Abstract

We consider some peculiarities of the evolution of processes of stimulated scattering in liquid transparent particles in the presence of ponderomotive action of a light field. We observed the occurrence of sharp deformations in the Descartes ring zone, which exceeds by more than 1 order of magnitude the deformations of the remaining particle surface. Investigation of the dynamics of the evolution of droplet deformations has made it possible to consider these deformations as the main cause of suppression of stimulated scattering indicated in the experiments. An analytical expression was derived to evaluate the decrease of the Q factor of droplet quasi-normal eigenmodes caused by perturbation of the particle shape from the spherical. Our study revealed that the larger the Q factor of the droplet eigenmodes, the greater the influence of surface deformation.

© 2000 Optical Society of America

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References

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  1. J.-Z. Zhang, D. H. Leach, R. K. Chang, “Photon lifetime within a droplet: temporal determination of elastic and stimulated Raman scattering,” Opt. Lett. 13, 270–272 (1988).
    [CrossRef] [PubMed]
  2. A. Biswas, R. L. Armstrong, R. G. Pinnick, “Stimulated Raman scattering threshold behavior of binary mixture micrometer-sized droplets,” Opt. Lett. 15, 1191–1193 (1990).
    [CrossRef] [PubMed]
  3. J.-G. Xie, T. E. Ruekgauer, R. L. Armstrong, R. G. Pinnick, “Suppression of stimulated Raman scattering from microdroplets by seeding with nanometer-sized latex particles,” Opt. Lett. 18, 340–342 (1993).
    [CrossRef] [PubMed]
  4. J.-G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, “Random occurrence of stimulated Raman scattering emission from liquid water microdroplets,” Appl. Opt. 33, 368–372 (1994).
    [CrossRef] [PubMed]
  5. J.-Z. Zhang, R. K. Chang, “Generation and suppression of stimulated Brillouin scattering in single liquid droplets,” J. Opt. Soc. Am. B 6, 151–153 (1989).
    [CrossRef]
  6. J.-Z. Zhang, G. Chen, 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]
  7. R. L. Armstrong, J.-G. Xie, T. E. Ruekgauer, R. G. Pinnick, “Energy-transfer-assisted lasing from microdroplets seeded with fluorescent sol,” Opt. Lett. 17, 943–945 (1992).
    [CrossRef] [PubMed]
  8. G. Chen, D. Q. Chowdhury, R. K. Chang, W.-F. Hsieh, “Laser-induced radiation leakage from microdroplets,” J. Opt. Soc. Am. B 10, 620–632 (1993).
    [CrossRef]
  9. J. B. Snow, S.-X. Qian, R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985).
    [CrossRef] [PubMed]
  10. G. Schweiger, “Observation of input and output structural resonances in the Raman spectrum of a single spheroidal dielectric microparticles,” Opt. Lett. 15, 156–158 (1990).
    [CrossRef] [PubMed]
  11. S.-X. Qian, R. K. Chang, “Multiorder Stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
    [CrossRef] [PubMed]
  12. W.-F. Hsieh, J.-Z. Zhang, R. K. Chang, “Time dependence of multiorder stimulated Raman scattering from single droplets,” Opt. Lett. 13, 497–499 (1988).
    [CrossRef] [PubMed]
  13. J.-Z. Zhang, D. H. Leach, R. K. Chang, “Photon lifetime within a droplet: temporal determination of elastic and stimulated Raman scattering,” Opt. Lett. 13, 270–272 (1988).
    [CrossRef] [PubMed]
  14. R. G. Pinnick, A. Biswas, P. Chylek, R. L. Armstrong, H. Latifi, E. Creegan, V. Srivastava, M. Jarzembski, “Stimulated Raman scattering in micrometer-sized droplets: time-resolved measurements,” Opt. Lett. 13, 494–496 (1988).
    [CrossRef] [PubMed]
  15. R. G. Pinnick, A. Biswas, J. Pendleton, R. L. Armstrong, “Aerosol-induced laser breakdown thresholds: effect of resonant particles,” Appl. Opt. 31, 311–317 (1992).
    [CrossRef] [PubMed]
  16. C. C. Lam, P. T. Leung, K. Young, “Explicit asymptotic formulas for the position, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1591 (1992).
    [CrossRef]
  17. M. A. Jarzembski, V. Srivastava, “Electromagnetic field enhancement in small liquid droplets using geometric optics,” Appl. Opt. 28, 4962–4965 (1989).
    [CrossRef] [PubMed]
  18. V. Srivastava, M. A. Jarzembski, “Laser-induced stimulated Raman scattering in the forward direction of a droplet: comparison of Mie theory with geometrical optics,” Opt. Lett. 16, 126–128 (1991).
    [CrossRef] [PubMed]
  19. J. G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, “Observations of Descartes ring stimulated Raman scattering in micrometer-sized water droplets,” Opt. Lett. 16, 1310–1312 (1991).
    [CrossRef] [PubMed]
  20. J. G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, J. D. Pendleton, “Physical basis for Descartes ring scattering in laser-irradiated microdroplets,” Opt. Lett. 16, 1817–1819 (1991).
    [CrossRef] [PubMed]
  21. J. M. Hartings, X. Pu, J. L. Cheung, R. K. Chang, “Laser-induced distortion for increased input coupling of light to droplet-cavity modes,” J. Opt. Soc. Am. B 14, 2842–2849 (1997).
    [CrossRef]
  22. L. A. Vainshtein, Open Resonators and Open Waveguides (Soviet Radio, Moscow, 1966).
  23. K. S. Shifrin, Light Scattering in Turbid Medium (Gittl, Moscow, 1951).
  24. L. D. Landau, E. M. Lifshits, Electrodynamics of Continuous Media (Gostekhizdat, Moscow, 1957).
  25. L. D. Landau, E. M. Lifshits, Hydrodynamics (Nauka, Moscow, 1988).
  26. A. A. Zemlyanov, “Stability of small deformations of transparent droplet in powerful light field,” Quantum Electron. 1, 2085–2088 (1974).
  27. V. E. Zuev, A. A. Zemlyanov, Yu. D. Kopytin, A. V. Kuzikovskii, High-Power Laser Radiation in Atmospheric Aerosols (Reidel, Dordrecht, The Netherlands, 1984).
  28. Yu. E. Geints, A. A. Zemlyanov, “Surface effect of the ponderomotive action of laser emission on liquid droplets,” Atmos. Oceanic Opt. 9, 1345–1352 (1996).
  29. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5192 (1990).
    [CrossRef] [PubMed]
  30. Yu. E. Geints, A. A. Zemlyanov, A. V. Pal’chikov, “Influence of a drop surface deformation on the process stimulated Raman scattering,” Atmos. Oceanic Opt. 10, 1553–1560 (1997).

