Abstract

We study the optical forces on particles, either dielectric or metallic, in or out their Mie resonances, near a subwavelength slit in extraordinary transmission regime. Calculations are two-dimensional, so that those particles are infinite cylinders. Illumination is with p-polarization. We show that the presence of the slit enhances by two orders of magnitude the transversal forces of optical tweezers from a beam alone. In addition, a drastically different effect of these particle resonances on the optical forces that they experience; namely, we demonstrate an enhancement of these forces, also of binding nature, at plasmon resonance wavelengths on metallic nanocylinders, whereas dielectric cylinders experience optical forces that decrease at wavelengths exciting their whispering gallery modes. Particles located at the entrance of the slit are easily bound to apertures due to the coincidence in the forward direction of scattering and gradient forces, but those particles at the exit of the slit suffer a competition between forward scattering force components and backward gradient forces which make more complex the bonding or antibonding nature of the resulting mechanical action.

© 2012 OSA

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2013

J. Gómez-Rivas, C. Schotsch, P. H. Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B68, 201306 (2003).

2011

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5, 349–356 (2011).
[CrossRef]

F. J. Valdivia-Valero and M. Nieto-Vesperinas, “Propagation of particle plasmons in sets of metallic nanocylinders at the exit of subwavelength slits,” J. Nanophotonics5, 053520 (2011).
[CrossRef]

D. C. Kohlgraf-Owens, S. Sukhov, and A. Dogariu, “Mapping the mechanical action of light,” Phys. Rev. A84, 011807(R) (2011).
[CrossRef]

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics5, 531–534 (2011).
[CrossRef]

J. J. Sáenz, “Laser tractor beams,” Nat. Photonics5, 514–515 (2011).
[CrossRef]

A. Novitsky, C. W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett.107, 203601 (2011).
[CrossRef] [PubMed]

F. J. Valdivia-Valero and M. Nieto-Vesperinas, “Enhanced transmission through subwavelength apertures by excitation of particle localized plasmons and nanojets,” Opt. Express19, 11545–11557 (2011).
[CrossRef] [PubMed]

2010

2009

A. O. Cakmak, K. Aydin, E. Colak, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Enhanced transmission through a subwavelength aperture using metamaterials,” Appl. Phys. Lett.95, 052103 (2009).
[CrossRef]

K. Aydin, A. O. Cakmak, L. Sahin, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Split-ring-resonator-coupled enhanced transmission through a single subwavelength aperture,” Phys. Rev. Lett.102, 013904 (2009).
[CrossRef] [PubMed]

Y. Q. Ye and Y. Jin, “Enhanced transmission of transverse electric waves through subwavelength slits in a thin metallic film,” Phys. Rev. E80, 036606 (2009).
[CrossRef]

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys.5, 915–919 (2009).
[CrossRef]

P. C. Chaumet and A. Rahmani, “Electromagnetic force and torque on magnetic and negative-index scatterers,” Opt. Express17, 2224–2234 (2009).
[CrossRef] [PubMed]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett.102, 113602 (2009).
[CrossRef] [PubMed]

2008

X. Cui, D. Erni, and C. Hafner, “Optical forces on metallic nanoparticles induced by a photonic nanojet,” Opt. Express16, 13560–13568 (2008).
[CrossRef] [PubMed]

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev.37, 42–55 (2008).
[CrossRef] [PubMed]

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photon. Rev.2, 136–159 (2008).
[CrossRef]

2007

N. García and M. Nieto-Vesperinas, “Theory of electromagnetic wave transmission through metallic gratings of subwavelenght slits,” J. Opt. A: Pure Appl. Opt.9, 490–495 (2007).
[CrossRef]

L. A. Blanco and M. Nieto-Vesperinas, “Optical forces near subwavelength apertures in metal discs,” J. Opt. A: Pure Appl. Opt.9, S235–S238 (2007).
[CrossRef]

2006

2005

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95, 103901 (2005).
[CrossRef] [PubMed]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys.98, 011101 (2005).
[CrossRef]

