Abstract

We consider the scattering of light by a spherical particle illuminated by two counterpropagating plane waves. Destructive and constructive interference of the two incident fields modifies the resonance contribution to the scattered and internal fields. The resonance contribution can vary between zero and twice the value of that associated with ordinary Mie scattering; the amount of the contribution is a function of the relative phase between the two beams.

© 1993 Optical Society of America

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References

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  1. P. Chýlek, “Partial wave resonances and the ripple structure of the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285–287 (1976).
    [Crossref]
  2. A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
    [Crossref]
  3. P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
    [Crossref]
  4. P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
    [Crossref] [PubMed]
  5. H. S. Bennett, G. J. Rosasco, “Resonances in the efficiency factor for absorption: Mie scattering theory,” Appl. Opt. 17, 491–493 (1978).
    [Crossref] [PubMed]
  6. G. J. Rosasco, H. S. Bennett, “Internal field resonance structure: implications for optical absorption and scattering by microscopic particles,” J. Opt. Soc. Am. 68, 1242–1250 (1978).
    [Crossref]
  7. A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
    [Crossref] [PubMed]
  8. P. R. Conwell, P. W. Barber, C. K. Rushfirth, “Resonant spectra of dielectric spheres,” J. Opt. Soc. Am. A 1, 62–67 (1984).
    [Crossref]
  9. B. A. Hunter, M. A. Box, B. Maier, “Resonance structure in weakly absorbing spheres,” J. Opt. Soc. Am. A 5, 1281–1286 (1988).
    [Crossref]
  10. J. A. Lock, “Cooperative effects among partial waves in Mie scattering,” J. Opt. Soc. Am. A 5, 2032–2044 (1988).
    [Crossref]
  11. J. D. Eversole, H. B. Lin, A. L. Houston, A. J. Campillo, “Spherical-cavity-mode assignment of optical resonances in microdroplets using elastic scattering,” J. Opt. Soc. Am. A 7, 2159–2168 (1990).
    [Crossref]
  12. G. Videen, W S. Bickel, “Light-scattering resonances in small spheres,” Phys. Rev. A 45, 6008–6012 (1992).
    [Crossref] [PubMed]
  13. P. Chýlek, H-B. Lin, J. D. Eversole, A. J. Campillo, “Effect of absorption on microdroplet resonant emission structure,” Opt. Lett. 16, 1723–1725 (1991).
    [Crossref]
  14. G. Videen, W. S. Bickel, J. M. Boyer, “Coherent fluorescent and scattering from a uniform sphere,” Phys. Rev. A 44, 1358–1365 (1991).
    [Crossref] [PubMed]
  15. H-B. Lin, A. L. Houston, J. D. Eversole, A. J. Campillo, P. Chýlek, “Internal scattering effects on microdroplet resonant emission structure,” Opt. Lett. 17, 970–972 (1992).
    [Crossref] [PubMed]
  16. R. Thurn, W. Kiefer, “Structural resonances observed in the Raman spectra of optically levitated liquid drops,” Appl. Opt. 24, 1515–1519 (1985).
    [Crossref] [PubMed]
  17. 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]
  18. R. G. Pinnick, A. Biswas, P. Chýlek, R. Armstrong, H. Latifi, E. Creegan, V. Srivastava, M. Jarzembski, G. Fernandez, “Stimulated Raman scattering in micrometer-sized droplets: time-resolved measurements,” Opt. Lett. 13, 494–496 (1988).
    [Crossref] [PubMed]
  19. W. F. Hsieh, J. H. Eickman, R. K. Chang, “Internal and external laser-induced avalanche breakdown of single droplets in an argon atmosphere,” J. Opt. Soc. Am. B 4, 1816–1820 (1987).
    [Crossref]
  20. R. K. Chang, J. H. Eickman, W. F. Hsieh, C. F. Wood, J. Z. Zhang, J. B. Zheng, “Laser-induced breakdown in large transparent water droplets,” Appl. Opt. 27, 2377–2385 (1988).
    [Crossref] [PubMed]
  21. P. Chýlek, M. A. Jarzembski, V. Srivastava, R. G. Pinnick, “Pressure dependence of the laser-induced breakdown thresholds of gases and droplets,” Appl. Opt. 29, 2303–2306 (1990).
    [Crossref] [PubMed]
  22. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  23. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  24. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  25. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  26. P. Chýlek, J. Zhan, “Interference structure of the Mie extinction cross section,” J. Opt. Soc. Am. A 6, 1846–1851 (1989).
    [Crossref]
  27. P. Chýlek, “Resonance structure of Mie scattering: distance between resonances,” J. Opt. Soc. Am. A 7, 1609–1613 (1990).
    [Crossref]

1992 (2)

1991 (2)

P. Chýlek, H-B. Lin, J. D. Eversole, A. J. Campillo, “Effect of absorption on microdroplet resonant emission structure,” Opt. Lett. 16, 1723–1725 (1991).
[Crossref]

G. Videen, W. S. Bickel, J. M. Boyer, “Coherent fluorescent and scattering from a uniform sphere,” Phys. Rev. A 44, 1358–1365 (1991).
[Crossref] [PubMed]

1990 (3)

1989 (1)

1988 (4)

1987 (1)

1985 (2)

1984 (1)

1981 (1)

1978 (4)

1977 (1)

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[Crossref]

1976 (1)

Armstrong, R.

