Abstract

We study the optical force arising when isolated gold nanowire pairs and metamaterials with a gold nanowire pair in the unit cell are illuminated with laser radiation. Firstly, we show that isolated nanowire pairs are subject to much stronger optical forces than nanospheres due to their stronger electric and magnetic dipole resonances. We also investigate the properties of the optical force as a function of the length of the nanowires and of the distance between the nanowires. Secondly, we study the optical force in a metamaterial that consists of a periodic array of nanowire pairs. We show that the ratio of the size of the unit cell to the length of the nanowires determines whether the electric dipole resonance leads to an attractive or a repulsive force, and we present the underlying physical mechanism for this effect.

© 2010 Optical Society of America

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  6. M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, "Harnessing optical forces in integrated photonic circuits," Nature 456, 480-484 (2008).
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  7. D. Van Thourhout, and J. Roels, "Optomechanical device actuation through the optical gradient force," Nat. Photonics 4, 211-217 (2010).
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  8. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, "Evanescent-wave bonding between optical waveguides," Opt. Lett. 30, 3042-3044 (2005).
    [CrossRef] [PubMed]
  9. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, "Controlling photonic structures using optical forces," Nature 462, 633-636 (2009).
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  10. T. J. Kippenberg, and K. J. Vahala, "Cavity optomechanics: Back-action at the mesoscale," Science 321, 1172-1176 (2008).
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  11. A. J. Hallock, P. L. Redmond, and L. E. Brus, "Optical forces between metallic particles," Proc. Natl. Acad. Sci. U.S.A. 102, 1280-1284 (2005).
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  12. P. Chu, and D. L. Mills, "Laser-induced forces in metallic nanosystems: The role of plasmon resonances," Phys. Rev. Lett. 99, 127401 (2007).
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  13. C. Rockstuhl, and H. P. Herzig, "Wavelength-dependent optical force on elliptical silver cylinders at plasmon resonance," Opt. Lett. 29, 2181-2183 (2004).
    [CrossRef] [PubMed]
  14. K. Halterman, J. M. Elson, and S. Singh, "Plasmonic resonances and electromagnetic forces between coupled silver nanowires," Phys. Rev. B 72, 075429 (2005).
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  15. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
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  16. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
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  17. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
    [CrossRef]
  18. D. R. Smith, W. J. Padilla, D. C. Vier, D. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  19. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the electric resonance of split-ring resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
    [CrossRef]
  20. T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402 (2004).
    [CrossRef] [PubMed]
  21. J. Garcia-Garcia, F. Martin, J. D. Baena, R. Marques, and L. Jelink, "On the resonances and polarizabilities of split-ring resonators," J. Appl. Phys. 98, 033103 (2005).
    [CrossRef]
  22. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
    [CrossRef] [PubMed]
  23. G. Dolling, C. Enkrich, M. Wegener, and C. M. Soukoulis, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005).
    [CrossRef] [PubMed]
  24. V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
    [CrossRef]
  25. P. B. Johnson, and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
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    [CrossRef]
  27. H.-S. Park, A. Agarwal, N. A. Kotov, and O. D. Lavrentovich, "Controllable side-by-side and end-to-end assembly of Au nanorods by lyotropic chromonic materials," Langmuir 24, 13833-13837 (2008).
    [CrossRef] [PubMed]
  28. J. Zhou, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006).
    [CrossRef] [PubMed]
  29. P. Gay-Balmaz, and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
    [CrossRef]
  30. R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, "Multi-gap individual and coupled split-ring resonator structures," Opt. Express 16, 18131-18144 (2008).
    [CrossRef] [PubMed]
  31. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low loss metamaterials based on classical electromagnetically induced transparency," Phys. Rev. Lett. 102, 053901 (2009).
    [CrossRef] [PubMed]
  32. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Planar designs for electromagnetically induced transparency in metamaterials," Opt. Express 17, 5595-5605 (2009).
    [CrossRef] [PubMed]
  33. N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, "A metamaterial analog of electromagnetically induced transparency," Phys. Rev. Lett. 101, 253903 (2008).
    [CrossRef] [PubMed]
  34. N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
    [CrossRef] [PubMed]

2010

D. Van Thourhout, and J. Roels, "Optomechanical device actuation through the optical gradient force," Nat. Photonics 4, 211-217 (2010).
[CrossRef]

2009

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, "Controlling photonic structures using optical forces," Nature 462, 633-636 (2009).
[CrossRef]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low loss metamaterials based on classical electromagnetically induced transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Planar designs for electromagnetically induced transparency in metamaterials," Opt. Express 17, 5595-5605 (2009).
[CrossRef] [PubMed]

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

2008

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, "A metamaterial analog of electromagnetically induced transparency," Phys. Rev. Lett. 101, 253903 (2008).
[CrossRef] [PubMed]