H. Rigneault, J. Capoulade, J. Dintinger, J. Wenger, N. Bonod, E. Popov, T. W. Ebbesen, and P. F. Lenne, “Enhancement of single-molecule fluorescence detection in subwavelength apertures,” Phys. Rev. Lett.95, 117401 (2005).
[CrossRef] [PubMed]

J. L. García-Pomar and M. Nieto-Vesperinas, “Waveguiding, collimation and subwavelength concentration in photonic crystals,” Opt. Express13, 7997–8007 (2005).
[CrossRef] [PubMed]

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” Opt. Express13, 8286–8295 (2005).
[CrossRef] [PubMed]

2004

H. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express12, 3629–3651 (2004).
[CrossRef] [PubMed]

S. Deng, W. Cai, and V. N. Astratov, “Numerical study of light propagation via whispering gallery modes in microcylinder coupled resonator optical waveguides,” Opt. Express12, 6468–6480 (2004).
[CrossRef] [PubMed]

V. N. Astratov, J. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett.85, 5508–5510 (2004).
[CrossRef]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Phil. Trans. R. Soc. Lond. A362, 719–737 (2004).
[CrossRef]

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single sub-wavelength aperture in a real metal,” Opt. Commun.239, 61–66 (2004).
[CrossRef]

2003

K. J. Vahala, “Optical microcavities,” Nature424, 839–846 (2003).
[CrossRef] [PubMed]

2002

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science297, 820–822 (2002).
[CrossRef] [PubMed]

J. R. Arias-González, M. Nieto-Vesperinas, and M. Lester, “Modeling photonic force microscopy with metallic particles under plasmon eigenmode excitation,” Phys. Rev. B65, 115402 (2002).
[CrossRef]

2001

2000

1999

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett.83, 2845–2848 (1999).
[CrossRef]

K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett.83, 4534–4537 (1999).
[CrossRef]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391, 667–669 (1998).
[CrossRef]

1997

A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface-corrugated waveguides,” Appl. Phys. Lett.71, 1912–1914 (1997).
[CrossRef]

A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett.71, 1912–1914 (1997).
[CrossRef]

1996

A. Madrazo, M. Nieto-Vesperinas, and N. García, “Exact calculation of Maxwell equations for a tip-metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B53, 3654–3657 (1996).
[CrossRef]

Y. Liu, G. J. Sonek, M. W. Berns, and B. J. Tromberg, “Physiological monitoring of optically trapped cells: assessing the effects of confinement by 1,064nm laser tweezers using microfluorometry,” Biophys. J.71, 2158–2167 (1996).
[CrossRef] [PubMed]

1995

H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, “Transcripting against an applied force,” Science270, 1653–1657 (1995).
[CrossRef] [PubMed]

1994

1993

1990

T. T. Perkins, D. E. Smith, R. G. Larson, and S. Chu, “,Stretching of a single tethered polymer in a uniform flow” Science268, 83–87 (1990).
[CrossRef]

1986

1979

N. García, V. Celli, and M. Nieto-Vesperinas, “Exact multiple scattering of light from surfaces,” Opt. Commun.30, 279–281 (1979).
[CrossRef]

N. Garcia, V. Celli, and M. Nieto-Vesperinas, “Exact multiple scattering of waves from random rough surfaces,” Opt. Commun.30, 279–281 (1979).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972).
[CrossRef]

Aizpurua, J.

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photon. Rev.2, 136–159 (2008).
[CrossRef]

Albaladejo, S.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett.102, 113602 (2009).
[CrossRef] [PubMed]

Alu, A.

A. Alu, F. Bilotti, N. Engheta, and L. Vegni, “Metamaterial covers over a small aperture,” IEEE Trans. Antennas Propag.54, 1632–1643 (2006).
[CrossRef]

Andreone, A.

Arias-González, J. R.

Ashili, S. P.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett.85, 5508–5510 (2004).
[CrossRef]

Ashkin, A.

Astratov, V. N.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett.85, 5508–5510 (2004).
[CrossRef]

S. Deng, W. Cai, and V. N. Astratov, “Numerical study of light propagation via whispering gallery modes in microcylinder coupled resonator optical waveguides,” Opt. Express12, 6468–6480 (2004).
[CrossRef] [PubMed]

Ates, D.