Ashkin, A.

A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
[Crossref] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[Crossref]

Barber, P. W.

Bennett, H. S.

Bickel, W S.

G. Videen, W S. Bickel, “Light-scattering resonances in small spheres,” Phys. Rev. A 45, 6008–6012 (1992).
[Crossref] [PubMed]

Bickel, W. S.

G. Videen, W. S. Bickel, J. M. Boyer, “Coherent fluorescent and scattering from a uniform sphere,” Phys. Rev. A 44, 1358–1365 (1991).
[Crossref] [PubMed]

Biswas, A.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Box, M. A.

Boyer, J. M.

G. Videen, W. S. Bickel, J. M. Boyer, “Coherent fluorescent and scattering from a uniform sphere,” Phys. Rev. A 44, 1358–1365 (1991).
[Crossref] [PubMed]

Campillo, A. J.

Chang, R. K.

Chýlek, P.

H-B. Lin, A. L. Houston, J. D. Eversole, A. J. Campillo, P. Chýlek, “Internal scattering effects on microdroplet resonant emission structure,” Opt. Lett. 17, 970–972 (1992).
[Crossref] [PubMed]

P. Chýlek, H-B. Lin, J. D. Eversole, A. J. Campillo, “Effect of absorption on microdroplet resonant emission structure,” Opt. Lett. 16, 1723–1725 (1991).
[Crossref]

P. Chýlek, M. A. Jarzembski, V. Srivastava, R. G. Pinnick, “Pressure dependence of the laser-induced breakdown thresholds of gases and droplets,” Appl. Opt. 29, 2303–2306 (1990).
[Crossref] [PubMed]

P. Chýlek, “Resonance structure of Mie scattering: distance between resonances,” J. Opt. Soc. Am. A 7, 1609–1613 (1990).
[Crossref]

P. Chýlek, J. Zhan, “Interference structure of the Mie extinction cross section,” J. Opt. Soc. Am. A 6, 1846–1851 (1989).
[Crossref]

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

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
[Crossref] [PubMed]

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

P. Chýlek, “Partial wave resonances and the ripple structure of the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285–287 (1976).
[Crossref]

Conwell, P. R.

Creegan, E.

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
[Crossref] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[Crossref]

Eickman, J. H.

Eversole, J. D.

Fernandez, G.

Houston, A. L.

Hsieh, W. F.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Hunter, B. A.

Jackson, J. D.

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

Jarzembski, M.

Jarzembski, M. A.

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Kiefer, W.

Kiehl, J. T.

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
[Crossref] [PubMed]

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

Ko, M. K. W.

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
[Crossref] [PubMed]

Latifi, H.

Lin, H. B.

Lin, H-B.

Lock, J. A.

Maier, B.

Pinnick, R. G.

Qian, S. X.

Rosasco, G. J.

Rushfirth, C. K.

Snow, J. B.

Srivastava, V.

Thurn, R.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Videen, G.

G. Videen, W S. Bickel, “Light-scattering resonances in small spheres,” Phys. Rev. A 45, 6008–6012 (1992).
[Crossref] [PubMed]

G. Videen, W. S. Bickel, J. M. Boyer, “Coherent fluorescent and scattering from a uniform sphere,” Phys. Rev. A 44, 1358–1365 (1991).
[Crossref] [PubMed]

Wood, C. F.

Zhan, J.

Zhang, J. Z.

Zheng, J. B.

Appl. Opt. (6)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (6)

J. Opt. Soc. Am. B (1)

Opt. Lett. (4)

Phys. Rev. A (3)

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

G. Videen, W. S. Bickel, J. M. Boyer, “Coherent fluorescent and scattering from a uniform sphere,” Phys. Rev. A 44, 1358–1365 (1991).
[Crossref] [PubMed]

G. Videen, W S. Bickel, “Light-scattering resonances in small spheres,” Phys. Rev. A 45, 6008–6012 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[Crossref]

Other (4)

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

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

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Figures (6)

Fig. 1
Fig. 1

Considered case of light scattering by a spherical particle illuminated by two counterpropagating plane waves.

