Abstract

Although science fiction literature and art portray extraordinary stories of people interacting with their images behind a mirror, we know that they are not real and belong to the realm of fantasy. However, it is well known that charges or magnets near a good electrical conductor experience real attractive or repulsive forces, respectively, originating in the interaction with their images. Here, we show strong interaction between an optical microcavity and its image under external illumination. Specifically, we use silicon nanospheres whose high refractive index makes well-defined optical resonances feasible. The strong interaction produces attractive and repulsive forces depending on incident wavelength, cavity-metal separation and resonance mode symmetry. These intense repulsive photonic forces warrant a new kind of optical levitation that allows us to accurately manipulate small particles, with important consequences for microscopy, optical sensing and control of light by light at the nanoscale.

© 2012 OSA

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2011

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5(6), 349–356 (2011).
[CrossRef]

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics5(6), 318–321 (2011).
[CrossRef] [PubMed]

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011).
[CrossRef] [PubMed]

E. Xifré-Pérez, R. Fenollosa, and F. Meseguer, “Low order modes in microcavities based on silicon colloids,” Opt. Express19(4), 3455–3463 (2011).
[CrossRef] [PubMed]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express19(6), 4815–4826 (2011).
[CrossRef] [PubMed]

2010

R. Zhao, P. Tassin, T. Koschny, and C. M. Soukoulis, “Optical forces in nanowire pairs and metamaterials,” Opt. Express18(25), 25665–25676 (2010).
[CrossRef] [PubMed]

T. Sannomiya and C. Hafner, “Multiple multipole program modelling for nano plasmonic sensors,” J. Comput. Theor. Nanoscience7(8), 1587–1595 (2010).
[CrossRef]

2009

E. Xifré-Pérez, F. J. García de Abajo, R. Fenollosa, and F. Meseguer, “Photonic binding in silicon-colloid microcavities,” Phys. Rev. Lett.103(10), 103902 (2009).
[CrossRef] [PubMed]

K. M. Hurst, C. B. Roberts, and W. R. Ashurst, “A gas-expanded liquid nanoparticle deposition technique for reducing the adhesion of silicon microstructures,” Nanotechnology20(18), 185303 (2009).
[CrossRef] [PubMed]

M. Righini, P. Ghenuche, S. Cherukulappurath, V. Myroshnychenko, F. J. García de Abajo, and R. Quidant, “Nano-optical trapping of Rayleigh particles and Escherichia coli bacteria with resonant optical antennas,” Nano Lett.9(10), 3387–3391 (2009).
[CrossRef] [PubMed]

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A.106(6), 1693–1698 (2009).
[CrossRef] [PubMed]

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

2008

R. Quidant and C. Girard, “Surface-plasmon-based optical manipulation,” Laser Photon. Rev.2(1-2), 47–57 (2008).
[CrossRef]

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett.100(18), 186804 (2008).
[CrossRef] [PubMed]

R. Fenollosa, F. Meseguer, and M. Tymczenko, “Silicon colloids: from microcavities to photonic sponges,” Adv. Mater. (Deerfield Beach Fla.)20(1), 95–98 (2008).
[CrossRef]

2007

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys.3(7), 477–480 (2007).
[CrossRef]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev.37(1), 42–55 (2007).
[CrossRef] [PubMed]

2006

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative index materials: new frontiers in optics,” Adv. Mater. (Deerfield Beach Fla.)18(15), 1941–1952 (2006).
[CrossRef]

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett.96(23), 238101 (2006).
[CrossRef] [PubMed]

2004

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

F. J. García de Abajo, “Momentum transfer to small particles by passing electron beams,” Phys. Rev. B70(11), 115422 (2004).
[CrossRef]

2003

D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 21–27 (2003).
[CrossRef] [PubMed]

1999

F. J. García de Abajo, “Multiple scattering of radiation in clusters of dielectrics,” Phys. Rev. B60(8), 6086–6102 (1999).
[CrossRef]

1995

1989

E. H. Brandt, “Levitation in physics,” Science243(4889), 349–355 (1989).
[CrossRef] [PubMed]

1987

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science235(4795), 1517–1520 (1987).
[CrossRef] [PubMed]

1984

I. V. Lindell, E. Alanen, and K. Mannersalo, “Exact image method for impedance computation of antennas above the ground,” IEEE Trans. Antenn. Propag.AP-33, 937–945 (1984).

