Abstract

Results of experimental measurements and theoretical calculations concerning the scattering of plane wave radiation by a system of two interacting spheres are presented. In particular, the complex scattering amplitude of such a system and the phenomena of specular resonances are addressed. Preliminary calculations of the two-sphere Muller matrix are also considered.

© 1986 Optical Society of America

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References

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  1. J. H. Bruning, Y. T. Lo, “Multiple Scattering of EM Waves by Spheres Part I—Multipole Expansion and Ray-Optical Solution,” IEEE Trans. Antennas Propag. AP-19, 378 (1971).
    [CrossRef]
  2. J. H. Bruning, Y. T. Lo, “Multiple Scattering by Spheres,” Tech. Rep. 69-5 (Antenna Laboratory, U. Illinois, Urbana, 1969).
  3. D. W. Schuerman, R. T. Wang, “Experimental Results of Multiple Scattering,” Final Rep., ARCSL-CR-81-003 (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Ground, MD, Nov.1981).
  4. R. T. Wang, J. M. Greenberg, D. W. Schuerman, “Experimental Results of Dependent Light Scattering by Two Spheres,” Opt. Lett. 6, 543 (1981).
    [CrossRef] [PubMed]
  5. G. W. Kattawar, C. E. Dean, “Electromagnetic Scattering from Two Dielectric Spheres: Comparison Between Theory and Experiment,” Opt. Lett. 8, 48 (1983).
    [CrossRef] [PubMed]
  6. R. T. Wang, “Extinction by Dumbells and Chains of Spheres,” in Proceedings, 1983 Scientific Conference on Obscuration and Aerosol Research, J. Farmer, R. H. Kohl, Eds. (U.S. Army Armament, Munitions, & Chemical Command, Aberdeen Proving Grounds, MD., 1984).
  7. R. C. Thompson, J. R. Bottiger, E. S. Fry, “Measurements of Polarized Light Interactions via the Müller Matrix,” Appl. Opt. 19, 1323 (1980).
    [CrossRef] [PubMed]

1983 (1)

1981 (1)

1980 (1)

1971 (1)

J. H. Bruning, Y. T. Lo, “Multiple Scattering of EM Waves by Spheres Part I—Multipole Expansion and Ray-Optical Solution,” IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

Bottiger, J. R.

Bruning, J. H.

J. H. Bruning, Y. T. Lo, “Multiple Scattering of EM Waves by Spheres Part I—Multipole Expansion and Ray-Optical Solution,” IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

J. H. Bruning, Y. T. Lo, “Multiple Scattering by Spheres,” Tech. Rep. 69-5 (Antenna Laboratory, U. Illinois, Urbana, 1969).

Dean, C. E.

Fry, E. S.

Greenberg, J. M.

Kattawar, G. W.

Lo, Y. T.

J. H. Bruning, Y. T. Lo, “Multiple Scattering of EM Waves by Spheres Part I—Multipole Expansion and Ray-Optical Solution,” IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

J. H. Bruning, Y. T. Lo, “Multiple Scattering by Spheres,” Tech. Rep. 69-5 (Antenna Laboratory, U. Illinois, Urbana, 1969).

Schuerman, D. W.

R. T. Wang, J. M. Greenberg, D. W. Schuerman, “Experimental Results of Dependent Light Scattering by Two Spheres,” Opt. Lett. 6, 543 (1981).
[CrossRef] [PubMed]

D. W. Schuerman, R. T. Wang, “Experimental Results of Multiple Scattering,” Final Rep., ARCSL-CR-81-003 (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Ground, MD, Nov.1981).

Thompson, R. C.

Wang, R. T.

R. T. Wang, J. M. Greenberg, D. W. Schuerman, “Experimental Results of Dependent Light Scattering by Two Spheres,” Opt. Lett. 6, 543 (1981).
[CrossRef] [PubMed]

D. W. Schuerman, R. T. Wang, “Experimental Results of Multiple Scattering,” Final Rep., ARCSL-CR-81-003 (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Ground, MD, Nov.1981).

R. T. Wang, “Extinction by Dumbells and Chains of Spheres,” in Proceedings, 1983 Scientific Conference on Obscuration and Aerosol Research, J. Farmer, R. H. Kohl, Eds. (U.S. Army Armament, Munitions, & Chemical Command, Aberdeen Proving Grounds, MD., 1984).

