Abstract

We present results of experiments to determine the spectral and angular dependence of nonlinear scattering by water microdroplets of radii ranging from 1 to 32 μm illuminated by ultrashort laser pulses. The main process observed is third-harmonic generation (THG). Moreover, in contrast with linear Mie scattering, the angular pattern of the THG is remarkably stable over the size range 8–32 μm.

[Optical Society of America ]

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References

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  1. J.-Z. Zhang , D. H. Leach , and R. K. Chang , Photon lifetime within a droplet: temporal determination of elastic and stimulated Raman scattering , Opt. Lett. OPLEDP 13 , 270 272 ( 1988
    [CrossRef] [PubMed]
  2. N. Dubreuil , J. C. Knight , D. K. Leventhal , V. Sandoghdar , J. Hare , and V. Lefe vre , Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres , Opt. Lett. OPLEDP 20 , 813 815 ( 1995
    [CrossRef] [PubMed]
  3. J. C. Knight , N. Dubreuil , V. Sandoghdar , J. Hare , V. Lefe vre-Seguin , J. M. Raimond , and S. Haroche , Mapping whispering-gallery modes in microspheres with a near-field probe , Opt. Lett. OPLEDP 20 , 1515 1517 ( 1995
    [CrossRef] [PubMed]
  4. D. Q. Chowdhury , S. C. Hill , and P. W. Barber , Time dependence of internal intensity of a dielectric sphere on and near resonance , J. Opt. Soc. Am. A JOAOD6 9 , 1364 1373 ( 1992
    [CrossRef]
  5. S.-X. Qian and R. K. Chang , Multiorder Stokes emission from micrometer-size droplets , Phys. Rev. Lett. PRLTAO 56 , 926 929 ( 1986
    [CrossRef] [PubMed]
  6. H.-B. Lin and A. J. Campillo , Cw nonlinear optics in droplet microcavities displaying enhanced gain , Phys. Rev. Lett. PRLTAO 73 , 2440 2443 ( 1994
    [CrossRef] [PubMed]
  7. J. B. Snow , S.-X. Quan , and R. K. Chang , Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances , Opt. Lett. OPLEDP 10 , 37 39 ( 1985
    [CrossRef] [PubMed]
  8. R. Thurn and W. Kiefer , Structural resonances observed in the Raman spectra of optically levitated liquid droplets , Appl. Opt. APOPAI 24 , 1515 1519 ( 1985
    [CrossRef] [PubMed]
  9. 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. OPLEDP 9 , 499 501 ( 1984
    [CrossRef] [PubMed]
  10. V. Sandoghdar , F. Treussart , J. Hare , V. Lefe vre-Seguin , J.-M. Raimond , and S. Haroche , Very low threshold whispering-gallery-mode microsphere laser , Phys. Rev. A PLRAAN 54 , R1777 R1780 ( 1996
    [CrossRef] [PubMed]
  11. W. P. Acker , D. H. Leach , and R. K. Chang , Third-order optical sum-frequency generation in micrometer-sized liquid droplets , Opt. Lett. OPLEDP 14 , 402 404 ( 1989
    [CrossRef] [PubMed]
  12. S. C. Hill , D. H. Leach , and R. K. Chang , Third-order optical sum-frequency generation in droplets: model with numerical third-harmonic generation , J. Opt. Soc. Am. B JOBPDE 10 , 16 33 ( 1993
    [CrossRef]
  13. D. H. Leach , R. K. Chang , W. P. Acker , and S. C. Hill , Third-order optical sum-frequency generation in droplets: experimental results , J. Opt. Soc. Am. B JOBPDE 10 , 34 45 ( 1993
    [CrossRef]
  14. J. Kasparian , B. Kra mer , J. P. Dewitz , S. Vajda , P. Rairoux , B. Vezin , V. Boutou , T. Leisner , W. Hu bner , J.-P. Wolf , L. Wo ste , and K. H. Bennemann , Angular dependence of third harmonic generation from microdroplets , Phys. Rev. Lett. PRLTAO 78 , 2952 2955 ( 1997
    [CrossRef]
  15. J. P. Dewitz , W. Hu bner , and K. H. Bennemann , Theory for nonlinear Mie-scattering from spherical metal clusters , Z. Phys. D ZDACE2 37 , 75 ( 1996
    [CrossRef]
  16. M. D. Duncan , R. Mahon , L. L. Tankersley , and J. Reintjes , Transient stimulated Raman amplification in hydrogen , J. Opt. Soc. Am. B JOBPDE 5 , 37 52 ( 1988
    [CrossRef]
  17. G. Hilfer and C. R. Menyuk , Stimulated Raman scattering in the transient limit , J. Opt. Soc. Am. B JOBPDE 7 , 739 749 ( 1990
    [CrossRef]
  18. M. Suzuki , K. Midorikawa , and H. Tashiro , Measurements of the temporal and spatial profiles of fully converted beams in stimulated Raman scattering , J. Opt. Soc. Am. B JOBPDE 8 , 1000 1002 ( 1991
    [CrossRef]
  19. L. Wo ste , C. Wedekind , H. Wille , P. Rairoux , B. Stein , S. Nikolov , C. Werner , S. Niedermeier , F. Ronneberger , H. Schillinger , and R. Sauerbrey , Femtosecond atmospheric lamp , Laser Optoelektron. LAOPD3 5 , 14 17 ( 1997

