Abstract

The power-flow lines of light interacting with a metallic nanoparticle, in the proximity of its plasmon resonance, form whirlpool-like nanoscale optical vortices. These vortices were independently observed using analytical Mie theory and 3D finite element numerical modelling of the Maxwell equations. Two different types of vortex have been detected. The outward vortex first penetrates the particle near its centerline then, on exiting the particle, the flow-lines turn away from the centerline and enter a spiral trajectory. Outward vortices are seen for the wavelengths shorter then the plasmon resonance. For the wavelengths longer that the plasmon resonance the vortex is inward: the power-flow lines pass around the sides of the particle before turning towards the centerline and entering the particle to begin their spiral trajectory.

© 2005 Optical Society of America

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References

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Ann. Physik

G. Mie, �??Beitrage zur optik truber medien, speziell kolloida ler metallosungen,�?? Ann. Physik 25, 377 (1908).
[CrossRef]

Appl. Phys. Lett.

H. Kuwata, H. Tamaru, K. Esumi, et. al., �??Resonant light scattering from metal nanoparticles: Practical analysis beyond Rayleigh approximation,�?? Appl. Phys. Lett. 83, 4625 (2003).
[CrossRef]

IBM J. Res. Dev.

J. V. Dave, �??Scattering of electromagnetic radiation by a large, absorbing sphere,�?? IBM J. Res. Dev. 13, 302 (1969).
[CrossRef]

J. Opt. A

H. F. Schouten, T. D. Visser, and G. Gbur, �??Diffraction of light at slits in plates of different materials,�?? J. Opt. A 6, (2004).
[CrossRef]

Special issue on singular optics, edited by M. V. Berry, M. Dennis, and M. Soskin, J. Opt. A 6 (2004).

J. Opt. B

H. F. Schouten, T. D. Visser, and D. Lenstra, �??Optical vortices near sub-wavelength structures,�?? J. Opt. B 6, (2004).
[CrossRef]

J. Opt. Soc. Am. A

Nature Materials

J. R. Krenn, �??Nanoparticle waveguides: watching energy transfer,�?? Nature Materials 2, 210�??211 (2003).
[CrossRef] [PubMed]

New. J. Phys.

C. Sonnichsen, T. Franzl, and T. Wilk, �??Plasmon resonances in large noble-metal clusters,�?? New. J. Phys. 4, 93.1�??93.8 (2002).
[CrossRef]

Phil. Trans. R. Soc. Lond. A

M. V. Berry, �??Exuberant interference: Rainbows, tides, edges, (de)coherence,�?? Phil. Trans. R. Soc. Lond. A 360, 1023�??1037 (2002).
[CrossRef]

Phys. Rev. B

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, �??Electromagnetic energy transfer and switching in nanoparticle chain-arrays below the diffraction limit,�?? Phys. Rev. B 62, R16356 (2000).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, �??Optical pulse propagation in metal nanoparticle chain waveguides,�?? Phys. Rev. B 67, 205402 (2003).
[CrossRef]

Z. B.Wang, B. S. Luk�??yanchuk, M. H. Hong, et. al., �??Energy flow around a small particle investigated by classical Mie theory,�?? Phys. Rev. B 70, 035418 (2004).
[CrossRef]

Phys. Rev. Lett.

J. R. Krenn, A. Dereux, and J. C.Weeber, �??Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,�?? Phys. Rev. Lett. 82, 2590�??2593 (1999).
[CrossRef]

Other

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

Handbook of Chemistry and Physics, edited by R. Lide (CRC Press, New York, 2000).

J. Jin, The Finite Element Method in Electromagnetics (John Wiley and Sons, New York, 2002).

M. Dorobantu, �??Efficient streamline computations on unstructured grids�??, Department of Numerical Analysis and Computing Science, Royal Institute for Technology, Stockholm (1997).

H. C. van der Hulst, Light Scattering by Small Particles (Wiley, New York, 1983).

Supplementary Material (2)

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Figures (3)

Fig. 1.
Fig. 1.

Map showing values of the real and imaginary parts of the dielectric constant (in red) at which vortex field structures appear. The dashed line at ε′ ~ -2.2 indicates the position of the plasmon resonance in a spherical nanoparticle with r ≈ 20 nm (λ/r = 20). The solid lines show the dispersion characteristics of the dielectric properties of silver.

Fig. 2.
Fig. 2.

[Movie 2.5 MB, 10.5 MB version] Mie Theory: powerflow distribution around a spherical nanoparticle with a radius of approximately 20 nm (λ/r = 20) in the plane containing the directions of propagation (from left to right) and polarization of the incident light. The colors indicate the absolute value of the Poynting vector, the white lines show the direction of powerflow. (a)ε=-2.0+i10.0,λ= 400 nm; (b)ε= -2.0+i1.0,λ= 400 nm; (c) ε= -2.0+i0.28 — the dielectric coefficient of silver at λ= 354 nm. Red dashed lines indicate outward vortex structure; (d) ε = -2.71 + i0.25 — the dielectric coefficient of silver at λ = 367 nm. Red dashed lines indicate inward vortex structure [15].

Fig. 3.
Fig. 3.

