Abstract

Advanced science and technology frequently encounters the need to detect particles in the micrometer and nanometer range of a given composition. While the scattering process of light by small particles is well documented, most conventional analytic methods employ wide illumination of large ensembles of particles. With such an approach, no information can be obtained about single particles due to their weak interaction. In this paper, we show that single particles can be classified with respect to their material composition by analyzing the scattering pattern of a focused Gaussian beam.

© 2011 Optical Society of America

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References

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  1. G. Gouesbet, B. Maheu, and G. Grehan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bormwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443(1988).
    [CrossRef]
  2. M. Kerker, “Scattering by a sphere,” in The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), pp. 27–93.
  3. M. Kerker, “The scattering functions for spheres,” in The Scattering of Light and Other Electromagnetic Radiation(Academic, 1969), pp. 97–185.
  4. H. C. van de Hulst, “Rigorous scattering theory for spheres of arbitrary size (Mie theory),” in Light Scattering by Small Particles (Dover, 1981), pp. 114–130.
  5. H. C. van de Hulst, “Non-absorbing spheres,” in Light Scattering by Small Particles (Dover, 1981), pp. 131–171.
  6. C.-W. Qiu and L.-W. Li, “Electromagnetic scattering by 3-D general anisotropic objects: a Hertz–Debye potential formulation,” in 2005 IEEE Antennas and Propagation Society International Symposium (IEEE, 2005), pp. 422–425.
  7. E. Hemo, B. Spektor, and J. Shamir, “Scattering of singular beams by subwavelength objects,” Appl. Opt. 50, 33–42(2011).
    [CrossRef] [PubMed]

2011

1988

Gouesbet, G.

Grehan, G.

Hemo, E.

Kerker, M.

M. Kerker, “Scattering by a sphere,” in The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), pp. 27–93.

M. Kerker, “The scattering functions for spheres,” in The Scattering of Light and Other Electromagnetic Radiation(Academic, 1969), pp. 97–185.

Li, L.-W.

C.-W. Qiu and L.-W. Li, “Electromagnetic scattering by 3-D general anisotropic objects: a Hertz–Debye potential formulation,” in 2005 IEEE Antennas and Propagation Society International Symposium (IEEE, 2005), pp. 422–425.

Maheu, B.

Qiu, C.-W.

C.-W. Qiu and L.-W. Li, “Electromagnetic scattering by 3-D general anisotropic objects: a Hertz–Debye potential formulation,” in 2005 IEEE Antennas and Propagation Society International Symposium (IEEE, 2005), pp. 422–425.

Shamir, J.

Spektor, B.

van de Hulst, H. C.

H. C. van de Hulst, “Rigorous scattering theory for spheres of arbitrary size (Mie theory),” in Light Scattering by Small Particles (Dover, 1981), pp. 114–130.

H. C. van de Hulst, “Non-absorbing spheres,” in Light Scattering by Small Particles (Dover, 1981), pp. 131–171.

Appl. Opt.

J. Opt. Soc. Am. A

Other

M. Kerker, “Scattering by a sphere,” in The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), pp. 27–93.

M. Kerker, “The scattering functions for spheres,” in The Scattering of Light and Other Electromagnetic Radiation(Academic, 1969), pp. 97–185.

H. C. van de Hulst, “Rigorous scattering theory for spheres of arbitrary size (Mie theory),” in Light Scattering by Small Particles (Dover, 1981), pp. 114–130.

H. C. van de Hulst, “Non-absorbing spheres,” in Light Scattering by Small Particles (Dover, 1981), pp. 131–171.

C.-W. Qiu and L.-W. Li, “Electromagnetic scattering by 3-D general anisotropic objects: a Hertz–Debye potential formulation,” in 2005 IEEE Antennas and Propagation Society International Symposium (IEEE, 2005), pp. 422–425.

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Figures (6)

Fig. 1
Fig. 1

Definition of the coordinate system.

Fig. 2
Fig. 2

Relative phase of the Mie coefficients for several materials. The complex refractive indices are indicated in the inset.

Fig. 3
Fig. 3

Scattered intensities from a sphere with a = 100 nm composed of several materials illuminated with a wavelength of 405 nm .

Fig. 4
Fig. 4

Binary version of the scattered intensity distributions of Fig. 3.

Fig. 5
Fig. 5

Scattered intensity distributions for spheres with a = 300 nm with different material composition.

Fig. 6
Fig. 6

Detector architecture at a nominal 10 mm distance from the scatterer.

Tables (1)

Tables Icon

Table 1 List of Calculated NIR Values for Selected Materials

Equations (14)

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2 U r 2 + k 2 U + 1 r 2 sin ( θ ) θ ( sin ( θ ) U θ ) + 1 r 2 sin 2 ( θ ) 2 U φ 2 = 0 .
E r = k E 0 n = 1 m = n + n c n g n , TM m a n · [ ζ n ( k r ) + ζ n ( k r ) ] P n | m | ( cos θ ) exp ( ı m φ ) ,
c n = 1 ı k ( ı ) n 2 n + 1 n ( n + 1 )
ζ n ( k r ) = k r · h n ( 2 ) ( k r ) = ( π k r 2 ) 1 2 H n + 1 2 ( 2 ) ( k r ) ,
E θ = E 0 r n = 1 m = n + n c n exp ( ı m φ ) · [ g n , TM m a n ζ n ( k r ) τ n | m | ( cos θ ) + m g n , TE m b n ζ n ( k r ) Π n | m | ( cos θ ) ] ,
E φ = ı E 0 r n = 1 m = n + n c n exp ( ı m φ ) · [ m g n , TM m a n ζ n ( k r ) Π n | m | ( cos θ ) + g n , TE m b n ζ n ( k r ) τ n | m | ( cos θ ) ] ,
τ n m ( cos θ ) = d d θ P n m ( cos θ ) ,
Π n m ( cos θ ) = P n m ( cos θ ) sin θ .
a n = Ψ n ( x ) Ψ n ( y ) M Ψ n ( x ) Ψ n ( y ) ζ n ( x ) Ψ n ( y ) M ζ n ( x ) Ψ n ( y ) ,
b n = M Ψ n ( x ) Ψ n ( y ) Ψ n ( x ) Ψ n ( y ) M ζ n ( x ) Ψ n ( y ) ζ n ( x ) Ψ n ( y ) ,
E r incident = E 0 k r 2 n = 1 m = n + n c n g n , TM m n ( n + 1 ) · Ψ n ( k r ) P n | m | ( cos θ ) exp ( ı m φ ) ,
H r incident = H 0 k r 2 n = 1 m = n + n c n g n , TE m n ( n + 1 ) · Ψ n ( k r ) P n | m | ( cos θ ) exp ( ı m φ ) ,
NIR = ( P ( d 1 ) + P ( d 2 ) P ( d 3 ) + P ( d 4 ) ) · P ( d 5 ) P ( d 5 ) | no scatterer ,
P ( d i ) = D i ( | E x | 2 + | E y | 2 ) d s ,

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