1997

Yu. E. Geints, A. A. Zemlyanov, A. V. Pal’chikov, “Influence of a drop surface deformation on the process stimulated Raman scattering,” Atmos. Oceanic Opt. 10, 1553–1560 (1997).

J. M. Hartings, X. Pu, J. L. Cheung, R. K. Chang, “Laser-induced distortion for increased input coupling of light to droplet-cavity modes,” J. Opt. Soc. Am. B 14, 2842–2849 (1997).
[CrossRef]

1996

Yu. E. Geints, A. A. Zemlyanov, “Surface effect of the ponderomotive action of laser emission on liquid droplets,” Atmos. Oceanic Opt. 9, 1345–1352 (1996).

1994

1993

1992

1991

1990

1989

1988

1986

S.-X. Qian, R. K. Chang, “Multiorder Stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
[CrossRef] [PubMed]

1985

1974

A. A. Zemlyanov, “Stability of small deformations of transparent droplet in powerful light field,” Quantum Electron. 1, 2085–2088 (1974).

Armstrong, R. L.

J.-G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, “Random occurrence of stimulated Raman scattering emission from liquid water microdroplets,” Appl. Opt. 33, 368–372 (1994).
[CrossRef] [PubMed]

J.-G. Xie, T. E. Ruekgauer, R. L. Armstrong, R. G. Pinnick, “Suppression of stimulated Raman scattering from microdroplets by seeding with nanometer-sized latex particles,” Opt. Lett. 18, 340–342 (1993).
[CrossRef] [PubMed]

R. L. Armstrong, J.-G. Xie, T. E. Ruekgauer, R. G. Pinnick, “Energy-transfer-assisted lasing from microdroplets seeded with fluorescent sol,” Opt. Lett. 17, 943–945 (1992).
[CrossRef] [PubMed]

