Q/Qext ≈ 1, necessitates lasing at lower L’s for higher-Q modes. In (g) the clusters in (e) and (f) are combined on an expanded scale. Note the similarity between this plot and experimental plots shown in Figs. 1 and 2.

Fig. 8
Fig. 8

Emission spectra observed from Rhodamine 6G in ethanol droplets, reproduced from Ref. 18. The lower and upper emission curves were obtained under 300- and 400-W/cm2 excitation intensities, respectively. The positions of the spectral peaks corresponding to various lasing and fluorescing modes correlate well with the predicted wavelength placement of the various MDR’s. Upward (downward) arrows refer to TE (TM) modes. Four orders of modes (l = 1–4) were observed lasing simultaneously.

Equations (8)

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P e = P o ( L + 2 π m x / Q ext 2 π m x / Q ext ) ,
P o = 2 I s A l ( 2 π m x Q ext ) ( g 0 L + 2 π m x / Q ext - 1 ) ,
P e 2 I S 0 A g 0 = 1 - L κ g 0 - 2 π m x Q ext κ g 0 ,
P 0 2 I S 0 A g 0 = ( 2 π m x Q ext κ g 0 ) ( 1 - L / κ g 0 - 2 π m x / Q ext κ g 0 L / κ g 0 + 2 π m x / Q ext κ g 0 ) .
P o = 2 I S 0 A g 0 ( 1 Q ext ) ( 1 L / 2 π m x + 1 / Q ext ) .
P o = 2 I S 0 A g 0 ( Q / Q ext ) .
( P o ) MDR = 2 I S 0 A g 0 N c ( Q Q ext ) ,
I cav = 2 I S 0 g 0 Q / π m x N c .

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