Atwater, H. A.

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys.98, 011101 (2005).
[CrossRef]

Aydin, K.

K. Aydin, A. O. Cakmak, L. Sahin, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Split-ring-resonator-coupled enhanced transmission through a single subwavelength aperture,” Phys. Rev. Lett.102, 013904 (2009).
[CrossRef] [PubMed]

A. O. Cakmak, K. Aydin, E. Colak, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Enhanced transmission through a subwavelength aperture using metamaterials,” Appl. Phys. Lett.95, 052103 (2009).
[CrossRef]

Backman, V.

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K. Aydin, A. O. Cakmak, L. Sahin, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Split-ring-resonator-coupled enhanced transmission through a single subwavelength aperture,” Phys. Rev. Lett.102, 013904 (2009).
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F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys.82, 729–787 (2010).
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F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95, 103901 (2005).
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[CrossRef]

Ozbay, E.

D. Ates, A. O. Cakmak, E. Colak, R. Zhao, C. M. Soukoulis, and E. Ozbay, “Transmission enhancement through deep subwavelength apertures using connected split ring resonators,” Opt. Express18, 3952–3966 (2010).
[CrossRef] [PubMed]

A. O. Cakmak, K. Aydin, E. Colak, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Enhanced transmission through a subwavelength aperture using metamaterials,” Appl. Phys. Lett.95, 052103 (2009).
[CrossRef]

K. Aydin, A. O. Cakmak, L. Sahin, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Split-ring-resonator-coupled enhanced transmission through a single subwavelength aperture,” Phys. Rev. Lett.102, 013904 (2009).
[CrossRef] [PubMed]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1998).

Pang, Y.

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys.5, 915–919 (2009).
[CrossRef]

Pelton, M.

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photon. Rev.2, 136–159 (2008).
[CrossRef]

Pendry, J. B.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett.83, 2845–2848 (1999).
[CrossRef]

Perkins, T. T.

T. T. Perkins, D. E. Smith, R. G. Larson, and S. Chu, “,Stretching of a single tethered polymer in a uniform flow” Science268, 83–87 (1990).
[CrossRef]

Popov, E.

H. Rigneault, J. Capoulade, J. Dintinger, J. Wenger, N. Bonod, E. Popov, T. W. Ebbesen, and P. F. Lenne, “Enhancement of single-molecule fluorescence detection in subwavelength apertures,” Phys. Rev. Lett.95, 117401 (2005).
[CrossRef] [PubMed]

Porto, J. A.

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95, 103901 (2005).
[CrossRef] [PubMed]

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett.83, 2845–2848 (1999).
[CrossRef]

Povinelli, M. L.

Qiu, C. W.

A. Novitsky, C. W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett.107, 203601 (2011).
[CrossRef] [PubMed]

Quidant, R.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5, 349–356 (2011).
[CrossRef]

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys.5, 915–919 (2009).
[CrossRef]

Rahmani, A.

P. C. Chaumet and A. Rahmani, “Electromagnetic force and torque on magnetic and negative-index scatterers,” Opt. Express17, 2224–2234 (2009).
[CrossRef] [PubMed]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Phil. Trans. R. Soc. Lond. A362, 719–737 (2004).
[CrossRef]

Reece, P.

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev.37, 42–55 (2008).
[CrossRef] [PubMed]

Righini, M.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5, 349–356 (2011).
[CrossRef]

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H. Rigneault, J. Capoulade, J. Dintinger, J. Wenger, N. Bonod, E. Popov, T. W. Ebbesen, and P. F. Lenne, “Enhancement of single-molecule fluorescence detection in subwavelength apertures,” Phys. Rev. Lett.95, 117401 (2005).
[CrossRef] [PubMed]

Sáenz, J. J.

J. J. Sáenz, “Laser tractor beams,” Nat. Photonics5, 514–515 (2011).
[CrossRef]

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express18, 11428–11443 (2010).
[CrossRef] [PubMed]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett.102, 113602 (2009).
[CrossRef] [PubMed]

A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett.71, 1912–1914 (1997).
[CrossRef]

A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface-corrugated waveguides,” Appl. Phys. Lett.71, 1912–1914 (1997).
[CrossRef]

Sahin, L.