Hilfer, G

Niedermeier, S

L. Wo ste , C. Wedekind , H. Wille , P. Rairoux , B. Stein , S. Nikolov , C. Werner , S. Niedermeier , F. Ronneberger , H. Schillinger , and R. Sauerbrey , Femtosecond atmospheric lamp , Laser Optoelektron. LAOPD3 5 , 14 17 ( 1997

Quan, S.-X

Wedekind, C

L. Wo ste , C. Wedekind , H. Wille , P. Rairoux , B. Stein , S. Nikolov , C. Werner , S. Niedermeier , F. Ronneberger , H. Schillinger , and R. Sauerbrey , Femtosecond atmospheric lamp , Laser Optoelektron. LAOPD3 5 , 14 17 ( 1997

Wolf, J.-P

J. Kasparian , B. Kra mer , J. P. Dewitz , S. Vajda , P. Rairoux , B. Vezin , V. Boutou , T. Leisner , W. Hu bner , J.-P. Wolf , L. Wo ste , and K. H. Bennemann , Angular dependence of third harmonic generation from microdroplets , Phys. Rev. Lett. PRLTAO 78 , 2952 2955 ( 1997
[CrossRef]

Other (19)

D. Q. Chowdhury , S. C. Hill , and P. W. Barber , Time dependence of internal intensity of a dielectric sphere on and near resonance , J. Opt. Soc. Am. A JOAOD6 9 , 1364 1373 ( 1992
[CrossRef]

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

H.-B. Lin and A. J. Campillo , Cw nonlinear optics in droplet microcavities displaying enhanced gain , Phys. Rev. Lett. PRLTAO 73 , 2440 2443 ( 1994
[CrossRef] [PubMed]

V. Sandoghdar , F. Treussart , J. Hare , V. Lefe vre-Seguin , J.-M. Raimond , and S. Haroche , Very low threshold whispering-gallery-mode microsphere laser , Phys. Rev. A PLRAAN 54 , R1777 R1780 ( 1996
[CrossRef] [PubMed]

J. Kasparian , B. Kra mer , J. P. Dewitz , S. Vajda , P. Rairoux , B. Vezin , V. Boutou , T. Leisner , W. Hu bner , J.-P. Wolf , L. Wo ste , and K. H. Bennemann , Angular dependence of third harmonic generation from microdroplets , Phys. Rev. Lett. PRLTAO 78 , 2952 2955 ( 1997
[CrossRef]

J. P. Dewitz , W. Hu bner , and K. H. Bennemann , Theory for nonlinear Mie-scattering from spherical metal clusters , Z. Phys. D ZDACE2 37 , 75 ( 1996
[CrossRef]

L. Wo ste , C. Wedekind , H. Wille , P. Rairoux , B. Stein , S. Nikolov , C. Werner , S. Niedermeier , F. Ronneberger , H. Schillinger , and R. Sauerbrey , Femtosecond atmospheric lamp , Laser Optoelektron. LAOPD3 5 , 14 17 ( 1997

