Abstract

The observed laser-induced distortion of a transparent micrometer-sized droplet [ Opt. Lett. 13, 916 ( 1988)] is analyzed theoretically. Electrostriction causes a pulling force on the droplet surface, exciting surface waves of different angular momenta. The resultant surface motion is solved, and the droplet shapes at later times agree with observation, only if the intensity is assumed to be twice the experimentally reported value. Possible reasons for the discrepancy are discussed.

© 1989 Optical Society of America

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References

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  1. J.-Z. Zhang and R. K. Chang, Opt. Lett. 13, 916 (1988).
    [CrossRef] [PubMed]
  2. F. N. H. Robinson, Phys. Rep. 16, 313 (1975);I. Brevik, Phys. Rep. 52, 133 (1979);L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960), pp. 64–69.
    [CrossRef]
  3. R. Peierls, Proc. R. Soc. London Ser. A 347, 475 (1976);Proc. R. Soc. London Ser. A 355, 141 (1977);R. V. Jones and J. C. S. Richards, Proc. R. Soc. London Ser. A 221, 480 (1954);R. V. Jones and B. Leslie, Proc. R. Soc. London Ser. A 360, 347 (1978);H. K. Wong and K. Young, Am. J. Phys. 45, 195 (1977).
    [CrossRef]
  4. A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 30, 139 (1973).
    [CrossRef]
  5. H. M. Lai and K. Young, Phys. Rev. A 14, 2329 (1976).
    [CrossRef]
  6. J. P. Gordon, Phys. Rev. A 8, 14 (1973).
    [CrossRef]
  7. H. M. Lai, W. M. Suen, and K. Young, Phys. Rev. Lett. 47, 177 (1981).
    [CrossRef]
  8. H. M. Lai, W. M. Suen, and K. Young, Phys. Rev. A 25, 1755 (1982).
    [CrossRef]
  9. J. S. Hoye and G. Stell, J. Chem. Phys. 72, 1597 (1980);H. M. Lai, K. Young, and W. M. Suen, Phys. Rev. A 34, 1458 (1986).
    [CrossRef] [PubMed]
  10. G. Mie, Ann. Phys. (Leipzig) 25, 377 (1908);M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  11. J. F. Owen, P. W. Barber, B. J. Messinger, and R. K. Chang, Opt. Lett. 6, 272 (1981);P. R. Cornwall, P. W. Barber, and C. K. Rushforth, J. Opt. Soc. Am. A 1, 62 (1984).
    [CrossRef] [PubMed]
  12. R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980);H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 273 (1984).
    [CrossRef] [PubMed]
  13. J. B. Snow, S.-X. Qian, and R. K. Chang, Opt. Lett. 10, 37 (1985);S.-X. Qian, J. B. Snow, and R. K. Chang, Opt. Lett. 10, 499 (1985);S.-X. Qian and R. K. Chang, Phys. Rev. Lett. 56, 926 (1986).
    [CrossRef] [PubMed]
  14. J.-Z. Zhang and R. K. Chang, J. Opt. Soc. Am. B 6, 151 (1989);S. M. Chitanvis and C. D. Cantrell, J. Opt. Soc. Am. B 6, 1326 (1989).
    [CrossRef]
  15. L. M. Folan, S. Arnold, and S. D. Druger, Chem. Phys. Lett. 118, 322 (1985).
    [CrossRef]
  16. H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 499 (1984);S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, Science 231, 486 (1986).
    [CrossRef] [PubMed]
  17. S. C. Ching, H. M. Lai, and K. Young, J. Opt. Soc. Am. B 4, 1995, 2004 (1987).
    [CrossRef]
  18. H. M. Lai, P. T. Leung, and K. Young, Phys. Rev. A 37, 1597 (1988).
    [CrossRef] [PubMed]
  19. P. T. Leung and K. Young, J. Chem. Phys. 89, 2894 (1988).
    [CrossRef]
  20. J.-Z. Zhang, D. H. Leach, and R. K. Chang, Opt. Lett. 13, 270 (1988);R. G. Pinnick, A. Biswas, P. Chýlek, R. L. Armstrong, H. Latifi, E. Creegan, V. Srivastava, M. Jarzembski, and G. Fernández, Opt. Lett. 13, 494 (1988);S. Arnold, Polytechnic University, Brooklyn, New York 11201 (personal communication).
    [CrossRef] [PubMed]
  21. H.-M. Tzeng, M. B. Long, R. K. Chang, and P. W. Barber, Opt. Lett. 10, 209 (1985).
    [CrossRef] [PubMed]
  22. H. M. Lai and K. Young, J. Acoust. Soc. Am. 72, 2000 (1982).
    [CrossRef]
  23. C. K. N. Patel and A. C. Tam, Rev. Mod. Phys. 53, 517 (1981).
    [CrossRef]
  24. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 771.
  25. A. R. Edmonds, Angular Momentum in Quantum Mechanics, 2nd ed. (Princeton, Princeton, N.J., 1960).
  26. K. L. Poon, M. Phil. Thesis (Chinese University of Hong Kong, Hong Kong, in preparation).
  27. D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, and R. K. Chang, Appl. Opt. 26, 1348 (1987).
    [CrossRef] [PubMed]
  28. H. Lamb, Hydrodynamics, 6th ed. (Cambridge U. Press, Cambridge, 1932), p. 639;S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford U. Press, Oxford, 1961), p. 466;W. H. Reid, Quart. Appl. Math. 18, 86 (1960).
  29. R. L. Armstrong, in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988), p. 203.