K. Aydin, A. O. Cakmak, L. Sahin, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Split-ring-resonator-coupled enhanced transmission through a single subwavelength aperture,” Phys. Rev. Lett.102, 013904 (2009).
[CrossRef] [PubMed]

Sburlan, S. E.

S. E. Sburlan, L. A. Blanco, and M. Nieto-Vesperinas, “Plasmon excitation in sets of nanoscale cylinders and spheres,” Phys. Rev. B73, 035403 (2006).
[CrossRef]

Schotsch, C.

J. Gómez-Rivas, C. Schotsch, P. H. Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B68, 201306 (2003).

Shi, E.

E. Shi, E. Xifr-Prez, F. J. Garca de Abajo, and F. Messeguer, “Looking through the mirror: optical microcavity-mirror image photonic interaction,” Opt. Express20, 11247–11255 (2012).
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Sonek, G. J.

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D. C. Kohlgraf-Owens, S. Sukhov, and A. Dogariu, “Mapping the mechanical action of light,” Phys. Rev. A84, 011807(R) (2011).
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H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, “Transcripting against an applied force,” Science270, 1653–1657 (1995).
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Thio, T.

H. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express12, 3629–3651 (2004).
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A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface corrugated optical waveguides,” Appl. Phys. Lett.71, 1912–1914 (1997).
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A. García-Martín, J. A. Torres, J. J. Sáenz, and M. Nieto-Vesperinas, “Transition from diffusive to localized regimes in surface-corrugated waveguides,” Appl. Phys. Lett.71, 1912–1914 (1997).
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Tromberg, B. J.

Y. Liu, G. J. Sonek, M. W. Berns, and B. J. Tromberg, “Physiological monitoring of optically trapped cells: assessing the effects of confinement by 1,064nm laser tweezers using microfluorometry,” Biophys. J.71, 2158–2167 (1996).
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[CrossRef]

K. Aydin, A. O. Cakmak, L. Sahin, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Split-ring-resonator-coupled enhanced transmission through a single subwavelength aperture,” Phys. Rev. Lett.102, 013904 (2009).
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A. Alu, F. Bilotti, N. Engheta, and L. Vegni, “Metamaterial covers over a small aperture,” IEEE Trans. Antennas Propag.54, 1632–1643 (2006).
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A. Novitsky, C. W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett.107, 203601 (2011).
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H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, “Transcripting against an applied force,” Science270, 1653–1657 (1995).
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E. Shi, E. Xifr-Prez, F. J. Garca de Abajo, and F. Messeguer, “Looking through the mirror: optical microcavity-mirror image photonic interaction,” Opt. Express20, 11247–11255 (2012).
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[CrossRef]

A. O. Cakmak, K. Aydin, E. Colak, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Enhanced transmission through a subwavelength aperture using metamaterials,” Appl. Phys. Lett.95, 052103 (2009).
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Biophys. J.

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Chem. Soc. Rev.

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IEEE Trans. Antennas Propag.

A. Alu, F. Bilotti, N. Engheta, and L. Vegni, “Metamaterial covers over a small aperture,” IEEE Trans. Antennas Propag.54, 1632–1643 (2006).
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J. Opt. A: Pure Appl. Opt.

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N. García and M. Nieto-Vesperinas, “Theory of electromagnetic wave transmission through metallic gratings of subwavelenght slits,” J. Opt. A: Pure Appl. Opt.9, 490–495 (2007).
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Laser Photon. Rev.

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Nat. Photonics

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics5, 531–534 (2011).
[CrossRef]

J. J. Sáenz, “Laser tractor beams,” Nat. Photonics5, 514–515 (2011).
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M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5, 349–356 (2011).
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Nat. Phys.

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys.5, 915–919 (2009).
[CrossRef]

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391, 667–669 (1998).
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Opt. Commun.

