Abstract

A wave optical calculation is made of the distortion of a micrometer-sized water droplet illuminated by a short laser pulse (duration, 0.4 µs). First we find electromagnetic surface forces, assuming that the surface is at rest; thereafter we find the distortion by using the linearized Navier–Stokes equation. We illustrate the motion as a function of time, up to 22 µs after passage of the pulse. This study generalizes the earlier one of Lai et al. [J. Opt. Soc. Am. B 6, 2430 (1989)] to the case of linear polarization and is in reasonable agreement with the experiment of Zhang and Chang [Opt. Lett. 13, 916 (1988)].

© 1999 Optical Society of America

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References

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  1. A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971); “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).
    [CrossRef]
  2. A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
    [CrossRef] [PubMed]
  3. G. Roosen, “La lévitation optique de sphères,” Can. J. Phys. 57, 1260–1279 (1979).
    [CrossRef]
  4. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
    [CrossRef] [PubMed]
  5. R. Gussgard, T. Lindmo, and I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. B 9, 1922–1930 (1992).
    [CrossRef]
  6. W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
    [CrossRef] [PubMed]
  7. K. F. Ren, G. Grehan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
    [CrossRef] [PubMed]
  8. A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
    [CrossRef] [PubMed]
  9. R. Pobre and C. Saloma, “Single Gaussian beam interaction with a Kerr microsphere: characteristics of the radiation force,” Appl. Opt. 36, 3515–3520 (1997).
    [CrossRef] [PubMed]
  10. R. Omori, T. Kobayashi, and A. Suzuki, “Observation of single-beam gradient-force optical trap for dielectric particles in air,” Opt. Lett. 22, 816–818 (1997).
    [CrossRef] [PubMed]
  11. K. T. Gahagan and G. A. Swartzlander, “Trapping of low-index microparticles in an optical vortex,” J. Opt. Soc. Am. B 15, 524–534 (1998).
    [CrossRef]
  12. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987); “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989).
    [CrossRef] [PubMed]
  13. A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
    [CrossRef]
  14. K. Svoboda and S. M. Block, “Biological application of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
    [CrossRef]
  15. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
    [CrossRef] [PubMed]
  16. S. Kawata and T. Sugiura, “Movement of micrometer-sized particles in the evanescent field of a laser beam,” Opt. Lett. 17, 772–774 (1992).
    [CrossRef] [PubMed]
  17. S. Chang, J. H. Jo, and S. S. Lee, “Theoretical calculations of optical force exerted on a dielectric sphere in the evanescent field generated with a totally-reflected focused gaussian beam,” Opt. Commun. 108, 133–143 (1994).
    [CrossRef]
  18. E. Almaas and I. Brevik, “Radiation forces on a micrometer-sized sphere in an evanescent field,” J. Opt. Soc. Am. B 12, 2429–2438 (1995).
    [CrossRef]
  19. J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
    [CrossRef]
  20. J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
    [CrossRef]
  21. Ø. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108–130 (1996).
    [CrossRef]
  22. 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]
  23. K. L. Poon, “Laser pulse induced electrostrictive distortion of liquid micro-droplet,” M. Phil. thesis (Chinese University of Hong Kong, Hong Kong, 1990), pp. 1–90.
  24. 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]
  25. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).
  26. I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133–201 (1979).
    [CrossRef]
  27. A. Ashkin and J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30, 139–142 (1973).
    [CrossRef]
  28. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
  29. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  30. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1981), p. 476.
  31. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1959).
  32. Yu. S. Barash and V. L. Ginzburg, Sov. Phys. Usp. 19, 263–270 (1976).
    [CrossRef]
  33. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 2nd ed. (Pergamon, Oxford, 1970), Sec. 20.