3D finite element modelling: powerflow distribution around an oblate spheroidal nanoparticle (with a semi-major axial radius of approximately 20 nm (λ/r = 20) and an aspect ratio of 2) in the plane containing the directions of propagation (from left to right) and polarization of the incident light. The colors indicate the absolute value of the Poynting vector, the white lines show the direction of powerflow. (a)ε=-3.52+i10.0,λ= 400 nm; (b)ε=-3.52+i10.0,λ= 400 nm; (c)ε= -3.37+i0.2 — the dielectric coefficient of silver at λ = 380 nm. Red dashed lines indicate outward vortex structure; (d) ε= -4.0+i0.2 — the dielectric coefficient of silver at λ = 392 nm. Red dashed lines indicate inward vortex structure [15].

Equations (23)

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2 E + k 2 E = 0 , 2 H + k 2 H = 0 ,
E ir = n = 1 E n ( cos ϕn ( n + 1 ) sin θ π n ( cos θ ) j n ( kr ) kr ) .
E = n = 1 E n ( cos ϕ π n ( cos θ ) j n ( kr ) i cos ϕ τ n ( cos θ ) [ kr j n ( kr ) ] kr ) .
E = n = 1 E n ( sin ϕ τ n ( cos θ ) j n ( kr ) + i sin ϕ π n ( cos θ ) [ kr j n ( kr ) ] kr ) .
E ir = k ω n = 1 E n ( i sin ϕn ( n + 1 ) sin θ π n ( cos θ ) j n ( kr ) kr ) .
H = k ω n = 1 E n ( sin ϕ π n ( cos θ ) j n ( kr ) + i sin ϕ τ n ( cos θ ) [ kr j n ( kr ) ] kr ) .
H = k ω n = 1 E n ( cos ϕ τ n ( cos θ ) j n ( kr ) + i cos ϕ π n ( cos θ ) [ kr j n ( kr ) ] kr ) .
E 1 r = n = 1 E n ( i d n cos ϕn ( n + 1 ) sin θ π n ( cos θ ) j n ( k 1 r ) k 1 r ) .
E = n = 1 E n ( c n cos ϕ π n ( cos θ ) j n ( k 1 r ) i d n cos ϕ τ n ( cos θ ) [ k 1 r j n ( k 1 r ) ] k 1 r ) .
E = n = 1 E n ( c n sin ϕ τ n ( cos θ ) j n ( kr ) + i d n sin ϕ π n ( cos θ ) [ k 1 r j n ( k 1 r ) ] k 1 r ) .
H ir = k 1 ω n = 1 E n ( i c n sin ϕn ( n + 1 ) sin θ π n ( cos θ ) j n ( k 1 r ) k 1 r ) .
H = k 1 ω n = 1 E n ( d n sin ϕ π n ( cos θ ) j n ( kr ) + i c n sin ϕ τ n ( cos θ ) [ k 1 r j n ( k 1 r ) ] k 1 r ) .
H = k 1 ω n = 1 E n ( d n cos ϕ τ n ( cos θ ) j n ( kr ) + i c n cos ϕ π n ( cos θ ) [ k 1 r j n ( k 1 r ) ] k 1 r ) .
E sr = n = 1 E n ( i a n cos ϕn ( n + 1 ) sin θ π n ( cos θ ) h n ( kr ) kr ) .
E = n = 1 E n ( b n cos ϕ π n ( cos θ ) h n ( kr ) + i a n cos ϕ τ n ( cos θ ) [ k r h n ( k r ) ] k r ) .
E = n = 1 E n ( b n sin ϕ τ n ( cos θ ) h n ( kr ) i a n sin ϕ π n ( cos θ ) [ kr h n ( kr ) ] kr ) .
H ir = k ω n = 1 E n ( i b n cos ϕn ( n + 1 ) sin θ π n ( cos θ ) h n ( kr ) kr ) .
H = k ω n = 1 E n ( a n sin ϕ π n ( cos θ ) h n ( kr ) + i b n sin ϕ τ n ( cos θ ) [ kr h n ( kr ) ] kr ) .
H = k ω n = 1 E n ( a n cos ϕ τ n ( cos θ ) h n ( kr ) + i b n cos ϕ π n ( cos θ ) [ kr h n ( kr ) ] kr ) .
a n = m 2 j n ( mx ) [ x j n ( x ) ] j n ( x ) [ mx j n ( mx ) ] m 2 j n ( mx ) [ x h n ( x ) ] h n ( x ) [ mx j n ( mx ) ] ,
b n = j n ( mx ) [ x j n ( x ) ] j n ( x ) [ mx j n ( mx ) ] j n ( mx ) [ x h n ( x ) ] h n ( x ) [ mx j n ( mx ) ] ,
c n = j n ( x ) [ x h n ( x ) ] h n ( x ) [ x j n ( mx ) ] j n ( mx ) [ x h n ( x ) ] h n ( x ) [ mx j n ( mx ) ] .
d n = m j n ( x ) [ x h n ( x ) ] m h n ( x ) [ x j n ( mx ) ] m 2 j n ( mx ) [ x h n ( x ) ] h n ( x ) [ mx j n ( mx ) ] .

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