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[CrossRef]

N. Garcia, V. Celli, and M. Nieto-Vesperinas, “Exact multiple scattering of waves from random rough surfaces,” Opt. Commun.30, 279–281 (1979).
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Opt. Express

J. L. García-Pomar and M. Nieto-Vesperinas, “Waveguiding, collimation and subwavelength concentration in photonic crystals,” Opt. Express13, 7997–8007 (2005).
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F. J. Valdivia-Valero and M. Nieto-Vesperinas, “Enhanced transmission through subwavelength apertures by excitation of particle localized plasmons and nanojets,” Opt. Express19, 11545–11557 (2011).
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F. J. Valdivia-Valero and M. Nieto-Vesperinas, “Resonance excitation and light concentration in sets of dielectric nanocylinders in front of a subwavelength aperture. Effects on extraordinary transmission,” Opt. Express18, 6740–6754 (2010).
[CrossRef] [PubMed]

P. C. Chaumet and A. Rahmani, “Electromagnetic force and torque on magnetic and negative-index scatterers,” Opt. Express17, 2224–2234 (2009).
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M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express18, 11428–11443 (2010).
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N. García and M. Bai, “Theory of transmission of light by subwavelenght cylindrical holes in metallic films,” Opt. Express14, 10028–10042 (2006).
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X. Cui, D. Erni, and C. Hafner, “Optical forces on metallic nanoparticles induced by a photonic nanojet,” Opt. Express16, 13560–13568 (2008).
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M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” Opt. Express13, 8286–8295 (2005).
[CrossRef] [PubMed]

H. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express12, 3629–3651 (2004).
[CrossRef] [PubMed]

D. Ates, A. O. Cakmak, E. Colak, R. Zhao, C. M. Soukoulis, and E. Ozbay, “Transmission enhancement through deep subwavelength apertures using connected split ring resonators,” Opt. Express18, 3952–3966 (2010).
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S. Deng, W. Cai, and V. N. Astratov, “Numerical study of light propagation via whispering gallery modes in microcylinder coupled resonator optical waveguides,” Opt. Express12, 6468–6480 (2004).
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E. Di Gennaro, I. Gallina, A. Andreone, G. Castaldi, and V. Galdi, “Experimental evidence of cut-wire-induced enhanced transmission of transverse-electric fields through sub-wavelength slits in a thin metallic screen,” Opt. Express18, 26769–26774 (2010).
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Opt. Lett.

Phil. Trans. R. Soc. Lond. A

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Phil. Trans. R. Soc. Lond. A362, 719–737 (2004).
[CrossRef]

Phys. Rev. A

D. C. Kohlgraf-Owens, S. Sukhov, and A. Dogariu, “Mapping the mechanical action of light,” Phys. Rev. A84, 011807(R) (2011).
[CrossRef]

Phys. Rev. B

J. R. Arias-González, M. Nieto-Vesperinas, and M. Lester, “Modeling photonic force microscopy with metallic particles under plasmon eigenmode excitation,” Phys. Rev. B65, 115402 (2002).
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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. B61, 14119–14127 (2000).
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A. Madrazo, M. Nieto-Vesperinas, and N. García, “Exact calculation of Maxwell equations for a tip-metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B53, 3654–3657 (1996).
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P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972).
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S. E. Sburlan, L. A. Blanco, and M. Nieto-Vesperinas, “Plasmon excitation in sets of nanoscale cylinders and spheres,” Phys. Rev. B73, 035403 (2006).
[CrossRef]

J. Gómez-Rivas, C. Schotsch, P. H. Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B68, 201306 (2003).

Phys. Rev. E

Y. Q. Ye and Y. Jin, “Enhanced transmission of transverse electric waves through subwavelength slits in a thin metallic film,” Phys. Rev. E80, 036606 (2009).
[CrossRef]

Phys. Rev. Lett.