1977

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett.38(23), 1351–1354 (1977).
[CrossRef]

1970

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970).
[CrossRef]

Aizpurua, J.

Alanen, E.

I. V. Lindell, E. Alanen, and K. Mannersalo, “Exact image method for impedance computation of antennas above the ground,” IEEE Trans. Antenn. Propag.AP-33, 937–945 (1984).

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science235(4795), 1517–1520 (1987).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett.38(23), 1351–1354 (1977).
[CrossRef]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970).
[CrossRef]

Ashurst, W. R.

K. M. Hurst, C. B. Roberts, and W. R. Ashurst, “A gas-expanded liquid nanoparticle deposition technique for reducing the adhesion of silicon microstructures,” Nanotechnology20(18), 185303 (2009).
[CrossRef] [PubMed]

Badenes, G.

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett.96(23), 238101 (2006).
[CrossRef] [PubMed]

Block, S. M.

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics5(6), 318–321 (2011).
[CrossRef] [PubMed]

Brandt, E. H.

E. H. Brandt, “Levitation in physics,” Science243(4889), 349–355 (1989).
[CrossRef] [PubMed]

Burresi, M.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Chantada, L.

Cherukulappurath, S.

M. Righini, P. Ghenuche, S. Cherukulappurath, V. Myroshnychenko, F. J. García de Abajo, and R. Quidant, “Nano-optical trapping of Rayleigh particles and Escherichia coli bacteria with resonant optical antennas,” Nano Lett.9(10), 3387–3391 (2009).
[CrossRef] [PubMed]

Dholakia, K.

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev.37(1), 42–55 (2007).
[CrossRef] [PubMed]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science235(4795), 1517–1520 (1987).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett.38(23), 1351–1354 (1977).
[CrossRef]

Economou, E. N.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative index materials: new frontiers in optics,” Adv. Mater. (Deerfield Beach Fla.)18(15), 1941–1952 (2006).
[CrossRef]

Engheta, N.

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

Fazal, F. M.

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics5(6), 318–321 (2011).
[CrossRef] [PubMed]

Fenollosa, R.

E. Xifré-Pérez, R. Fenollosa, and F. Meseguer, “Low order modes in microcavities based on silicon colloids,” Opt. Express19(4), 3455–3463 (2011).
[CrossRef] [PubMed]

E. Xifré-Pérez, F. J. García de Abajo, R. Fenollosa, and F. Meseguer, “Photonic binding in silicon-colloid microcavities,” Phys. Rev. Lett.103(10), 103902 (2009).
[CrossRef] [PubMed]

R. Fenollosa, F. Meseguer, and M. Tymczenko, “Silicon colloids: from microcavities to photonic sponges,” Adv. Mater. (Deerfield Beach Fla.)20(1), 95–98 (2008).
[CrossRef]

Froufe-Pérez, L. S.

García de Abajo, F. J.

E. Xifré-Pérez, F. J. García de Abajo, R. Fenollosa, and F. Meseguer, “Photonic binding in silicon-colloid microcavities,” Phys. Rev. Lett.103(10), 103902 (2009).
[CrossRef] [PubMed]

M. Righini, P. Ghenuche, S. Cherukulappurath, V. Myroshnychenko, F. J. García de Abajo, and R. Quidant, “Nano-optical trapping of Rayleigh particles and Escherichia coli bacteria with resonant optical antennas,” Nano Lett.9(10), 3387–3391 (2009).
[CrossRef] [PubMed]

F. J. García de Abajo, “Momentum transfer to small particles by passing electron beams,” Phys. Rev. B70(11), 115422 (2004).
[CrossRef]

F. J. García de Abajo, “Multiple scattering of radiation in clusters of dielectrics,” Phys. Rev. B60(8), 6086–6102 (1999).
[CrossRef]

García-Etxarri, A.

Ghenuche, P.