1998 (1)

1997 (3)

1996 (2)

K. F. Ren, G. Grehan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

Ø. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108–130 (1996).
[CrossRef]

1995 (1)

1994 (3)

S. Chang, J. H. Jo, and S. S. Lee, “Theoretical calculations of optical force exerted on a dielectric sphere in the evanescent field generated with a totally-reflected focused gaussian beam,” Opt. Commun. 108, 133–143 (1994).
[CrossRef]

K. Svoboda and S. M. Block, “Biological application of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef]

W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
[CrossRef] [PubMed]

1992 (3)

1990 (1)

A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

1989 (2)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

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]

1988 (2)

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]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

1986 (1)

1980 (1)

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
[CrossRef] [PubMed]

1979 (2)

G. Roosen, “La lévitation optique de sphères,” Can. J. Phys. 57, 1260–1279 (1979).
[CrossRef]

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133–201 (1979).
[CrossRef]

1976 (1)

Yu. S. Barash and V. L. Ginzburg, Sov. Phys. Usp. 19, 263–270 (1976).
[CrossRef]

1973 (1)

A. Ashkin and J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30, 139–142 (1973).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Almaas, E.

Ashkin, A.

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
[CrossRef] [PubMed]

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[CrossRef] [PubMed]

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30, 139–142 (1973).
[CrossRef]

Barash, Yu. S.

Yu. S. Barash and V. L. Ginzburg, Sov. Phys. Usp. 19, 263–270 (1976).
[CrossRef]

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Berns, M. W.

Bjorkholm, J. E.

Block, S. M.

K. Svoboda and S. M. Block, “Biological application of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef]

Brevik, I.

Chang, R. K.

Chang, S.

S. Chang, J. H. Jo, and S. S. Lee, “Theoretical calculations of optical force exerted on a dielectric sphere in the evanescent field generated with a totally-reflected focused gaussian beam,” Opt. Commun. 108, 133–143 (1994).
[CrossRef]

Chu, S.

Dziedzic, J. M.

A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30, 139–142 (1973).
[CrossRef]

Euteneuer, U.

A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

Farsund, Ø.

Ø. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108–130 (1996).
[CrossRef]

Felderhof, B. U.

Ø. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108–130 (1996).
[CrossRef]

Gahagan, K. T.

Ginzburg, V. L.

Yu. S. Barash and V. L. Ginzburg, Sov. Phys. Usp. 19, 263–270 (1976).
[CrossRef]

Gouesbet, G.

Grehan, G.

Gussgard, R.

Jo, J. H.

S. Chang, J. H. Jo, and S. S. Lee, “Theoretical calculations of optical force exerted on a dielectric sphere in the evanescent field generated with a totally-reflected focused gaussian beam,” Opt. Commun. 108, 133–143 (1994).
[CrossRef]

Kawata, S.

Kobayashi, T.

Lai, H. M.

Lee, S. S.

S. Chang, J. H. Jo, and S. S. Lee, “Theoretical calculations of optical force exerted on a dielectric sphere in the evanescent field generated with a totally-reflected focused gaussian beam,” Opt. Commun. 108, 133–143 (1994).
[CrossRef]

Leung, P. T.

Lindmo, T.

Omori, R.

Pobre, R.

Poon, K. L.

Ren, K. F.

Roosen, G.

G. Roosen, “La lévitation optique de sphères,” Can. J. Phys. 57, 1260–1279 (1979).
[CrossRef]

Saloma, C.

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Schliwa, M.

A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

Schütze, K.

A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

Sonek, G. J.

Sugiura, T.

Suzuki, A.

Svoboda, K.

K. Svoboda and S. M. Block, “Biological application of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef]

Swartzlander, G. A.

Wright, W. H.

Young, K.

Zhang, J. Z.

Annu. Rev. Biophys. Biomol. Struct. (1)

K. Svoboda and S. M. Block, “Biological application of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef]

Appl. Opt. (3)

Biophys. J. (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

Can. J. Phys. (1)

G. Roosen, “La lévitation optique de sphères,” Can. J. Phys. 57, 1260–1279 (1979).
[CrossRef]

J. Appl. Phys. (2)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

J. Opt. Soc. Am. B (4)

Nature (London) (1)

A. Ashkin, K. Schütze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
[CrossRef]

Opt. Commun. (1)

S. Chang, J. H. Jo, and S. S. Lee, “Theoretical calculations of optical force exerted on a dielectric sphere in the evanescent field generated with a totally-reflected focused gaussian beam,” Opt. Commun. 108, 133–143 (1994).
[CrossRef]

