Abstract

Arbitrary electromagnetic (EM) scattering of a zero-order Bessel beam by a homogeneous water sphere in air is investigated. The radial components of the electric and magnetic scattering fields are expressed using a partial wave series involving the beam-shape coefficients, scattering coefficients of the sphere, and half-conical angle of the wavenumber components of the beam. The 3D scattering directivity plots in the far-field region are evaluated using a numerical integration procedure. It is shown here that shifting the sphere off the axis of wave propagation breaks the symmetry in the directivity patterns. Moreover, the scattering strongly depends on the half-cone angle of the beam. This investigation could provide a useful test of finite element codes for the evaluation of EM scattering and radiation forces, which are important in optical tweezers and related particle manipulation applications.

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References

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  1. G. Mie, Ann. Phys. 330, 377 (1908).
    [CrossRef]
  2. H. C. van de Hulst, Light Scattering by Small Particles(Wiley, 1957).
  3. P. W. Dusel, M. Kerker, and D. D. Cooke, J. Opt. Soc. Am. 69, 55 (1979).
    [CrossRef]
  4. R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Springer-Verlag, 1982).
  5. J. A. Lock, Appl. Opt. 34, 559 (1995).
    [CrossRef] [PubMed]
  6. J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 64, 1632 (1988).
    [CrossRef]
  7. J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  8. Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
    [CrossRef]
  9. J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
    [CrossRef]
  10. Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555 (1995).
    [CrossRef]
  11. S. R. Mishra, Opt. Commun. 85, 159 (1991).
    [CrossRef]
  12. S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 55, 2709 (1989).
    [CrossRef]
  13. S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 59, 1798 (1991).
    [CrossRef]
  14. G. M. Hale and M. R. Querry, Appl. Opt. 12, 555(1973).
    [CrossRef] [PubMed]
  15. T. Rother, in Electromagnetic Wave Scattering on Nonspherical Particles (Springer, 2009), pp. 197–233.
    [CrossRef]

1998 (1)

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

1995 (2)

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

J. A. Lock, Appl. Opt. 34, 559 (1995).
[CrossRef] [PubMed]

1991 (2)

S. R. Mishra, Opt. Commun. 85, 159 (1991).
[CrossRef]

S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 59, 1798 (1991).
[CrossRef]

1989 (2)

S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 55, 2709 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

1988 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 64, 1632 (1988).
[CrossRef]

1987 (1)

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

1979 (1)

1973 (1)

1908 (1)

G. Mie, Ann. Phys. 330, 377 (1908).
[CrossRef]

Alexander, D. R.

S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 59, 1798 (1991).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 55, 2709 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 64, 1632 (1988).
[CrossRef]

Barton, J. P.

S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 59, 1798 (1991).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 55, 2709 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 64, 1632 (1988).
[CrossRef]

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

Cooke, D. D.

Durnin, J.

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Dusel, P. W.

Eberly, J. H.

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Hale, G. M.

Kerker, M.

Lock, J. A.

Miceli, J.

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Mie, G.

G. Mie, Ann. Phys. 330, 377 (1908).
[CrossRef]

Mishra, S. R.

S. R. Mishra, Opt. Commun. 85, 159 (1991).
[CrossRef]

Newton, R. G.

R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Springer-Verlag, 1982).

Olivík, M.

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

Querry, M. R.

Rother, T.

T. Rother, in Electromagnetic Wave Scattering on Nonspherical Particles (Springer, 2009), pp. 197–233.
[CrossRef]

Schaub, S. A.

S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 59, 1798 (1991).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 55, 2709 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 64, 1632 (1988).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles(Wiley, 1957).

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

Ann. Phys. (1)

G. Mie, Ann. Phys. 330, 377 (1908).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 55, 2709 (1989).
[CrossRef]

S. A. Schaub, J. P. Barton, and D. R. Alexander, Appl. Phys. Lett. 59, 1798 (1991).
[CrossRef]

J. Appl. Phys. (2)

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 64, 1632 (1988).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

J. Mod. Opt. (1)

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

S. R. Mishra, Opt. Commun. 85, 159 (1991).
[CrossRef]

Phys. Rev. Lett. (1)

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Other (3)

H. C. van de Hulst, Light Scattering by Small Particles(Wiley, 1957).

R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Springer-Verlag, 1982).

T. Rother, in Electromagnetic Wave Scattering on Nonspherical Particles (Springer, 2009), pp. 197–233.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Magnitude of the far-field scattering form functions of a plane EM wave (i.e., β = 0 ° ) incident upon a water sphere for the scattered electric [(a)–(c)] and magnetic [(d)–(f)] far fields. The plots in (a), (d) correspond to k a = 1.5 ; (b), (e) to k a = 5 ; and (c), (f) to k a = 12 , respectively.