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (1)

J. H. Bruning, Y. T. Lo, “Multiple Scattering of EM Waves by Spheres Part I—Multipole Expansion and Ray-Optical Solution,” IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

Opt. Lett. (2)

Other (3)

J. H. Bruning, Y. T. Lo, “Multiple Scattering by Spheres,” Tech. Rep. 69-5 (Antenna Laboratory, U. Illinois, Urbana, 1969).

D. W. Schuerman, R. T. Wang, “Experimental Results of Multiple Scattering,” Final Rep., ARCSL-CR-81-003 (U.S. Army Chemical Systems Laboratory, Aberdeen Proving Ground, MD, Nov.1981).

R. T. Wang, “Extinction by Dumbells and Chains of Spheres,” in Proceedings, 1983 Scientific Conference on Obscuration and Aerosol Research, J. Farmer, R. H. Kohl, Eds. (U.S. Army Armament, Munitions, & Chemical Command, Aberdeen Proving Grounds, MD., 1984).

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Figures (10)

Fig. 1
Fig. 1

Scattering geometry.

Fig. 2
Fig. 2

Plot of intensity vs α illustrating the effect of both orientation and separation of the two-sphere system on the scattered fields. Plots of the interference pattern of two noninteracting spheres (n.i.s.) are also shown for the two separations considered to better understand the effects of dependent scattering. Since the exact calculations parallel the experimental results quite closely, the same dashed line is used to identify those calculations for both separations: (a), the case of γ = π/2; (b) that of γ = 0.

Fig. 3
Fig. 3

Same as in Fig. 2 except β = 90°.

Fig. 4
Fig. 4

Same as in Fig. 2 except β = 110°.

Fig. 5
Fig. 5

P-Q plots for the case of contacting spheres. The orientation angle α ranges from 0 to 90° in steps of 5° with α = 0° corresponding to the point where the two polarizations converge. The diamond corresponds to the case of noninteracting spheres. Since the observations are made in the forward direction, the values of P and Q for this latter case are independent of α and are also equal to the values calculated for a single sphere provided that one consistently normalizes both P and Q to the maximum geometric cross section of the particle.

Fig. 6
Fig. 6

Same as in Fig. 5 but with kd = 9.68.

Fig. 7
Fig. 7

Müller matrix elements for the particle orientation α = 0. For all orientations it was found that, as in the case of a single sphere, P43 = −P34 and P22 = P11 when the field point remained in the x-z plane. P11 was used to normalize all remaining elements.

Fig. 8
Fig. 8

Same as in Fig. 7 except α = 45°

Fig. 9
Fig. 9

Same as in Fig. 7 except α = 90°

Fig. 10
Fig. 10

Orientation average of the above matrix elements. 〈P11〉 was obtained from an average of scattered fields, whereas all other elements were averaged directly and then normalized against 〈P11〉.

Equations (7)

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E a b = i exp ( i k r ) k r [ S a ( k r , θ , ϕ ; α ) + exp ( - i k d cos θ ) S b ( k r , θ , ϕ ; α ) ] = i exp ( i k r ) k r S a ( k r , θ + α , ϕ ) { 1 + exp [ i k d ( cos α - cos θ ) ] } .
Q = 4 π k 2 G Re [ S γ ( β = 0 ) ] .
Q = 2 ( k a ) 2 Re [ S γ ( β = 0 ) ] .
P = 2 ( k a ) 2 Im [ S γ ( β ) ] .
P ˜ = [ P 11 P 12 0 0 P 12 P 11 0 0 0 0 P 33 P 34 0 0 - P 34 P 33 ] ,
P 11 = ( S 0 2 + S π / 2 2 ) / 2 , P 12 = ( S 0 2 - S π / 2 2 ) / 2 , P 33 = Re ( S π / 2 S 0 * ) , and P 34 = Im ( S 0 S π / 2 * ) .
( E s E s ) = exp ( i k r ) i k r [ S 2 ( = S 0 ) S 3 S 4 S 1 ( = S π / 2 ) ] ( E i E i ) .

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