Abstract

We numerically show that both repulsive and attractive (bipolar) optical forces can be exerted on a dielectric or metallic cylindrical nanoparticle by a totally internal refracted wave. This requires that the particles possesses either a whispering gallery (WG) resonance or a localized surface plasmon (LSP) resonance. We further explore the force spectrum that is governed by competition between the separation-dependent resonant Q factor and the coupling strength of the nanoparticle to the evanescent wave. In spite of a much smaller Q of the LSP as compare to the WG resonances, the metallic particle gains much stronger trapping force.

© 2010 Optical Society of America

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Corrections

J. J. Xiao, H. H. Zheng, Y. X. Sun, and Y. Yao, "Bipolar optical forces on dielectric and metallic nanoparticles by evanescent wave: erratum," Opt. Lett. 35, 1853-1853 (2010)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-35-11-1853

References

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    [CrossRef]
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    [CrossRef]
  18. The TM resonant modes of a circular cylinder of radii a and with refractive index n in vacuum, are determined by the complex roots k̃0a of the transcendental equation Jm′(ka)Hm(k̃0a)−nJm(ka)Hm′(k̃0a)=0, where k̃0=ω̃/c is the vacuum wave number, k=nk0, Jm(x) and Hm(x) the mth order Bessel function and Hankel function of the first kind. The prime indicates derivative with respect to the argument. The solutions of the above equation are obtained in the complex plane of k̃0a. Consequently, the quality factor Q of a resonant mode is Q=−Re(k̃0a)/2 Im(k̃0a).

2009 (4)

K. Wang, E. Schonbrun, and K. B. Crozier, Nano Lett. 9, 2623 (2009).
[CrossRef] [PubMed]

Y. C. Jian, J. J. Xiao, and J. P. Huang, J. Phys. Chem. C 113, 17170 (2009).
[CrossRef]

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 1553 (2009).

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

2008 (1)

2007 (4)

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

T. M. Grzegorczyk and J. A. Kong, Opt. Express 15, 8010 (2007).
[CrossRef] [PubMed]

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, J. Phys. B 40, S249 (2007).
[CrossRef]

2006 (2)

K. Dholakia and P. Reece, Nanotoday 1, 18 (2006).

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, Phys. Rev. Lett. 96, 238101 (2006).
[CrossRef] [PubMed]

2003 (2)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

T. Iida and H. Ishihara, Phys. Rev. Lett. 90, 057403 (2003).
[CrossRef] [PubMed]

1992 (1)

1987 (1)

A. Ashkin and J. Dziedzic, Science 235, 1517 (1987).
[CrossRef] [PubMed]

1983 (1)

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

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Ashkin, A.

A. Ashkin and J. Dziedzic, Science 235, 1517 (1987).
[CrossRef] [PubMed]

Badenes, G.

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, Phys. Rev. Lett. 96, 238101 (2006).
[CrossRef] [PubMed]

Bohren, C. F.

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

Brixner, T.

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, J. Phys. B 40, S249 (2007).
[CrossRef]

Chan, C. T.

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 1553 (2009).

J. J. Xiao and C. T. Chan, J. Opt. Soc. Am. B 25, 1553 (2008).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Crozier, K. B.

K. Wang, E. Schonbrun, and K. B. Crozier, Nano Lett. 9, 2623 (2009).
[CrossRef] [PubMed]

Dholakia, K.

K. Dholakia and P. Reece, Nanotoday 1, 18 (2006).

Dziedzic, J.

A. Ashkin and J. Dziedzic, Science 235, 1517 (1987).
[CrossRef] [PubMed]

Eichenfield, M.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

García de Abajo, F. J.

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, J. Phys. B 40, S249 (2007).
[CrossRef]

Grier, D. G.

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

Grzegorczyk, T. M.

Heckenberg, N. R.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

Huang, J. P.

Y. C. Jian, J. J. Xiao, and J. P. Huang, J. Phys. Chem. C 113, 17170 (2009).
[CrossRef]

Huffman, D. R.

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

Iida, T.

T. Iida and H. Ishihara, Phys. Rev. Lett. 90, 057403 (2003).
[CrossRef] [PubMed]

Ishihara, H.

T. Iida and H. Ishihara, Phys. Rev. Lett. 90, 057403 (2003).
[CrossRef] [PubMed]

Jian, Y. C.

Y. C. Jian, J. J. Xiao, and J. P. Huang, J. Phys. Chem. C 113, 17170 (2009).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kawata, S.

Kong, J. A.

Li, M.

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

Lin, Z. F.

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 1553 (2009).