M. Righini, P. Ghenuche, S. Cherukulappurath, V. Myroshnychenko, F. J. García de Abajo, and R. Quidant, “Nano-optical trapping of Rayleigh particles and Escherichia coli bacteria with resonant optical antennas,” Nano Lett.9(10), 3387–3391 (2009).
[CrossRef] [PubMed]

Girard, C.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett.100(18), 186804 (2008).
[CrossRef] [PubMed]

R. Quidant and C. Girard, “Surface-plasmon-based optical manipulation,” Laser Photon. Rev.2(1-2), 47–57 (2008).
[CrossRef]

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys.3(7), 477–480 (2007).
[CrossRef]

Gómez-Medina, R.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 21–27 (2003).
[CrossRef] [PubMed]

Gu, M.

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev.37(1), 42–55 (2007).
[CrossRef] [PubMed]

Hafner, C.

T. Sannomiya and C. Hafner, “Multiple multipole program modelling for nano plasmonic sensors,” J. Comput. Theor. Nanoscience7(8), 1587–1595 (2010).
[CrossRef]

Hecht, B.

Heideman, R.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Hurst, K. M.

K. M. Hurst, C. B. Roberts, and W. R. Ashurst, “A gas-expanded liquid nanoparticle deposition technique for reducing the adhesion of silicon microstructures,” Nanotechnology20(18), 185303 (2009).
[CrossRef] [PubMed]

Juan, M. L.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5(6), 349–356 (2011).
[CrossRef]

Kafesaki, M.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative index materials: new frontiers in optics,” Adv. Mater. (Deerfield Beach Fla.)18(15), 1941–1952 (2006).
[CrossRef]

Kampfrath, T.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Koschny, T.

Kuipers, L.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Leinse, A.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Lindell, I. V.

I. V. Lindell, E. Alanen, and K. Mannersalo, “Exact image method for impedance computation of antennas above the ground,” IEEE Trans. Antenn. Propag.AP-33, 937–945 (1984).

Liu, Y.

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011).
[CrossRef] [PubMed]

López, C.

Mannersalo, K.

I. V. Lindell, E. Alanen, and K. Mannersalo, “Exact image method for impedance computation of antennas above the ground,” IEEE Trans. Antenn. Propag.AP-33, 937–945 (1984).

Merlin, R.

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A.106(6), 1693–1698 (2009).
[CrossRef] [PubMed]

Meseguer, F.

E. Xifré-Pérez, R. Fenollosa, and F. Meseguer, “Low order modes in microcavities based on silicon colloids,” Opt. Express19(4), 3455–3463 (2011).
[CrossRef] [PubMed]

E. Xifré-Pérez, F. J. García de Abajo, R. Fenollosa, and F. Meseguer, “Photonic binding in silicon-colloid microcavities,” Phys. Rev. Lett.103(10), 103902 (2009).
[CrossRef] [PubMed]

R. Fenollosa, F. Meseguer, and M. Tymczenko, “Silicon colloids: from microcavities to photonic sponges,” Adv. Mater. (Deerfield Beach Fla.)20(1), 95–98 (2008).
[CrossRef]

Myroshnychenko, V.

M. Righini, P. Ghenuche, S. Cherukulappurath, V. Myroshnychenko, F. J. García de Abajo, and R. Quidant, “Nano-optical trapping of Rayleigh particles and Escherichia coli bacteria with resonant optical antennas,” Nano Lett.9(10), 3387–3391 (2009).
[CrossRef] [PubMed]

Nieto-Vesperinas, M.

Novotny, L.

Oulton, R. F.

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011).
[CrossRef] [PubMed]

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Petrov, D.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett.100(18), 186804 (2008).
[CrossRef] [PubMed]

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett.96(23), 238101 (2006).
[CrossRef] [PubMed]

Pohl, D. W.

Quidant, R.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5(6), 349–356 (2011).
[CrossRef]

M. Righini, P. Ghenuche, S. Cherukulappurath, V. Myroshnychenko, F. J. García de Abajo, and R. Quidant, “Nano-optical trapping of Rayleigh particles and Escherichia coli bacteria with resonant optical antennas,” Nano Lett.9(10), 3387–3391 (2009).
[CrossRef] [PubMed]

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett.100(18), 186804 (2008).
[CrossRef] [PubMed]

R. Quidant and C. Girard, “Surface-plasmon-based optical manipulation,” Laser Photon. Rev.2(1-2), 47–57 (2008).
[CrossRef]

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys.3(7), 477–480 (2007).
[CrossRef]

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett.96(23), 238101 (2006).
[CrossRef] [PubMed]

Reece, P.