Fig. 2
Fig. 2

Magnitude of the far-field scattering form functions for a zero-order Bessel EM beam with β = 55 ° , for the scattered electric [(a)–(c)] and magnetic [(d)–(f)] far fields. The plots in (a), (d) correspond to k a = 1.5 , (b), (e) to k a = 5 ; and (c), (f) to k a = 12 , respectively.

Fig. 3
Fig. 3

The same as in Fig. 3; however, the sphere is shifted off the axis of the incident beam in both the x and y directions such that the offset (in arbitrary units) is ( x , y ) offset = ( 0.75 ; 0.75 ) .

Fig. 4
Fig. 4

Magnitude of the far-field scattering form functions for the scattered electric [(a)–(c)] and magnetic [(d)–(f)] far fields from a homogeneous water sphere placed off axially [ ( x , y ) offset = ( 0.75 ; 0.75 ) ] with respect to the axis of an incident zero-order Bessel EM beam at k a = 12 for various values of the half-cone angle β. In (a), (d)  β = 15 ° , in (b), (e)  β = 40 ° , and in (c), (f)  β = 75 ° , respectively.

Equations (17)

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E r s c ( r , θ , ϕ ) = a 2 r 2 n = 1 m = n n n ( n + 1 ) a n m ( k a ) ξ n ( 1 ) ( k r ) Y n m ( θ , ϕ ) ,
H r s c ( r , θ , ϕ ) = a 2 r 2 n = 1 m = n n n ( n + 1 ) b n m ( k a ) ξ n ( 1 ) ( k r ) Y n m ( θ , ϕ ) ,
a n m = [ ψ n ( n ¯ k a ) ψ n ( k a ) n ¯ ψ n ( n ¯ k a ) ψ n ( k a ) n ¯ ψ n ( n ¯ k a ) ξ n ( 1 ) ( k a ) ψ n ( n ¯ k a ) ξ n ( 1 ) ( k a ) ] A n m ,
b n m = [ n ¯ ψ n ( n ¯ k a ) ψ n ( k a ) ψ n ( n ¯ k a ) ψ n ( k a ) ψ n ( n ¯ k a ) ξ n ( 1 ) ( k a ) n ¯ ψ n ( n ¯ k a ) ξ n ( 1 ) ( k a ) ] B n m ,
A n m ( k a ) = 1 n ( n + 1 ) ψ n ( k a ) 0 2 π 0 π sin θ E r inc ( a , θ , ϕ ) Y n m * ( θ , ϕ ) d θ d ϕ ,
B n m ( k a ) = 1 n ( n + 1 ) ψ n ( k a ) 0 2 π 0 π sin θ H r inc ( a , θ , ϕ ) Y n m * ( θ , ϕ ) d θ d ϕ ,
{ E r inc ( a , θ , ϕ ) H r inc ( a , θ , ϕ ) } = { E x inc H x inc } r = a sin θ cos ϕ + { E y inc H y inc } r = a sin θ sin ϕ + { E z inc H z inc } r = a cos θ ,
E x inc = 1 2 E 0 [ ( 1 + k z k k R 2 x 2 k 2 R 2 ) J 0 ( k R R ) k R ( y 2 x 2 ) k 2 R 3 J 1 ( k R R ) ] exp ( i k z z ) ,
E y inc = 1 2 E 0 x y [ 2 k R k 2 R 3 J 1 ( k R R ) ( k R 2 k 2 R 2 ) J 0 ( k R R ) ] exp ( i k z z ) ,
E z inc = 1 2 i E 0 x k R ( 1 + k z k ) k R J 1 ( k R R ) exp ( i k z z ) .
H x inc = ε E y inc ,
H y inc = ε 1 2 E 0 [ ( 1 + k z k k R 2 y 2 k 2 R 2 ) J 0 ( k R R ) k R ( x 2 y 2 ) k 2 R 3 J 1 ( k R R ) ] exp ( i k z z ) ,
H z inc = ε 1 2 i E 0 y k R ( 1 + k z k ) k R J 1 ( k R R ) exp ( i k z z ) .
{ ψ n ( q ) sin ( q n π / 2 ) , ξ n ( 1 ) ( q ) i ( n + 1 ) exp ( i q ) .
f E ( k a , θ , ϕ ) = n = 1 m = n n n ( n + 1 ) i ( n + 1 ) a n m Y n m ( θ , ϕ ) ,
f H ( k a , θ , ϕ ) = n = 1 m = n n n ( n + 1 ) i ( n + 1 ) b n m Y n m ( θ , ϕ ) .
A n m ( k a ) | plane wave = i ( n + 1 ) ( k a ) 2 π ( 2 n + 1 ) n ( n + 1 ) δ m 1 ,

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