Abstract

We investigate the optical forces acting on a metallic nanoparticle when the nanoparticle is introduced within a photonic nanojet (PNJ). Optical forces at resonance and off-resonance conditions of the microcylinder or nanoparticle are investigated. Under proper polarization conditions, the whispering gallery mode can be excited in the microcylinder, even at off resonance provided that scattering from the nanoparticle is strong enough. The optical forces are enhanced at resonance either of the single microcylinder or of the nanoparticle with respect to the forces under off-resonant illuminations. We found that the optical forces acting on the nanoparticle depend strongly on the dielectric permittivity of the nanoparticle, as well as on the intensity and the beam width of the PNJ. Hence, metallic sub-wavelength nanoparticle can be efficiently trapped by PNJs. Furthermore, the PNJ’s attractive force can be simply changed to a repulsive force by varying the polarization of the incident beam. The changed sign of the force is related to the particle’s polarizability and the excitation of localized surface plasmons in the nanoparticle.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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2007

2006

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, "Experimental confirmation of backscattering enhancement induced by a photonic jet," Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

V. Sandoghdar, E. Klotzsch, V. Jacobsen, A. Renn, U. Hakanson, M. Agio, I. Gerhardt, J. Seelig, and G. Wrigge, "Optical detection of very small nonfluorescent nanoparticles," CHIMIA 60, 761-764 (2006).
[CrossRef]

2005

2004

2003

2000

P. C. Chaumet and M. Nieto-Vesperinas, "Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate," Phys. Rev. B. 61, 14119-14127 (2000).
[CrossRef]

1972

P. Johnson and R. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4730-4739 (1972).
[CrossRef]

Agio, M.

V. Sandoghdar, E. Klotzsch, V. Jacobsen, A. Renn, U. Hakanson, M. Agio, I. Gerhardt, J. Seelig, and G. Wrigge, "Optical detection of very small nonfluorescent nanoparticles," CHIMIA 60, 761-764 (2006).
[CrossRef]

Arias-Gonzalez, J. R.

Backman, V.

Challener, W. A.

Chaumet, P. C.

P. C. Chaumet and M. Nieto-Vesperinas, "Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate," Phys. Rev. B. 61, 14119-14127 (2000).
[CrossRef]

Chen, Z.

Christy, R.

P. Johnson and R. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4730-4739 (1972).
[CrossRef]

Gerhardt, I.

V. Sandoghdar, E. Klotzsch, V. Jacobsen, A. Renn, U. Hakanson, M. Agio, I. Gerhardt, J. Seelig, and G. Wrigge, "Optical detection of very small nonfluorescent nanoparticles," CHIMIA 60, 761-764 (2006).
[CrossRef]

Hakanson, U.

V. Sandoghdar, E. Klotzsch, V. Jacobsen, A. Renn, U. Hakanson, M. Agio, I. Gerhardt, J. Seelig, and G. Wrigge, "Optical detection of very small nonfluorescent nanoparticles," CHIMIA 60, 761-764 (2006).
[CrossRef]

Heifetz, A.

A. Heifetz, J. J. Simpson, S. C. Kong, A. Taflove, and V. Backman, "Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere," Opt. Express 15, 17334-17342 (2007).
[CrossRef] [PubMed]

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, "Experimental confirmation of backscattering enhancement induced by a photonic jet," Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

Herzig, H. P.

Huang, K.

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, "Experimental confirmation of backscattering enhancement induced by a photonic jet," Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

Itagi, V.

Jacobsen, V.

V. Sandoghdar, E. Klotzsch, V. Jacobsen, A. Renn, U. Hakanson, M. Agio, I. Gerhardt, J. Seelig, and G. Wrigge, "Optical detection of very small nonfluorescent nanoparticles," CHIMIA 60, 761-764 (2006).
[CrossRef]

Johnson, P.

P. Johnson and R. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4730-4739 (1972).
[CrossRef]

Klotzsch, E.

V. Sandoghdar, E. Klotzsch, V. Jacobsen, A. Renn, U. Hakanson, M. Agio, I. Gerhardt, J. Seelig, and G. Wrigge, "Optical detection of very small nonfluorescent nanoparticles," CHIMIA 60, 761-764 (2006).
[CrossRef]

Kong, S. C.

Li, X.

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, "Experimental confirmation of backscattering enhancement induced by a photonic jet," Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

X. Li, Z. Chen, A. Taflove, and V. Backman, "Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets," Opt. Express 13, 526-533 (2005).
[CrossRef] [PubMed]

Nieto-Vesperinas, M.

Quidant, R.

Ratner, M. A.

Renn, A.

V. Sandoghdar, E. Klotzsch, V. Jacobsen, A. Renn, U. Hakanson, M. Agio, I. Gerhardt, J. Seelig, and G. Wrigge, "Optical detection of very small nonfluorescent nanoparticles," CHIMIA 60, 761-764 (2006).
[CrossRef]

Rockstuhl, C.

Sahakian, A. V.

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, "Experimental confirmation of backscattering enhancement induced by a photonic jet," Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

Sandoghdar, V.

V. Sandoghdar, E. Klotzsch, V. Jacobsen, A. Renn, U. Hakanson, M. Agio, I. Gerhardt, J. Seelig, and G. Wrigge, "Optical detection of very small nonfluorescent nanoparticles," CHIMIA 60, 761-764 (2006).
[CrossRef]

Seelig, J.