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev.37(1), 42–55 (2007).
[CrossRef] [PubMed]

Righini, M.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5(6), 349–356 (2011).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic view of the mirror image method. (a) Schematic view of the mirror image method for a single electrical charge. The direction of the force between the charge and the metal is shown in left panel. (b) Schematic view of the mirror image method for a magnetic dipole. The direction of the force on magnet is shown in left panel. (c) Schematic view of the mirror image method applied to a microcavity (grey sphere) near a metallic conductor. The thick dark red arrow indicates the incident EM wave. The thin dark red arrow indicates the (H) field direction of the incident EM wave. The upper inset shows the directions of the incident (E) and (H) fields in the x-y plane (the planar surface is at z = 0). The lower inset shows the direction of (E) and (H) fields in the image, along with the corresponding electric and magnetic image dipoles. We also show the direction of the forces acting on the optical cavity originating in electric and magnetic dipoles.

Fig. 2
Fig. 2

Scattering efficiency of a single silicon sphere, immersed in vacuum (red line) and water (blue line), as a function of light wavelength. The scattering efficiency of single PS sphere in vacuum (black dash line) is also plotted. The E and H field intensity distribution of silicon sphere in vacuum for some of the Mie modes are also shown above. The radius of both silicon and PS spheres is 230 nm.

Fig. 3
Fig. 3

Optical force on a silicon nanosphere near a PEC surface. (a) Distribution of Ex, Ez and Hy field components within the x-z plane for a silicon nanosphere near a PEC surface at wavelengths of 1434 nm (TMD, upper panels) and 1744 nm (TED, lower panels). (b) Optical force along the z direction (black solid curve obtained from FDTD, grey dash line curve obtained from MESME, red dotted curve obtained from integration only the magnetic part of the Maxwell tensor, blue dotted curve obtained from integration of the electric part of Maxwell tensor [30, 31]; left axis) and maximum of the Ez and Hy fields (blue and red dashed curves, respectively; right axis) acting on a silicon sphere separated by a 10 nm gap from a PEC surface as a function of wavelength. The sphere radius is 230 nm. The light intensity is 10mW/μm2. (c) Ex, Ez and Hy field distributions in the x-z plane for two neighbouring spheres at 1434 nm (TMD, upper panels) and 1744 nm (TED, lower panels). (d) Optical force along the z direction (black solid curve; left axis) and maximum Ez and Hy fields (blue and red dashed curves, respectively; right axis) for two spheres separately irradiated by counter-propagating incident light with π phase difference as a function of wavelength. The sphere size and light intensity is the same as in (a). The separation between the two spheres is 20 nm.

Fig. 4
Fig. 4

Optical force on a silicon nanosphere near a real metal. (a) Optical force along the z direction (black solid curve obtained from FDTD, grey dash line curve obtained from MESME; left axis) and maximum Ez and Hy fields (blue and red dashed curves, respectively; right axis) for a silicon sphere in vacuum separated by a 10 nm gap from a gold surface as a function of wavelength. The sphere radius is 230 nm. The light intensity is 10 mW/��m2. (b) Ex, Ez and Hy field distributions in the x-z plane for a silicon sphere in vacuum at wavelengths of 1490 nm (TMD, upper panels) and 1750 nm (TED, lower panels). (c) Same as (a) for a silicon sphere suspended in water near a gold surface. (d) Ex, Ez and Hy field distributions in the x-z plane for a sphere in water near a gold surface at 1582 nm (TMD, upper panels) and 1894 nm (TED, lower panels).

Fig. 5
Fig. 5

Optical force in different media as a function of sphere-metal separation and sphere dynamic motion. (a) Optical force (red curve) along the z direction for a silicon sphere in vacuum near a gold surface as a function of silicon-gold gap distance. The wavelength of incident light is 1490 nm. The radius of the sphere is 230 nm. The light intensity is 10 mW/��m2. The van der Waals (vdW) force (black curve) is shown for comparison (see main text for details). (b) Same as (a) with silicon sphere in water near a gold surface. The laser wavelength is 1582 nm in all cases.

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