K. Aydin, A. O. Cakmak, L. Sahin, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Split-ring-resonator-coupled enhanced transmission through a single subwavelength aperture,” Phys. Rev. Lett.102, 013904 (2009).
[CrossRef] [PubMed]

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95, 103901 (2005).
[CrossRef] [PubMed]

K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett.83, 4534–4537 (1999).
[CrossRef]

H. Rigneault, J. Capoulade, J. Dintinger, J. Wenger, N. Bonod, E. Popov, T. W. Ebbesen, and P. F. Lenne, “Enhancement of single-molecule fluorescence detection in subwavelength apertures,” Phys. Rev. Lett.95, 117401 (2005).
[CrossRef] [PubMed]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett.102, 113602 (2009).
[CrossRef] [PubMed]

A. Novitsky, C. W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett.107, 203601 (2011).
[CrossRef] [PubMed]

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett.83, 2845–2848 (1999).
[CrossRef]

Rev. Mod. Phys.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys.82, 729–787 (2010).
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Science

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[CrossRef] [PubMed]

T. T. Perkins, D. E. Smith, R. G. Larson, and S. Chu, “,Stretching of a single tethered polymer in a uniform flow” Science268, 83–87 (1990).
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H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science297, 820–822 (2002).
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Other

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer Science + Business Media LLC, New York, 2007).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, Cambridge, 2005).
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E. Shi, E. Xifr-Prez, F. J. Garca de Abajo, and F. Messeguer, “Looking through the mirror: optical microcavity-mirror image photonic interaction,” Opt. Express20, 11247–11255 (2012).
[CrossRef]

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1998).

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Figures (15)

Fig. 1
Fig. 1

Schematic illustration of the geometry of the slit transmission and force calculations: An incident p-polarized Gaussian beam, (see main text), with magnetic vector Hz and Poynting vector Sy impinges from below an Al slab of width D and thickness h, containing and aperture of width d. Notice that D is the horizontal size of the window of the simulation space, in whose boundaries low reflection conditions are set. At those boundaries that coincide with the exterior limit of the metallic slab, a conductor condition is selected, (see [40]). When a cylinder of radius r is placed, the transmitted intensity is evaluated as follows: For dielectric (Si) particles, the time averaged energy flow norm | < Sy > | is calculated inside the cylinder circle cross section. For metallic (Ag) cylinders, one determines | < Sy > | in an annulus of exterior and interior radii: re and r, respectively. The circumference Σ of radius re, is also used to perform the integration of Eq. (1), no matter whether the cylinder is dielectric or metallic. An analogous procedure applies if the particle is placed below the aperture entrance.

Fig. 2
Fig. 2

(a) Detail of the time-averaged energy flux (< S(r) > in arrows and | < S(r) > | in the color spatial distribution) concentrated in the slit exit practiced in an Al slab, (slab width D = 19.920μm, slab thickness h = 857.6nm, slit width d = 428.8nm) and in a Si cylinder (radius r = 200nm) tangent to the exit plane of the slit. The Gaussian beam at wavelength λ = 1170nm, with σ = 3μm, incides from below. (b) Time-averaged energy flow norm | < S(r) > | versus wavelength λ transmitted by the slit alone (black curve with squares) and in presence of the dielectric cylinder (red curve with circles). The calculations of these intensities, with and without cylinder, are explained in Fig. 1 and in the main text above.

Fig. 3
Fig. 3

(a) The Si cylinder is now tangent to the entrance plane of the slit. All parameters are like in Figs. 2(a) and 2(b). Time-averaged energy flow norm | < S(r) > | against wavelength λ: transmitted by the slit (black curve with squares), and concentrated in the cylinder (red curve with circles). (b) Two cylinders are now present: one above the slit exit, like in Fig. 2(a), and another tangent to the entrance plane of the slit, like in Fig. 3(a). Time-averaged energy flow norm | < S(r) > | versus wavelengt λ concentrated in the lower cylinder (black curve with squares) and in the upper one (red curve with circles).

Fig. 4
Fig. 4

(a) Detail of the spatial distribution of | < S(r) > | (colors) and local forces (white arrows) exerted on the surface of the upper dielectric cylinder of Fig. 2(a), at the same illumination (λ = 1170nm). The forces are evaluated on the circle of radius re = 210nm surrounding the cylinder section, (see Fig. 1). The particle is tangent to the exit plane of the slit, and horizontally shifted 135nm from the center towards the right edge. (b) The same for the cylinder below the slit, tangent to its entrance plane and 135nm horizontally moved towards the right. The illumination is the same as in (a), (λ = 1170nm).