R. G. Pinnick, A. Biswas, J. Pendleton, R. L. Armstrong, “Aerosol-induced laser breakdown thresholds: effect of resonant particles,” Appl. Opt. 31, 311–317 (1992).
[CrossRef] [PubMed]

J. G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, “Observations of Descartes ring stimulated Raman scattering in micrometer-sized water droplets,” Opt. Lett. 16, 1310–1312 (1991).
[CrossRef] [PubMed]

J. G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, J. D. Pendleton, “Physical basis for Descartes ring scattering in laser-irradiated microdroplets,” Opt. Lett. 16, 1817–1819 (1991).
[CrossRef] [PubMed]

A. Biswas, R. L. Armstrong, R. G. Pinnick, “Stimulated Raman scattering threshold behavior of binary mixture micrometer-sized droplets,” Opt. Lett. 15, 1191–1193 (1990).
[CrossRef] [PubMed]

R. G. Pinnick, A. Biswas, P. Chylek, R. L. Armstrong, H. Latifi, E. Creegan, V. Srivastava, M. Jarzembski, “Stimulated Raman scattering in micrometer-sized droplets: time-resolved measurements,” Opt. Lett. 13, 494–496 (1988).
[CrossRef] [PubMed]

Barber, P. W.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5192 (1990).
[CrossRef] [PubMed]

Biswas, A.

Chang, R. K.

J. M. Hartings, X. Pu, J. L. Cheung, R. K. Chang, “Laser-induced distortion for increased input coupling of light to droplet-cavity modes,” J. Opt. Soc. Am. B 14, 2842–2849 (1997).
[CrossRef]

G. Chen, D. Q. Chowdhury, R. K. Chang, W.-F. Hsieh, “Laser-induced radiation leakage from microdroplets,” J. Opt. Soc. Am. B 10, 620–632 (1993).
[CrossRef]

J.-Z. Zhang, G. Chen, 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]

J.-Z. Zhang, R. K. Chang, “Generation and suppression of stimulated Brillouin scattering in single liquid droplets,” J. Opt. Soc. Am. B 6, 151–153 (1989).
[CrossRef]

W.-F. Hsieh, J.-Z. Zhang, R. K. Chang, “Time dependence of multiorder stimulated Raman scattering from single droplets,” Opt. Lett. 13, 497–499 (1988).
[CrossRef] [PubMed]

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

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

S.-X. Qian, R. K. Chang, “Multiorder Stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
[CrossRef] [PubMed]

J. B. Snow, S.-X. Qian, R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985).
[CrossRef] [PubMed]

Chen, G.

Cheung, J. L.

Chowdhury, D. Q.

Chylek, P.

Creegan, E.

Geints, Yu. E.

Yu. E. Geints, A. A. Zemlyanov, A. V. Pal’chikov, “Influence of a drop surface deformation on the process stimulated Raman scattering,” Atmos. Oceanic Opt. 10, 1553–1560 (1997).

Yu. E. Geints, A. A. Zemlyanov, “Surface effect of the ponderomotive action of laser emission on liquid droplets,” Atmos. Oceanic Opt. 9, 1345–1352 (1996).

Gu, J.

Hartings, J. M.

Hill, S. C.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5192 (1990).
[CrossRef] [PubMed]

Hsieh, W.-F.

Jarzembski, M.

Jarzembski, M. A.

Kopytin, Yu. D.

V. E. Zuev, A. A. Zemlyanov, Yu. D. Kopytin, A. V. Kuzikovskii, High-Power Laser Radiation in Atmospheric Aerosols (Reidel, Dordrecht, The Netherlands, 1984).

Kuzikovskii, A. V.

V. E. Zuev, A. A. Zemlyanov, Yu. D. Kopytin, A. V. Kuzikovskii, High-Power Laser Radiation in Atmospheric Aerosols (Reidel, Dordrecht, The Netherlands, 1984).

Lai, H. M.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5192 (1990).
[CrossRef] [PubMed]

Lam, C. C.

Landau, L. D.

L. D. Landau, E. M. Lifshits, Hydrodynamics (Nauka, Moscow, 1988).

L. D. Landau, E. M. Lifshits, Electrodynamics of Continuous Media (Gostekhizdat, Moscow, 1957).

Latifi, H.

Leach, D. H.

Leung, P. T.