1989 (1)

1988 (4)

1987 (2)

1985 (3)

1984 (1)

1982 (2)

H. M. Lai and K. Young, J. Acoust. Soc. Am. 72, 2000 (1982).
[CrossRef]

H. M. Lai, W. M. Suen, and K. Young, Phys. Rev. A 25, 1755 (1982).
[CrossRef]

1981 (3)

1980 (2)

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980);H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 273 (1984).
[CrossRef] [PubMed]

J. S. Hoye and G. Stell, J. Chem. Phys. 72, 1597 (1980);H. M. Lai, K. Young, and W. M. Suen, Phys. Rev. A 34, 1458 (1986).
[CrossRef] [PubMed]

1976 (2)

H. M. Lai and K. Young, Phys. Rev. A 14, 2329 (1976).
[CrossRef]

R. Peierls, Proc. R. Soc. London Ser. A 347, 475 (1976);Proc. R. Soc. London Ser. A 355, 141 (1977);R. V. Jones and J. C. S. Richards, Proc. R. Soc. London Ser. A 221, 480 (1954);R. V. Jones and B. Leslie, Proc. R. Soc. London Ser. A 360, 347 (1978);H. K. Wong and K. Young, Am. J. Phys. 45, 195 (1977).
[CrossRef]

1975 (1)

F. N. H. Robinson, Phys. Rep. 16, 313 (1975);I. Brevik, Phys. Rep. 52, 133 (1979);L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960), pp. 64–69.
[CrossRef]

1973 (2)

A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 30, 139 (1973).
[CrossRef]

J. P. Gordon, Phys. Rev. A 8, 14 (1973).
[CrossRef]

1908 (1)

G. Mie, Ann. Phys. (Leipzig) 25, 377 (1908);M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Armstrong, R. L.

R. L. Armstrong, in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988), p. 203.

Arnold, S.

L. M. Folan, S. Arnold, and S. D. Druger, Chem. Phys. Lett. 118, 322 (1985).
[CrossRef]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 30, 139 (1973).
[CrossRef]

Barber, P. W.

Benincasa, D. S.

Benner, R. E.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980);H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 273 (1984).
[CrossRef] [PubMed]

Chang, R. K.