M. D. Duncan , R. Mahon , L. L. Tankersley , and J. Reintjes , Transient stimulated Raman amplification in hydrogen , J. Opt. Soc. Am. B JOBPDE 5 , 37 52 ( 1988
[CrossRef]

G. Hilfer and C. R. Menyuk , Stimulated Raman scattering in the transient limit , J. Opt. Soc. Am. B JOBPDE 7 , 739 749 ( 1990
[CrossRef]

M. Suzuki , K. Midorikawa , and H. Tashiro , Measurements of the temporal and spatial profiles of fully converted beams in stimulated Raman scattering , J. Opt. Soc. Am. B JOBPDE 8 , 1000 1002 ( 1991
[CrossRef]

S. C. Hill , D. H. Leach , and R. K. Chang , Third-order optical sum-frequency generation in droplets: model with numerical third-harmonic generation , J. Opt. Soc. Am. B JOBPDE 10 , 16 33 ( 1993
[CrossRef]

D. H. Leach , R. K. Chang , W. P. Acker , and S. C. Hill , Third-order optical sum-frequency generation in droplets: experimental results , J. Opt. Soc. Am. B JOBPDE 10 , 34 45 ( 1993
[CrossRef]

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. OPLEDP 9 , 499 501 ( 1984
[CrossRef] [PubMed]

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

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

W. P. Acker , D. H. Leach , and R. K. Chang , Third-order optical sum-frequency generation in micrometer-sized liquid droplets , Opt. Lett. OPLEDP 14 , 402 404 ( 1989
[CrossRef] [PubMed]

R. Thurn and W. Kiefer , Structural resonances observed in the Raman spectra of optically levitated liquid droplets , Appl. Opt. APOPAI 24 , 1515 1519 ( 1985
[CrossRef] [PubMed]

N. Dubreuil , J. C. Knight , D. K. Leventhal , V. Sandoghdar , J. Hare , and V. Lefe vre , Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres , Opt. Lett. OPLEDP 20 , 813 815 ( 1995
[CrossRef] [PubMed]

J. C. Knight , N. Dubreuil , V. Sandoghdar , J. Hare , V. Lefe vre-Seguin , J. M. Raimond , and S. Haroche , Mapping whispering-gallery modes in microspheres with a near-field probe , Opt. Lett. OPLEDP 20 , 1515 1517 ( 1995
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for nonlinear scattering measurements of microdroplets: z, polarization direction of the laser; ϕ, angle between the scattering plane and the yz plane; θ, scattering (polar) angle toward the xz plane. PMT, photomultiplier tube.

Fig. 2
Fig. 2

Wavelength dependence of the intensity emitted at 32° by a water droplet with a radius of 25 μm (ka194). The incident laser power is 1.7×1013 W cm-2, and the captured solid angle is 1.8×10-2 sr. Inset, third-harmonic peak at lower laser fluence (1013 W cm-2).

Fig. 3
Fig. 3

Angular distribution of the THG from water microdroplets with radius a10.5 μm (ka81) in both azimuthal planes (ϕ=0 and ϕ=90°) with the same scale.

Fig. 4
Fig. 4

Comparison of the standard Mie pattern at the wavelength corresponding to the THG and nonlinear Mie computations with the experimental results for water microdroplets with radius a10.5 μm (ka81).

Fig. 5
Fig. 5

Angular pattern of the THG from water microdroplets with radii ranging from 9.4 to 32 μm (ka72250) in the ϕ=0 plane in the near-forward direction.

Fig. 6
Fig. 6

Angular pattern of the THG from water microdroplets with radii ranging from 8.1 to 26 μm (ka63200) in the ϕ=90° plane in the near-backward direction.

Fig. 7
Fig. 7

Angular pattern of the THG from a cloud of water microdroplets with a radius distribution centered at a1 μm (ka7.8) in the near-forward direction.

Equations (2)

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dPTHGdΩ=σ(3)Ip3,
Δν=1λ n2 dIdt,

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