C. C. Lam, P. T. Leung, K. Young, “Explicit asymptotic formulas for the position, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1591 (1992).
[CrossRef]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5192 (1990).
[CrossRef] [PubMed]

Lifshits, E. M.

L. D. Landau, E. M. Lifshits, Electrodynamics of Continuous Media (Gostekhizdat, Moscow, 1957).

L. D. Landau, E. M. Lifshits, Hydrodynamics (Nauka, Moscow, 1988).

Pal’chikov, A. V.

Yu. E. Geints, A. A. Zemlyanov, A. V. Pal’chikov, “Influence of a drop surface deformation on the process stimulated Raman scattering,” Atmos. Oceanic Opt. 10, 1553–1560 (1997).

Pendleton, J.

Pendleton, J. D.

Pinnick, R. G.

J.-G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, “Random occurrence of stimulated Raman scattering emission from liquid water microdroplets,” Appl. Opt. 33, 368–372 (1994).
[CrossRef] [PubMed]

J.-G. Xie, T. E. Ruekgauer, R. L. Armstrong, R. G. Pinnick, “Suppression of stimulated Raman scattering from microdroplets by seeding with nanometer-sized latex particles,” Opt. Lett. 18, 340–342 (1993).
[CrossRef] [PubMed]

R. L. Armstrong, J.-G. Xie, T. E. Ruekgauer, R. G. Pinnick, “Energy-transfer-assisted lasing from microdroplets seeded with fluorescent sol,” Opt. Lett. 17, 943–945 (1992).
[CrossRef] [PubMed]

R. G. Pinnick, A. Biswas, J. Pendleton, R. L. Armstrong, “Aerosol-induced laser breakdown thresholds: effect of resonant particles,” Appl. Opt. 31, 311–317 (1992).
[CrossRef] [PubMed]

J. G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, J. D. Pendleton, “Physical basis for Descartes ring scattering in laser-irradiated microdroplets,” Opt. Lett. 16, 1817–1819 (1991).
[CrossRef] [PubMed]

J. G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, “Observations of Descartes ring stimulated Raman scattering in micrometer-sized water droplets,” Opt. Lett. 16, 1310–1312 (1991).
[CrossRef] [PubMed]

A. Biswas, R. L. Armstrong, R. G. Pinnick, “Stimulated Raman scattering threshold behavior of binary mixture micrometer-sized droplets,” Opt. Lett. 15, 1191–1193 (1990).
[CrossRef] [PubMed]

R. G. Pinnick, A. Biswas, P. Chylek, R. L. Armstrong, H. Latifi, E. Creegan, V. Srivastava, M. Jarzembski, “Stimulated Raman scattering in micrometer-sized droplets: time-resolved measurements,” Opt. Lett. 13, 494–496 (1988).
[CrossRef] [PubMed]

Pu, X.

Qian, S.-X.

Ruekgauer, T. E.

Schweiger, G.

Shifrin, K. S.

K. S. Shifrin, Light Scattering in Turbid Medium (Gittl, Moscow, 1951).

Snow, J. B.

Srivastava, V.

Vainshtein, L. A.

L. A. Vainshtein, Open Resonators and Open Waveguides (Soviet Radio, Moscow, 1966).

Xie, J. G.

Xie, J.-G.

Young, K.

C. C. Lam, P. T. Leung, K. Young, “Explicit asymptotic formulas for the position, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1591 (1992).
[CrossRef]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5192 (1990).
[CrossRef] [PubMed]

Zemlyanov, A. A.

Yu. E. Geints, A. A. Zemlyanov, A. V. Pal’chikov, “Influence of a drop surface deformation on the process stimulated Raman scattering,” Atmos. Oceanic Opt. 10, 1553–1560 (1997).

Yu. E. Geints, A. A. Zemlyanov, “Surface effect of the ponderomotive action of laser emission on liquid droplets,” Atmos. Oceanic Opt. 9, 1345–1352 (1996).

A. A. Zemlyanov, “Stability of small deformations of transparent droplet in powerful light field,” Quantum Electron. 1, 2085–2088 (1974).

V. E. Zuev, A. A. Zemlyanov, Yu. D. Kopytin, A. V. Kuzikovskii, High-Power Laser Radiation in Atmospheric Aerosols (Reidel, Dordrecht, The Netherlands, 1984).