Michael, C. P.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Ng, J.

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 1553 (2009).

Nieminen, T. A.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

Painter, O.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Perahia, R.

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

Pernice, W. H. P.

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

Petrov, D.

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, Phys. Rev. Lett. 96, 238101 (2006).
[CrossRef] [PubMed]

Pfeifer, R. N. C.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

Pfeiffer, W.

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, J. Phys. B 40, S249 (2007).
[CrossRef]

Quidant, R.

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, Phys. Rev. Lett. 96, 238101 (2006).
[CrossRef] [PubMed]

Reece, P.

K. Dholakia and P. Reece, Nanotoday 1, 18 (2006).

Rubinsztein-Dunlop, H.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

Schonbrun, E.

K. Wang, E. Schonbrun, and K. B. Crozier, Nano Lett. 9, 2623 (2009).
[CrossRef] [PubMed]

Sugiura, T.

Tang, H. X.

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

Volpe, G.

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, Phys. Rev. Lett. 96, 238101 (2006).
[CrossRef] [PubMed]

Wang, K.

K. Wang, E. Schonbrun, and K. B. Crozier, Nano Lett. 9, 2623 (2009).
[CrossRef] [PubMed]

Xiao, J. J.

Y. C. Jian, J. J. Xiao, and J. P. Huang, J. Phys. Chem. C 113, 17170 (2009).
[CrossRef]

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 1553 (2009).

J. J. Xiao and C. T. Chan, J. Opt. Soc. Am. B 25, 1553 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

J. J. Xiao, J. Ng, Z. F. Lin, and C. T. Chan, Appl. Phys. Lett. 94, 1553 (2009).

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, J. Phys. B 40, S249 (2007).
[CrossRef]

J. Phys. Chem. C (1)

Y. C. Jian, J. J. Xiao, and J. P. Huang, J. Phys. Chem. C 113, 17170 (2009).
[CrossRef]

Nano Lett. (1)

K. Wang, E. Schonbrun, and K. B. Crozier, Nano Lett. 9, 2623 (2009).
[CrossRef] [PubMed]

Nanotoday (1)

K. Dholakia and P. Reece, Nanotoday 1, 18 (2006).

Nat. Photonics (2)

M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nat. Photonics 1, 416 (2007).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).
[CrossRef]

Nature (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. Lett. (2)

T. Iida and H. Ishihara, Phys. Rev. Lett. 90, 057403 (2003).
[CrossRef] [PubMed]

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, Phys. Rev. Lett. 96, 238101 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Rev. Mod. Phys. 79, 1197 (2007).
[CrossRef]

Science (1)

A. Ashkin and J. Dziedzic, Science 235, 1517 (1987).
[CrossRef] [PubMed]

Other (2)

The TM resonant modes of a circular cylinder of radii a and with refractive index n in vacuum, are determined by the complex roots k̃0a of the transcendental equation Jm′(ka)Hm(k̃0a)−nJm(ka)Hm′(k̃0a)=0, where k̃0=ω̃/c is the vacuum wave number, k=nk0, Jm(x) and Hm(x) the mth order Bessel function and Hankel function of the first kind. The prime indicates derivative with respect to the argument. The solutions of the above equation are obtained in the complex plane of k̃0a. Consequently, the quality factor Q of a resonant mode is Q=−Re(k̃0a)/2 Im(k̃0a).

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

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Figures (4)

Fig. 1
Fig. 1

Optical forces on a dielectric circular cylinder at TM polarization. (a) In absence of substrate, (b)–(d) in presence of substrate: WG resonances induce a series of regime with negative vertical force.

Fig. 2
Fig. 2

Similar to Fig. 2. Surface plasmon resonance induces a negative force regime. Here σ is the surface-to-surface separation. The dielectric function of silver over the visible is shown in (e).

Fig. 3
Fig. 3

Contour of optical forces ( × 10 19   N / m ) on circular dielectric cylinder at TM polarization, in the separation-wavelength ( d λ ) domain. (a) is for F x and (b) is for F y . The distinct resonances are labeled accordingly and their Q’s are shown.

Fig. 4
Fig. 4

Similar to Fig. 3 but for silver particle of radius a = 100   nm .

Equations (2)

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H z ( y ) = H z ( 0 ) exp ( i y k 0 2 k 2 ) ,     k 0 = ϵ ω c ,
T ( r ) = 1 2 Re [ ϵ E ( r ) E ( r ) + μ H ( r ) H ( r ) 1 4 ( ϵ | E ( r ) | 2 + μ | H ( r ) | 2 ) I ] .

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