J.-Z. Zhang and R. K. Chang, J. Opt. Soc. Am. B 6, 151 (1989);S. M. Chitanvis and C. D. Cantrell, J. Opt. Soc. Am. B 6, 1326 (1989).
[CrossRef]

J.-Z. Zhang, D. H. Leach, and R. K. Chang, Opt. Lett. 13, 270 (1988);R. G. Pinnick, A. Biswas, P. Chýlek, R. L. Armstrong, H. Latifi, E. Creegan, V. Srivastava, M. Jarzembski, and G. Fernández, Opt. Lett. 13, 494 (1988);S. Arnold, Polytechnic University, Brooklyn, New York 11201 (personal communication).
[CrossRef] [PubMed]

J.-Z. Zhang and R. K. Chang, Opt. Lett. 13, 916 (1988).
[CrossRef] [PubMed]

D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, and R. K. Chang, Appl. Opt. 26, 1348 (1987).
[CrossRef] [PubMed]

H.-M. Tzeng, M. B. Long, R. K. Chang, and P. W. Barber, Opt. Lett. 10, 209 (1985).
[CrossRef] [PubMed]

J. B. Snow, S.-X. Qian, and R. K. Chang, Opt. Lett. 10, 37 (1985);S.-X. Qian, J. B. Snow, and R. K. Chang, Opt. Lett. 10, 499 (1985);S.-X. Qian and R. K. Chang, Phys. Rev. Lett. 56, 926 (1986).
[CrossRef] [PubMed]

H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 499 (1984);S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, Science 231, 486 (1986).
[CrossRef] [PubMed]

J. F. Owen, P. W. Barber, B. J. Messinger, and R. K. Chang, Opt. Lett. 6, 272 (1981);P. R. Cornwall, P. W. Barber, and C. K. Rushforth, J. Opt. Soc. Am. A 1, 62 (1984).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980);H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 273 (1984).
[CrossRef] [PubMed]

Ching, S. C.

Druger, S. D.

L. M. Folan, S. Arnold, and S. D. Druger, Chem. Phys. Lett. 118, 322 (1985).
[CrossRef]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 30, 139 (1973).
[CrossRef]

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics, 2nd ed. (Princeton, Princeton, N.J., 1960).

Folan, L. M.

L. M. Folan, S. Arnold, and S. D. Druger, Chem. Phys. Lett. 118, 322 (1985).
[CrossRef]

Gordon, J. P.

J. P. Gordon, Phys. Rev. A 8, 14 (1973).
[CrossRef]

Hoye, J. S.

J. S. Hoye and G. Stell, J. Chem. Phys. 72, 1597 (1980);H. M. Lai, K. Young, and W. M. Suen, Phys. Rev. A 34, 1458 (1986).
[CrossRef] [PubMed]

Hsieh, W.-F.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 771.

Lai, H. M.

H. M. Lai, P. T. Leung, and K. Young, Phys. Rev. A 37, 1597 (1988).
[CrossRef] [PubMed]

S. C. Ching, H. M. Lai, and K. Young, J. Opt. Soc. Am. B 4, 1995, 2004 (1987).
[CrossRef]

H. M. Lai and K. Young, J. Acoust. Soc. Am. 72, 2000 (1982).
[CrossRef]

H. M. Lai, W. M. Suen, and K. Young, Phys. Rev. A 25, 1755 (1982).
[CrossRef]

H. M. Lai, W. M. Suen, and K. Young, Phys. Rev. Lett. 47, 177 (1981).
[CrossRef]

H. M. Lai and K. Young, Phys. Rev. A 14, 2329 (1976).
[CrossRef]

Lamb, H.

H. Lamb, Hydrodynamics, 6th ed. (Cambridge U. Press, Cambridge, 1932), p. 639;S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford U. Press, Oxford, 1961), p. 466;W. H. Reid, Quart. Appl. Math. 18, 86 (1960).

Leach, D. H.

Leung, P. T.

H. M. Lai, P. T. Leung, and K. Young, Phys. Rev. A 37, 1597 (1988).
[CrossRef] [PubMed]

P. T. Leung and K. Young, J. Chem. Phys. 89, 2894 (1988).
[CrossRef]

Long, M. B.

Messinger, B. J.

Mie, G.

G. Mie, Ann. Phys. (Leipzig) 25, 377 (1908);M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Owen, J. F.

J. F. Owen, P. W. Barber, B. J. Messinger, and R. K. Chang, Opt. Lett. 6, 272 (1981);P. R. Cornwall, P. W. Barber, and C. K. Rushforth, J. Opt. Soc. Am. A 1, 62 (1984).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980);H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 273 (1984).
[CrossRef] [PubMed]

Patel, C. K. N.