Fig. 5
Fig. 5

(a) X-component < F x T > of the time-averaged total electromagnetic force exerted on the Si cylinder above the slit [shown in Fig. 4(a)], as it moves from x = 0 to the right. Left vertical axis, black square and red circle curves stand for the case in which the cylinder in presence of the slit is out (λ = 1280nm) or in [λ = 1170nm, see Fig. 2(b)] resonance, respectively. These values are compared to those for the Si cylinder illuminated by the same Gaussian beam in absence of slit, (see the right vertical axis). The non-resonant and resonant cases are shown by the green up- and blue down-triangle curves, respectively. (b) The same study for the Y-component < F y T > of the time-averaged total electromagnetic force.

Fig. 6
Fig. 6

(a) X-component < F x T > of the time-averaged total electromagnetic force exerted on the Si cylinder below the slit (shown in Fig. 4(b)), as it moves to the right from x = 0. Black square and red circle curves stand for the case in which the cylinder in presence of the slit is out (λ = 1305nm) or in (λ = 1200nm) resonance, respectively. (b) The same for the Y-component < F y T > of the time-averaged total electromagnetic force.

Fig. 7
Fig. 7

(a) X-component < F x T > of the time-averaged total electromagnetic force exerted on the lower Si cylinder in presence of the slit and of the upper cylinder. The lower particle moves horizontally towards the right corner of the slit. Black square and red circle curves stand for the case in which the lower cylinder is out (λ = 1290nm) or in (λ = 1200nm) resonance, respectively. (b) The same study for the Y-component < F y T > of the time-averaged total electromagnetic force. (c) Spatial distribution of Hz(r) in the configuration analyzed in (a) and (b) when the lower cylinder is resonant (λ = 1200nm). (d) The same as in (c) for the case in which no cylinder is resonant (λ = 1290nm).

Fig. 8
Fig. 8

(a) X-component < F x T > of the time-averaged total electromagnetic force exerted on the upper Si cylinder, in presence of the slit and of the lower cylinder. The upper particle moves horizontally towards the right corner of the slit. Black square and red circle curves stand for the upper cylinder being out (λ = 1290nm) or in (λ = 1235nm) resonance, respectively. (b) The same for the Y-component < F y T > of the time-averaged total electromagnetic forces.

Fig. 9
Fig. 9

(a) An Ag cylinder is placed tangent to the exit plane of a slit practiced in an Al slab, (slab width D = 5.096μm, slab thickness h = 219.4nm, slit width d = 109.7nm). The radius of the cylinder is r = 30nm. The curves show the time-averaged energy flow norm | < S(r) > | against wavelength λ, transmitted by the slit alone (black curve with squares), and that concentrated on the cylinder cross-section (red curve with triangles) when the latter is placed as explained above. (cf. Fig. 1 and the text explaining the evaluation of the transmitted | < S(r) > |. The incident beam has σ = 1.3μm. (b) The cylinder is now placed below, at 40nm from the entrance plane of the slit. The curves show: time-averaged energy flow norm | < S(r) > | versus wavelength λ transmitted by the slit (black curve with squares), and | < S(r) > | concentrated on the lower cylinder surface (red curve with circles). Notice that while the circle curve is obtained on integration of | < S(r) > | in the annulus of radii: r = 30nm and re = 35nm surrounding the lower cylinder, the annulus leading to the square curve is drawn in vacuum above the slit. (c) Both Ag cylinders are simultaneously placed with the slit. The curves show: Time-averaged energy flow norm | < S(r) > | versus wavelength λ concentrated on the surface of the lower cylinder (black curve with squares) and that on the surface of the upper cylinder (red curve with circles), respectively.