Zhang, J.-Z.

Zuev, V. E.

V. E. Zuev, A. A. Zemlyanov, Yu. D. Kopytin, A. V. Kuzikovskii, High-Power Laser Radiation in Atmospheric Aerosols (Reidel, Dordrecht, The Netherlands, 1984).

Appl. Opt.

Atmos. Oceanic Opt.

Yu. E. Geints, A. A. Zemlyanov, “Surface effect of the ponderomotive action of laser emission on liquid droplets,” Atmos. Oceanic Opt. 9, 1345–1352 (1996).

Yu. E. Geints, A. A. Zemlyanov, A. V. Pal’chikov, “Influence of a drop surface deformation on the process stimulated Raman scattering,” Atmos. Oceanic Opt. 10, 1553–1560 (1997).

J. Opt. Soc. Am. B

Opt. Lett.

R. G. Pinnick, A. Biswas, P. Chylek, R. L. Armstrong, H. Latifi, E. Creegan, V. Srivastava, M. Jarzembski, “Stimulated Raman scattering in micrometer-sized droplets: time-resolved measurements,” Opt. Lett. 13, 494–496 (1988).
[CrossRef] [PubMed]

J. B. Snow, S.-X. Qian, R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985).
[CrossRef] [PubMed]

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

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

W.-F. Hsieh, J.-Z. Zhang, R. K. Chang, “Time dependence of multiorder stimulated Raman scattering from single droplets,” Opt. Lett. 13, 497–499 (1988).
[CrossRef] [PubMed]

G. Schweiger, “Observation of input and output structural resonances in the Raman spectrum of a single spheroidal dielectric microparticles,” Opt. Lett. 15, 156–158 (1990).
[CrossRef] [PubMed]

A. Biswas, R. L. Armstrong, R. G. Pinnick, “Stimulated Raman scattering threshold behavior of binary mixture micrometer-sized droplets,” Opt. Lett. 15, 1191–1193 (1990).
[CrossRef] [PubMed]

V. Srivastava, M. A. Jarzembski, “Laser-induced stimulated Raman scattering in the forward direction of a droplet: comparison of Mie theory with geometrical optics,” Opt. Lett. 16, 126–128 (1991).
[CrossRef] [PubMed]

J. G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, “Observations of Descartes ring stimulated Raman scattering in micrometer-sized water droplets,” Opt. Lett. 16, 1310–1312 (1991).
[CrossRef] [PubMed]

J. G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, J. D. Pendleton, “Physical basis for Descartes ring scattering in laser-irradiated microdroplets,” Opt. Lett. 16, 1817–1819 (1991).
[CrossRef] [PubMed]

R. L. Armstrong, J.-G. Xie, T. E. Ruekgauer, R. G. Pinnick, “Energy-transfer-assisted lasing from microdroplets seeded with fluorescent sol,” Opt. Lett. 17, 943–945 (1992).
[CrossRef] [PubMed]

J.-G. Xie, T. E. Ruekgauer, R. L. Armstrong, R. G. Pinnick, “Suppression of stimulated Raman scattering from microdroplets by seeding with nanometer-sized latex particles,” Opt. Lett. 18, 340–342 (1993).
[CrossRef] [PubMed]

Phys. Rev. A

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5192 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett.

S.-X. Qian, R. K. Chang, “Multiorder Stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
[CrossRef] [PubMed]

Quantum Electron.

A. A. Zemlyanov, “Stability of small deformations of transparent droplet in powerful light field,” Quantum Electron. 1, 2085–2088 (1974).

Other

V. E. Zuev, A. A. Zemlyanov, Yu. D. Kopytin, A. V. Kuzikovskii, High-Power Laser Radiation in Atmospheric Aerosols (Reidel, Dordrecht, The Netherlands, 1984).

L. A. Vainshtein, Open Resonators and Open Waveguides (Soviet Radio, Moscow, 1966).

K. S. Shifrin, Light Scattering in Turbid Medium (Gittl, Moscow, 1951).

L. D. Landau, E. M. Lifshits, Electrodynamics of Continuous Media (Gostekhizdat, Moscow, 1957).

L. D. Landau, E. M. Lifshits, Hydrodynamics (Nauka, Moscow, 1988).

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Figures (10)

Fig. 1
Fig. 1

Geometric scheme of a plane wave incident on a spherical droplet. Positions of beams with different impact parameters φ i are shown. Angular positions of secondary refractive point θ i are defined by Snell’s law.