C. K. N. Patel and A. C. Tam, Rev. Mod. Phys. 53, 517 (1981).
[CrossRef]

Peierls, R.

R. Peierls, Proc. R. Soc. London Ser. A 347, 475 (1976);Proc. R. Soc. London Ser. A 355, 141 (1977);R. V. Jones and J. C. S. Richards, Proc. R. Soc. London Ser. A 221, 480 (1954);R. V. Jones and B. Leslie, Proc. R. Soc. London Ser. A 360, 347 (1978);H. K. Wong and K. Young, Am. J. Phys. 45, 195 (1977).
[CrossRef]

Poon, K. L.

K. L. Poon, M. Phil. Thesis (Chinese University of Hong Kong, Hong Kong, in preparation).

Qian, S.-X.

Robinson, F. N. H.

F. N. H. Robinson, Phys. Rep. 16, 313 (1975);I. Brevik, Phys. Rep. 52, 133 (1979);L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960), pp. 64–69.
[CrossRef]

Snow, J. B.

Stell, G.

J. S. Hoye and G. Stell, J. Chem. Phys. 72, 1597 (1980);H. M. Lai, K. Young, and W. M. Suen, Phys. Rev. A 34, 1458 (1986).
[CrossRef] [PubMed]

Suen, W. M.

H. M. Lai, W. M. Suen, and K. Young, Phys. Rev. A 25, 1755 (1982).
[CrossRef]

H. M. Lai, W. M. Suen, and K. Young, Phys. Rev. Lett. 47, 177 (1981).
[CrossRef]

Tam, A. C.

C. K. N. Patel and A. C. Tam, Rev. Mod. Phys. 53, 517 (1981).
[CrossRef]

Tzeng, H.-M.

Wall, K. F.

Young, K.

P. T. Leung and K. Young, J. Chem. Phys. 89, 2894 (1988).
[CrossRef]

H. M. Lai, P. T. Leung, and K. Young, Phys. Rev. A 37, 1597 (1988).
[CrossRef] [PubMed]

S. C. Ching, H. M. Lai, and K. Young, J. Opt. Soc. Am. B 4, 1995, 2004 (1987).
[CrossRef]

H. M. Lai and K. Young, J. Acoust. Soc. Am. 72, 2000 (1982).
[CrossRef]

H. M. Lai, W. M. Suen, and K. Young, Phys. Rev. A 25, 1755 (1982).
[CrossRef]

H. M. Lai, W. M. Suen, and K. Young, Phys. Rev. Lett. 47, 177 (1981).
[CrossRef]

H. M. Lai and K. Young, Phys. Rev. A 14, 2329 (1976).
[CrossRef]

Zhang, J.-Z.

Ann. Phys. (Leipzig) (1)

G. Mie, Ann. Phys. (Leipzig) 25, 377 (1908);M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Appl. Opt. (1)

Chem. Phys. Lett. (1)

L. M. Folan, S. Arnold, and S. D. Druger, Chem. Phys. Lett. 118, 322 (1985).
[CrossRef]

J. Acoust. Soc. Am. (1)

H. M. Lai and K. Young, J. Acoust. Soc. Am. 72, 2000 (1982).
[CrossRef]

J. Chem. Phys. (2)

J. S. Hoye and G. Stell, J. Chem. Phys. 72, 1597 (1980);H. M. Lai, K. Young, and W. M. Suen, Phys. Rev. A 34, 1458 (1986).
[CrossRef] [PubMed]

P. T. Leung and K. Young, J. Chem. Phys. 89, 2894 (1988).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (6)

Phys. Rep. (1)

F. N. H. Robinson, Phys. Rep. 16, 313 (1975);I. Brevik, Phys. Rep. 52, 133 (1979);L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960), pp. 64–69.
[CrossRef]

Phys. Rev. A (4)

H. M. Lai and K. Young, Phys. Rev. A 14, 2329 (1976).
[CrossRef]

J. P. Gordon, Phys. Rev. A 8, 14 (1973).
[CrossRef]

H. M. Lai, W. M. Suen, and K. Young, Phys. Rev. A 25, 1755 (1982).
[CrossRef]

H. M. Lai, P. T. Leung, and K. Young, Phys. Rev. A 37, 1597 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 30, 139 (1973).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980);H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 273 (1984).
[CrossRef] [PubMed]