Fig. 10
Fig. 10

Detail of the spatial distribution of | < S(r) > | (color) and of the local forces (arrows) exerted on the upper Ag cylinder, resonantly illuminated by a Gaussian beam of σ = 1.3μm at λ = 335.1nm, evaluated on the circumference of radius re = 35nm surrounding its cross section. The cylinder is tangent to the exit plane of the slit and moved to the right 35nm from x = 0. (b) The same for the lower Ag cylinder, at the same illumination wavelength, now 40nm down from the entrance plane of the slit and moved 20nm towards its right corner.

Fig. 11
Fig. 11

(a) X-component < F x T > of the time-averaged total electromagnetic force exerted on the upper Ag cylinder in presence of the slit [cf. Fig. 10(a)], as the cylinder moves from x = 0 towards the right edge of the slit. Black square and red circle curves stand for the cylinder out (λ = 500.0nm) or in (λ = 335.1nm) resonance, respectively. (b) The same for the Y-component < F y T > of the time-averaged total electromagnetic force.

Fig. 12
Fig. 12

(a) X-component < F x T > of the time-averaged total electromagnetic force exerted on the lower Ag cylinder, in presence of the slit [cf. Fig. 10(b)], as it moves from x = 0 to the right. Black square and red circle curves stand for the cylinder illuminated out (λ = 500nm) or in (λ = 335.1nm) resonance, respectively. (b) The same for the Y-component < F y T > of the time-averaged total electromagnetic force.

Fig. 13
Fig. 13

(a) X-component < F x T > of the time-averaged total electromagnetic force exerted on the lower Ag cylinder, in presence of the slab and of the upper Ag cylinder, as shown in Fig. 11(a). This lower particle moves towards the right edge of the slit. Black square and red circle curves stand for the lower Ag cylinder out (λ = 500.0nm) or in (λ = 330.6nm) resonance, respectively. (b) The same for the Y-component < F y T > of the time-averaged total electromagnetic force. (c) Detail of a snapshot of Hz(r) at a certain time instant for λ = 330.6nm at which the lower cylinder is resonant. (d) The same as in (c) for the case in which no cylinder is resonant (λ = 500.0nm).

Fig. 14
Fig. 14

(a) X-component < F x T > of the time-averaged total electromagnetic force exerted on the upper Ag cylinder, in presence of the slab and of the lower cylinder, as shown in Fig. 11(a), as the upper particle moves from x = 0 to the right. Black square and red circle curves stand for the case in which the upper cylinder is illuminated out (λ = 500.0nm) or in (λ = 326.3nm) resonance, respectively. (b) The same for the Y-component < F y T > of the time-averaged total electromagnetic force.

Fig. 15
Fig. 15

Schematic illustration of the geometry for the calculations of the force when a cylinder of radius r is placed near the slit. The components of the local electromagnetic force, < F x l > and < F y l >, are evaluated along the exterior circle of radius re (red curve). In our calculations re = 210nm and re = 35nm when r = 200nm (dielectric cylinder) and r = 30nm (metallic cylinder), respectively. The integration of these local forces over the four segments into which the exterior circle is divided, yields the total electromagnetic force Cartesian components ( < F x T > and < F y T >).

Tables (1)

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Table 1 Physical operators and variables needed to calculate the local forces and their equivalence in FEMLAB language.

Equations (2)

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< F em > = Σ [ ɛ / 2 Re { ( E n ) E * } ɛ / 4 ( E E * ) n + μ / 2 Re { ( H n ) H * } μ / 4 ( H H * ) n ] d A ,
< F x l > ( E ) = 0.5 Re [ ɛ r ɛ 0 ( E x n x d , u + E y n y d , u ) Conj [ E x ] 0.5 ɛ r ɛ 0 | E | 2 n x d , u ] , < F x l > ( H ) = 0.5 Re [ 0.5 μ r μ 0 | H | 2 n x d , u ] , < F x l > = < F x l > ( E ) + < F x l > ( H ) . < F y l > ( E ) = 0.5 Re [ ɛ r ɛ 0 ( E x n x d , u + E y n y d , u ) Conj [ E y ] 0.5 ɛ r ɛ 0 | E | 2 n y d , u ] , < F y l > ( H ) = 0.5 Re [ 0.5 μ r μ 0 | H | 2 n y d , u ] , < F y l > = < F y l > ( E ) + < F y l > ( H ) .

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