Fig. 2
Fig. 2

Dependence of angular positions of beam secondary refractive point θ i on impact parameter φ i for different droplet matters indices of refraction n in . Points depict the critical angle θ i Desc, which defines the DR size on the particle shadow hemisphere.

Fig. 3
Fig. 3

Dependence of relative surface intensity B on polar angle θ in spherical droplets made of different liquids (water, benzene, CS2). Angle θ = 180° corresponds to the center of the droplet shadow hemisphere.

Fig. 4
Fig. 4

Calculated shape of droplets (water, CS2) distorted by ponderomotive deformations at a fixed time of t = 13.2 ns. The scale of the deformations is magnified by factor of 100.

Fig. 5
Fig. 5

Dependence of ponderomotive deformation amplitude of droplets with radius a 0 = 40 µm on the polar angle θ for (a) benzene and (b) water.

Fig. 6
Fig. 6

Time dependence of SRS initiation and disappearance on relative peak intensity in the pumping pulse (expressed as a percentage of SRS threshold intensity I 0 = 30 GW/cm2).21 Open circles denote the time when the SRS signal appears, the filled squares indicate when the SRS signal disappears. The curves delimit the time interval within which pumping pulses can generate SRS in droplets.

Fig. 7
Fig. 7

Relative ponderomotive deformation amplitude of ethanol droplets (a 0 = 40 µm) as a function of relative peak intensity in the pumping pulse. Calculations were performed based on the initiation and disappearance times of SRS shown in Fig. 6. The two curves limit the interval of deformation magnitude where the SRS generation takes place.

Fig. 8
Fig. 8

Schematic of a microdroplet that shows the spatial intensity distribution of three different m eigenmodes of the same n and l.

Fig. 9
Fig. 9

Dependence of the quality factor Q D of the perturbed sphere on quality factor Q 0 of the unperturbed sphere for different values of surface deformation amplitude ξ A .

Fig. 10
Fig. 10

Estimated values of Q D for the SRS process in a 40-µm ethanol droplet derived from Eq. (22) and from the data in Fig. 7. The dashed line represents the upper limit of Q caused by thermocapillary droplet vibrations.

Equations (28)

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

rot rot Er, t+εac22 Er, tt2+4πσc2Er, tt=-4πc22t2PNr, t,
2PNr, tt2+2T2PNr, tt+ω02PNr, t=2N0ωvib|μ12|3 ΔNEr, t, ΔNt+ΔN-ΔNeT1=2N0ωvibPNr, ttEr, t; PNr, t=αNEr, t,
Er, t=n AntEnr,
d2Antdt2+ωnQnabdAntdt+ωn21-i2Qnr2Ant=-4πεaVnEnr2PNr, tt2dr,
θi=2 arcsinn1nasin φi-φi,
θi*=2 arcsinn1nasin φi*-φi*,
φi*=arctan4n12-na2na2-n121/2.
vt+vv=vΔv-1/ρp-fE, div v=0,
fE=18π ρεaρT E2.
dFdt=Ft+vF=0,
p-ρ8πεaρTE2-p1-α1R1+1R2+fni0=ηvixk+vkxink0.
f=εa-18πεa-1En02+E2
tVρv22dV=-Sρvv22+pρ-vρdS-V σikvixkdV-VfEvdV.
lb=a0Re-1/2,
v=Φ,
ξθ, φ, t=0t Φdt,
tSρΦv2dS+S2αa0+p1v dS+α SL2-2a02 ξvdS+η/2 S v2dS=S fvdS,
L=-ir×=-iθ 1sin θθ-φ φ
L2=1sin θθsin θ θ+1sin2 θ2φ2; ξ=|ξ|.
Φr, θ, φ, t=ln Φlntra0l Ylnθ, φ,
d2ξldt2+2tldξldt+Ωl2ξl=lflta0ρ,
flt=0π ft, θYl0*θsin θ dθ;
tl=a022v2l+1l-1
Ωl=ll-1l+2αρa031/2
δLξ¯m a002π F1ϑdϑ,
δx=x-x0=x0ξ¯mqnm,
QDx=Q01+x-x02/Δx2,
QDx=Q01+qnmξ¯mQ02.

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