H. M. Lai, W. M. Suen, and K. Young, Phys. Rev. Lett. 47, 177 (1981).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

R. Peierls, Proc. R. Soc. London Ser. A 347, 475 (1976);Proc. R. Soc. London Ser. A 355, 141 (1977);R. V. Jones and J. C. S. Richards, Proc. R. Soc. London Ser. A 221, 480 (1954);R. V. Jones and B. Leslie, Proc. R. Soc. London Ser. A 360, 347 (1978);H. K. Wong and K. Young, Am. J. Phys. 45, 195 (1977).
[CrossRef]

Rev. Mod. Phys. (1)

C. K. N. Patel and A. C. Tam, Rev. Mod. Phys. 53, 517 (1981).
[CrossRef]

Other (5)

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 771.

A. R. Edmonds, Angular Momentum in Quantum Mechanics, 2nd ed. (Princeton, Princeton, N.J., 1960).

K. L. Poon, M. Phil. Thesis (Chinese University of Hong Kong, Hong Kong, in preparation).

H. Lamb, Hydrodynamics, 6th ed. (Cambridge U. Press, Cambridge, 1932), p. 639;S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford U. Press, Oxford, 1961), p. 466;W. H. Reid, Quart. Appl. Math. 18, 86 (1960).

R. L. Armstrong, in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988), p. 203.

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Figures (6)

Fig. 1
Fig. 1

Dependence of Fl on x. Curves are labeled by the value of l. The calculation was performed at values of the size parameter x shown by the points; the lines joining the points are only to guide the eye and do not represent the value of Fl when x coincides with a sharp resonance.

Fig. 2
Fig. 2

F(a, θ) versus θ for x = 500 calculated by summing Eq. (14) up to lmax = 40. Because of the truncation in l, this figure gives only the long-wavelength behavior.

Fig. 3
Fig. 3

Individual hl(t) in units of a versus time t. Curves are labeled by values of l.

Fig. 4
Fig. 4

Displacement h in units of a in front (θ = 0, solid curves) and at the back (θ = π, dashed curves) versus time t (a) for short times, (b) for long times. Results are calculated by summing up to lmax = 40. The oscillation periods corresponding to l = 2, 3, 4 are indicated in (b).

Fig. 5
Fig. 5

Computed droplet shapes at various times Δt after the end of the laser pulse, using twice the experimentally reported intensity. The numbers indicate Δt in microseconds. Laser irradiation is from the left.

Fig. 6
Fig. 6

Two ways of representating the force. The dotted areas indicate the regions of high field: (a) as a surface force [Eq. (40a)], (b) as a force in the interior pushing the fluid into the region of high field [Eq. (40b)].

Tables (1)

Tables Icon

Table 1 Values of Fl for X = 500

Equations (45)