Opt. Lett. (4)

Phys. Rep. (1)

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133–201 (1979).
[CrossRef]

Phys. Rev. Lett. (1)

A. Ashkin and J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30, 139–142 (1973).
[CrossRef]

Physica A (1)

Ø. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108–130 (1996).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853–4860 (1997).
[CrossRef] [PubMed]

Science (1)

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

Yu. S. Barash and V. L. Ginzburg, Sov. Phys. Usp. 19, 263–270 (1976).
[CrossRef]

Other (9)

L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 2nd ed. (Pergamon, Oxford, 1970), Sec. 20.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).

K. L. Poon, “Laser pulse induced electrostrictive distortion of liquid micro-droplet,” M. Phil. thesis (Chinese University of Hong Kong, Hong Kong, 1990), pp. 1–90.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1981), p. 476.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1959).

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971); “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).
[CrossRef]

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987); “Internal cell manipulation using infrared laser traps,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989).
[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Relative elevation h/a=(h0+h2)/a versus polar angle θ in the xz plane (ϕ=0) when α=0.2 and Δt=4 µs. Laser irradiation is from the left. Solid curve, unpolarized radiation, h=h0; dotted curve, increment h2 arising from linear polarization in the eˆx direction.

Fig. 2
Fig. 2

Same as Fig. 1 but with α=5.

Fig. 3
Fig. 3

Ratio h/a=(h0+h2 cos 2ϕ)/a versus azimuthal angle ϕ in the plane orthogonal to the z axis where the linear polarization is of greatest importance (θ25°). Direction ϕ=0 is the polarization direction. α=5, Δt=4 µs.

Fig. 4
Fig. 4

Ratio h/a=(h0+h2)/a versus polar angle θ in the xz plane (ϕ=0). Linear polarization, α=5, Δt=2 µs.

Fig. 5
Fig. 5

Same as Fig. 4 but at Δt=8 µs.

Fig. 6
Fig. 6

Same as Fig. 5 but at Δt=22 µs.

Fig. 7
Fig. 7

Same as Fig. 1 but with α=500.

Fig. 8
Fig. 8

Same as Fig. 4 but with α=500.

Fig. 9
Fig. 9

Same as Fig. 8 but at Δt=6 µs.

Fig. 10
Fig. 10

Same as Fig. 9 but at Δt=16 µs.

Tables (1)

Tables Icon

Table 1 Values of Coefficients Fl and Fl2

Equations (50)