Fig. 2
Fig. 2

Scattering efficiency for the case of in-phase (α = 0) incident fields. All even an and odd bn vanish, and contributions from odd an and even bn resonances are doubled. At lower values of the size parameter x the an and bn+1 resonances overlap. Alternate peaks vanish and double. At larger values of the size parameter each resonance peak is separated from its neighbors and two peaks alternately vanish and double. The smooth background remains unchanged.

Fig. 3
Fig. 3

Same as Fig. 2, but for out-of-phase (α = π ) incident fields.

Fig. 4
Fig. 4

Real parts of an and bn for n = 3, 4, and 5 and for refractive index m = 1.4647.

Fig. 5
Fig. 5

Scattering diagram for the case of a spherical particle with refractive index m = 1.4647 and size parameter x = 6. The diagram is symmetrical with respect to the forward and the backward directions in the case of α = 0 and α = π.

Fig. 6
Fig. 6

Internal field intensity of four resonance locations (considered in Ref. 8) in the case of ordinary Mie scattering (a) and for two incident beams (b) with relative phase α = 0.

Equations (25)

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E i + = E o + n = 1 E n [ M o 1 n ( 1 ) i N e 1 n ( 1 ) ] .
E n = i n 2 n + 1 n ( n + 1 ) .
E i = E o n = 1 E n ( 1 ) n [ M o 1 n ( 1 ) + i N e 1 n ( 1 ) ] .
E i = E i + + exp ( i α ) E i .
E i = E o n = 1 E n { M o 1 n ( 1 ) [ 1 + ( 1 ) n exp ( i α ) ] i N e 1 n ( 1 ) [ 1 ( 1 ) n exp ( i α ) ] } .
E int = E o n = 1 E n [ D n M o 1 n ( 1 ) i C n N e 1 n ( 1 ) ] .
E s = E o n = 1 E n [ i A n N e 1 n ( 3 ) B n M o 1 n ( 3 ) ] .
H i = k ω E o n = 1 E n { M e 1 n ( 1 ) [ 1 ( 1 ) n e i α ] + i N o 1 n ( 1 ) [ 1 + ( 1 ) n exp ( i α ) ] } ,
H int = k m ω E o n = 1 E n [ C n M e 1 n ( 1 ) + i D n N o 1 n ( 1 ) ] .
H S = k ω E o n = 1 E n [ i B n N o 1 n ( 3 ) + A n M e 1 n ( 3 ) ] .
A n = [ 1 ( 1 ) n exp ( i α ) ] a n .
B n = [ 1 + ( 1 ) n exp ( i α ) ] b n .
C n = [ 1 ( 1 ) n exp ( i α ) ] c n .
D n = [ 1 + ( 1 ) n exp ( i α ) ] d n .
W sca = 1 2 Re 0 2 π 0 π ( E s × H s * ) r 2 ( sin θ ) d θ d ϕ ,
W ext = 1 2 Re 0 2 π 0 π ( E i × H s * + E s × H i * ) r 2 ( sin θ ) d θ d ϕ .
Q sca = W sca / I i .
Q ext = W ext / I i .
Q sca = 4 x 2 n = 1 ( 2 n + 1 ) × { [ cos 2 ( α / 2 ) sin 2 ( α / 2 ) ] | a n | 2 + [ sin 2 ( α / 2 ) cos 2 ( α / 2 ) ] | b n | 2 } .
Q ext = 4 x 2 n = 1 ( 2 n + 1 ) × { [ cos 2 ( α / 2 ) sin 2 ( α / 2 ) ] Re ( a n ) + [ sin 2 ( α / 2 ) cos 2 ( α / 2 ) ] Re ( b n ) } .
S 1 ( θ ) = n = 1 2 n + 1 2 n ( n + 1 ) [ A n π n ( cos θ ) + B n τ n ( cos θ ) ]
S 2 ( θ ) = n = 1 2 n + 1 2 n ( n + 1 ) [ A n τ n ( cos θ ) + B n π n ( cos θ ) ] .
i ( θ ) = | S 1 ( θ ) | 2 + | S 2 ( θ ) | 2 = i ( θ ) + i ( θ ) .
E o 2 2 n = 1 { ( 2 n + 1 ) j n 2 ( mkr ) | c n | 2 + [ ( n + 1 ) j n 1 2 ( mkr ) + n j n + 1 2 ( mkr ) ] | d n | 2 } .
2 E o 2 n = 1 { ( 2 n + 1 ) j n 2 ( mkr ) [ cos 2 ( α / 2 ) sin 2 ( α / 2 ) ] | c n | 2 + [ ( n + 1 ) j n 1 2 ( mkr ) + n j n + 1 2 ( mkr ) ] [ sin 2 ( α / 2 ) cos 2 ( α / 2 ) ] | d n | 2 } .

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