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

ρ [ v / t + ( v ) v ] + p μ 2 v = f ,
f 1 = f 1 + f 2 + f 3 ,
f 1 = ½ ( κ ) 0 E 2 ,
f 2 = ½ ( γ 0 E 2 ) ,
f 3 = 0 ( κ 1 ) t ( E × B ) .
κ ( r ) = { κ = n 2 r < a 1 r > a ,
γ = ( κ 1 ) + ( κ 1 ) 2 / 3.
p = p ½ γ 0 E 2 ,
κ = ( n 2 1 ) δ ( r a ) n ̂ ,
E = E t + E n = E t + D n / [ 0 κ ( r ) ] ,
( κ ) 0 E 2 = [ κ ( r ) ] 0 E t 2 + [ κ ( r ) / κ ( r ) 2 ] ( D n 2 / 0 ) = [ κ ( r ) ] 0 E t 2 { [ 1 / κ ( r ) ] } D n 2 / 0 .
( κ ) 0 E 2 = ( n 2 1 ) 0 [ E t 2 + D n 2 / ( 0 2 n 2 ) ] δ ( r a ) n ̂ ,
( κ ) 0 E 2 = ( n 2 1 ) 0 ( E t 2 + n 2 E n 2 ) δ ( r a ) n ̂ ,
( r , t ) 0 ( E t 2 + n 2 E n 2 ) [ I ( t ) / c ] F ( r ) ,
f 1 = ½ ( n 2 1 ) ( I / c ) F ( r ) δ ( r a ) n ̂ .
F ( r = a , θ ) = l = 0 F l P l ( cos θ ) ,
x = 2 π a / λ = k a ,
E = 1 2 l = 1 i l [ 4 π ( 2 l + 1 ) ] 1 / 2 { α l j l ( ξ ) X l , 1 + ( β l / k ) × [ j l ( ξ ) X l , 1 ] } ,
X l , m = L Y l , m / [ l ( l + 1 ) ] 1 / 2 ,
α 1 = 2 i x 2 [ j l h l ( 1 ) j l h l ( 1 ) ] 1 ,
β l = 2 i x 2 [ n 2 j l h l ( 1 ) j l h l ( 1 ) + ( n 2 1 ) j l h l ( 1 ) / x ] 1 ,
1 n k × [ j l ( ξ ) X l , m ] = 1 ξ ξ ( ξ j l ) n ̂ × X l , m + i [ l ( l + 1 ) ] 1 / 2 ( j l / ξ ) n ̂ Y l , m .
E t α A + β B , n E n β C ,
F α 2 A 2 + 2 α β AB + β 2 B 2 + β 2 C 2 .
F = π 2 l 1 l 2 i l 1 l 2 [ ( 2 l 1 + 1 ) ( 2 l 2 + 1 ) ] 1 / 2 α l 2 * a l 1 j l 2 j l 1 X l 2 , 1 * X l 1 , 1 ,
F l = [ 4 π ( 2 l + 1 ) ] 1 / 2 8 l 1 l 2 [ ( 2 l 1 + 1 ) ( 2 l 1 + 1 ) ] 1 / 2 S l 1 l 2 × d Ω X l 2 , 1 * Y l , 0 X l 1 , 1 ,
S l 1 l 2 = i l 1 l 2 α l 2 * α l 1 j l 2 ( nx ) j l 1 ( nx ) .
F l = 1 8 l 1 l 2 ( 2 l 1 + 1 ) ( 2 l 2 + 1 ) S l 1 l 2 C ( l 1 l 2 l , 000 ) 2 cos 2 θ 12 ,
cos θ 12 = l 1 ( l 1 + 1 ) + l 2 ( l 2 + 1 ) l ( l + 1 ) 2 [ l 1 ( l 1 + 1 ) l 2 ( l 2 + 1 ) ] 1 / 2 .
I ( t ) = I 0 ( t / τ ) exp ( t / τ ) ,
ρ v t + p μ 2 v = f 1 .
r ( θ , t ) = a + h ( θ , t ) ,
h ( θ , t ) = l = 1 h l ( t ) P l ( cos θ )
l + Γ l l + ω l 2 h l = 0 ,
ω l 2 = l ( l + 2 ) ( l 1 ) γ s / ( ρ a 3 ) ,
Γ l = 2 ( 2 l + 1 ) ( l 1 ) μ / ( ρ a 2 ) .
Δ p = ½ ( n 2 1 ) ( I / c ) F ( a , θ ) ,
l + Γ l l + ω l 2 h l = A l ( t / τ ) e ( t / τ ) ,
A l = 1 2 ( n 2 1 ) I 0 c ρ a l F l .
l A l τ .
h l l / ω l n 2 1 2 I 0 τ c ( a ρ γ s ) 1 / 2 F l l ,
h ( θ , t ) a n 2 1 2 I 0 τ c ( 1 ρ γ s a ) 1 / 2 × i ( F l l ) sin ω l t exp ( Γ l t / 2 ) P l ( cos θ ) ,
( θ , t ) = υ n ( r = a + h , θ , t ) υ n ( r = a , θ , t ) .
f = f 1 = ½ ( κ ) 0 E 2 ,
f = f 1 + f 2 = ½ [ ( κ 1 ) 0 E 2 ] ½ ( κ ) 0 E 2 = ½ ( n 2 1 ) 0 ( E 2 ) ,

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