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

f=-12E2+12E2ρρS+κ-1c2t(E×H),
f=-02E2κ+06[E2(κ-1)(κ+2)].
σAM=-02a-a+drE2dκdr=02(n2-1)(Et2+n2Er2)a-,
σel.str.=-(0/6)E2(a-)(n2-1)(n2+2).
E(i)=E0eˆx exp(ikextz),B(i)=E0ceˆy exp(ikextz),
α=kexta,r˜=r/a.
E(i)=E0l=1m=-llikextaE(l, m)×jl(αr˜)Xlm+aM(l, m)jl(αr˜)Xlm,
B(i)=E0cl=1m=-llaE(l, m)jl(αr˜)Xlm-ikextaM(l, m)×jl(αr˜)Xlm,
aE(l, m)=-il+1π(2l+1)(δm1-δm,-1),
aM(l, m)=ilπ(2l+1)(δm1+δm,-1).
Er(i)=E0 cos ϕ(αr˜)2l=1il+1(2l+1)ψl(αr˜)Pl1,
Eθ(i)=-E0 cos ϕαr˜l=1il(2l+1)l(l+1)×ψl(αr˜)Pl1sin θ-iψl(αr˜)dPl1dθ,
Eϕ(i)=E0 sin ϕαr˜l=1il(2l+1)l(l+1)×ψl(αr˜)dPl1dθ-iψl(αr˜)Pl1sin θ.
Er(s)=E0 cos ϕ(αr˜)2l=1il+1(2l+1)al(s)ξl(1)(αr˜)Pl1,
Eθ(s)=-E0 cos ϕαr˜l=1il(2l+1)l(l+1)×bl(s)ξl(1)(αr˜)Pl1sin θ-ial(s)ξl(1)(αr˜)dPl1dθ,
Eϕ(s)=E0 sin ϕαr˜l=1il(2l+1)l(l+1)×bl(s)ξl(1)(αr˜)dPl1dθ-ial(s)ξl(1)(αr˜)Pl1sin θ.
Er(w)=E0 cos ϕ(nαr˜)2l=1il+1(2l+1)al(w)ψl(nar˜)Pl1,
Eθ(w)=-E0 cos ϕαr˜l=1il(2l+1)l(l+1)×bl(w)ψl(nαr˜)Pl1sin θ-inal(w)ψl(nαr˜)dPl1dθ,
Eϕ(w)=E0 sin ϕαr˜l=1il(2l+1)l(l+1)×bl(w)ψl(nαr˜)dPl1dθ-inal(w)ψl(nαr˜)Pl1sin θ.
al(w)=innψl(nα)ξl(1)(α)-ψl(nα)ξl(1)(α),
bl(w)=iψl(nα)ξl(1)(α)-nψl(nα)ξl(1)(α),
IT(t)=I0ωτt exp(-ωτt),
Ft=|Et(w)(a)|2E02,Fr=|Er(w)(a)|2E02
σAM=n2-12cIT(t)(Ft+n2Fr).
ρvt=-p+μ2v+012[|E|2(n2-1)(n2+2)],
ρvt=-pAM+μ2v.
pAM(r, t)=l=0m=-llplm(t)r˜lPlm(cos θ)exp(imϕ),
h(θ, ϕ, t)=l=1m=-llhlm(t)Plm(cos θ)exp(imϕ),
σAM(θ, ϕ, t)=n2-12cIT(t)l=0m=-llFlmPlm(cos θ)exp(imϕ),
Δpsurf.tens.=2Ta+Ta2l=1m=-ll(l2+l-2)hlm×Plm(cos θ)exp(imϕ)
Δpsurf.tens.-σAM=pAM-2µvrr,
2Ta-n2-12cIT(t)F00=p00(t),
Ta2(l2+l-2)hlm(t)-n2-12cIT(t)Flm(t)=plm(t).
h¨lm(t)+ωl2hlm(t)=n2-12clρaIT(t)Flm,
h¨lm(t)+2δlmh¨lm(t)+ωl2hlm(t)=0,
Elm=4πρla2l+1(l+m)!(l-m)!Clm2.
E˙lm(kin)=-μv2·dS,
E˙lm(kin)=-8πμal(l-1)(l+m)!(l-m)!Clm2.
δlmδl=μρa2(2l2-l-1).
h˙lm(t)+2δlmh˙lm(t)+ωl2hlm(t)=(I0l/2ρac)(n2-1)Flmωτt exp(-ωτt)
hlm(t)=t exp(-ωτt)ωτ2-2δlωτ+ωl2+2(ωτ-δl)exp(-ωτt)(ωτ2-2δlωτ+ωl2)2+[(ωτ-δl)2-γl2]sin γlt-2γl(ωτ-δl)cos γltγl(ωτ2-2δlωτ+ωl2)2×exp(-δlt)I0lωτ2ρac(n2-1)Flm,
F(θ, ϕ)=Ft(θ, ϕ)+n2Fr(θ, ϕ)
Flm=2l+14π(l-m)!(l+m)!×F(θ, ϕ)Plm(cos θ)exp(-imϕ)dΩ.
Fl=2l+12Funpol.(θ)Pl(cos θ)d(cos θ).
Fl,-2=(l+2)!(l-2)!Fl2,
R(θ, ϕ, t)=a+l=1[hl(t)Pl(cos θ)+2hl2(t)Pl2(cos θ)cos 2ϕ]a+h0(θ, t)+h2(θ, t)cos 2ϕ.
ρ=103kg/m3,n=1.33,μ=10-3Pas,
T=0.070 N/m,a=50µm,
I0=0.80(1.60)GW/cm2,τ=0.40 µs.
al(w)=2l+1nl-1(ln2+l+1),bl(w)=1nl+1.

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