V. Sandoghdar, E. Klotzsch, V. Jacobsen, A. Renn, U. Hakanson, M. Agio, I. Gerhardt, J. Seelig, and G. Wrigge, "Optical detection of very small nonfluorescent nanoparticles," CHIMIA 60, 761-764 (2006).
[CrossRef]

Simpson, J. J.

Taflove, A.

Wong, V.

Wrigge, G.

V. Sandoghdar, E. Klotzsch, V. Jacobsen, A. Renn, U. Hakanson, M. Agio, I. Gerhardt, J. Seelig, and G. Wrigge, "Optical detection of very small nonfluorescent nanoparticles," CHIMIA 60, 761-764 (2006).
[CrossRef]

Zelenina, A. S.

Appl. Phys. Lett.

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, "Experimental confirmation of backscattering enhancement induced by a photonic jet," Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

CHIMIA

V. Sandoghdar, E. Klotzsch, V. Jacobsen, A. Renn, U. Hakanson, M. Agio, I. Gerhardt, J. Seelig, and G. Wrigge, "Optical detection of very small nonfluorescent nanoparticles," CHIMIA 60, 761-764 (2006).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. B

P. Johnson and R. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4730-4739 (1972).
[CrossRef]

Phys. Rev. B.

P. C. Chaumet and M. Nieto-Vesperinas, "Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate," Phys. Rev. B. 61, 14119-14127 (2000).
[CrossRef]

Other

Ch. Hafner, Post-Modern Electromagnetics (Wiley, Chichester, 1999).

http://max-1.ethz.ch.

Supplementary Material (2)

» Media 1: AVI (1356 KB)     
» Media 2: AVI (1587 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Schematic drawing of the overall structure. The separation between the dielectric microcylinder and the particle is indicated by the distance l. The picture shows the time-averaged Poynting vector field for a Ez-polarized plane wave excitation from the left at an operation wavelength of 400 nm. The emergent PNJ is clearly observed.

Fig. 2.
Fig. 2.

(a) (Media 1) Evolution of the Poynting vector field when a metallic nanoparticle (indicated by the small red circle) is crossing the PNJ generated by the dielectric microcylinder (indicated by the green circle). The silver nanoparticle has a diameter of 120 nm and is moving downwards along the y-direction. The overall structure is excited by an Ez-polarized plane wave from the left having an operation wavelength of 400 nm. The horizontal separation l between the particle and the microcylinder is 40 nm. (b) Components of the optically induced force exerted on the nanoparticle while performing the aforementioned transit through the PNJ.

Fig. 3.
Fig. 3.

(a) Calculation of the optically induced force on the silver particle (diameter 20 nm) when the nanoparticle is moving downwards along the y-direction with a horizontal separation l=300 nm for the configuration depicted in Fig. 2(a). (b) The same setting but now with a 10 nm separation distance. In both cases the structure is excited by a plane wave with E-polarization from the left at an operation wavelength of 400 nm.

Fig. 4.
Fig. 4.

(a) (Media 2) Distribution of the electric field (Ez) within the microcylinder-nanoparticle system when the metallic nanoparticle (diameter 120 nm) is moving along the x-axis. (b) Evolution of the x-component of the resulting optically induced force for increasing separation distances. The overall structure is excited by an Ez-polarized plane wave from the left at an operation wavelength of 400 nm.

Fig. 5.
Fig. 5.

Evolution of the optically induced force (x-component) on the metallic nanoparticle for the case where the particle is moving along x-axis. The particle’s diameter is 20 nm. The overall structure is illuminated by a Hz-polarized plane wave for three different operating wavelengths.

Fig. 6.
Fig. 6.

(a) Computed lateral field intensity profiles when the particle is moving along the y-direction, the configuration shown in Fig. 2(a) is used here too. The separation distance between the microcylinder and nanoparticle is 40 nm in x-direction and the diameter of the silver nanoparticle is 120 nm. The wavelength is 400 nm. The fields are monitored on the x axis at a distance of 2.1 µm from the surface of the microcylinder; (b) The optically induced force for H-polarization [same configuration as in Fig. 2(a)].

Fig. 7.
Fig. 7.

Calculation of the optically induced force under resonance conditions. (a) For E-polarization; the resonance wavelength of the microcylinder is 383nm. Inset: electric field (Ez component) distribution of the WGM. (b) For H-polarization; the resonance wavelength of the nanoparticle is 350nm. Inset: electric field distribution of the metallic nanoparticle at 350nm.

Equations (5)

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E zi ( r , φ ) = A i 0 E J 0 ( kr ) + n = 1 N i A in E J n ( kr ) cos ( n φ ) + B in E J n ( kr ) sin ( n φ )
H zi ( r , φ ) = A i 0 H J 0 ( kr ) + n = 1 N i A in H J n ( kr ) cos ( n φ ) + B in H J n ( kr ) sin ( n φ )
E zi ( r , φ ) = a i 0 E H 0 ( kr ) + n = 1 N i a in H H n ( kr ) cos ( n φ ) + a in E H n ( kr ) sin ( n φ )
H zi ( r , φ ) = a i 0 H H 0 ( kr ) + n = 1 N i a in H H n ( kr ) cos ( n φ ) + b in H H n ( kr ) sin ( n φ )
F = s [ ε 2 · Re { ( E . n ) E * } ε 4 · ( E · E * ) n + μ 2 · Re { ( H · n ) n * } μ 4 · ( H · H * ) n ] · d A

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