M. N’Gom, J. Ringnalda, J. F. Mansfield, A. Agarwal, N. Kotov, N. J. Zaluzec, and T. B. Norris, "Single particle plasmon spectroscopy of silver nanowires and gold nanorods," Nano Lett. 8, 3200-3204 (2008).
[CrossRef]

H.-S. Park, A. Agarwal, N. A. Kotov, and O. D. Lavrentovich, "Controllable side-by-side and end-to-end assembly of Au nanorods by lyotropic chromonic materials," Langmuir 24, 13833-13837 (2008).
[CrossRef] [PubMed]

R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, "Multi-gap individual and coupled split-ring resonator structures," Opt. Express 16, 18131-18144 (2008).
[CrossRef] [PubMed]

T. J. Kippenberg, and K. J. Vahala, "Cavity optomechanics: Back-action at the mesoscale," Science 321, 1172-1176 (2008).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, "Harnessing optical forces in integrated photonic circuits," Nature 456, 480-484 (2008).
[CrossRef]

2007

P. Chu, and D. L. Mills, "Laser-induced forces in metallic nanosystems: The role of plasmon resonances," Phys. Rev. Lett. 99, 127401 (2007).
[CrossRef] [PubMed]

2006

J. Zhou, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006).
[CrossRef] [PubMed]

2005

A. J. Hallock, P. L. Redmond, and L. E. Brus, "Optical forces between metallic particles," Proc. Natl. Acad. Sci. U.S.A. 102, 1280-1284 (2005).
[CrossRef] [PubMed]

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, "Evanescent-wave bonding between optical waveguides," Opt. Lett. 30, 3042-3044 (2005).
[CrossRef] [PubMed]

K. Halterman, J. M. Elson, and S. Singh, "Plasmonic resonances and electromagnetic forces between coupled silver nanowires," Phys. Rev. B 72, 075429 (2005).
[CrossRef]

J. Garcia-Garcia, F. Martin, J. D. Baena, R. Marques, and L. Jelink, "On the resonances and polarizabilities of split-ring resonators," J. Appl. Phys. 98, 033103 (2005).
[CrossRef]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, and C. M. Soukoulis, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

2004

C. Rockstuhl, and H. P. Herzig, "Wavelength-dependent optical force on elliptical silver cylinders at plasmon resonance," Opt. Lett. 29, 2181-2183 (2004).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the electric resonance of split-ring resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef] [PubMed]

2002

P. Gay-Balmaz, and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, D. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

1998

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

S. Chu, "Nobel lecture: The manipulation of neutral particles," Rev. Mod. Phys. 70, 685-706 (1998).
[CrossRef]

C. Cohen-Tannoudji, "Nobel lecture: Manipulating atoms with photons," Rev. Mod. Phys. 70, 707-719 (1998).
[CrossRef]

W. D. Phillips, "Nobel lecture: Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
[CrossRef]

1972

P. B. Johnson, and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Agarwal, A.

H.-S. Park, A. Agarwal, N. A. Kotov, and O. D. Lavrentovich, "Controllable side-by-side and end-to-end assembly of Au nanorods by lyotropic chromonic materials," Langmuir 24, 13833-13837 (2008).
[CrossRef] [PubMed]

M. N’Gom, J. Ringnalda, J. F. Mansfield, A. Agarwal, N. Kotov, N. J. Zaluzec, and T. B. Norris, "Single particle plasmon spectroscopy of silver nanowires and gold nanorods," Nano Lett. 8, 3200-3204 (2008).
[CrossRef]

Aydin, K.

R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, "Multi-gap individual and coupled split-ring resonator structures," Opt. Express 16, 18131-18144 (2008).
[CrossRef] [PubMed]

Baehr-Jones, T.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, "Harnessing optical forces in integrated photonic circuits," Nature 456, 480-484 (2008).
[CrossRef]

Baena, J. D.

J. Garcia-Garcia, F. Martin, J. D. Baena, R. Marques, and L. Jelink, "On the resonances and polarizabilities of split-ring resonators," J. Appl. Phys. 98, 033103 (2005).
[CrossRef]

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Brus, L. E.

A. J. Hallock, P. L. Redmond, and L. E. Brus, "Optical forces between metallic particles," Proc. Natl. Acad. Sci. U.S.A. 102, 1280-1284 (2005).
[CrossRef] [PubMed]

Cai, W. S.

V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Capasso, F.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, "Evanescent-wave bonding between optical waveguides," Opt. Lett. 30, 3042-3044 (2005).
[CrossRef] [PubMed]

Chen, L.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, "Controlling photonic structures using optical forces," Nature 462, 633-636 (2009).
[CrossRef]

Chettiar, U. K.

V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Christy, R. W.

P. B. Johnson, and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Chu, P.

P. Chu, and D. L. Mills, "Laser-induced forces in metallic nanosystems: The role of plasmon resonances," Phys. Rev. Lett. 99, 127401 (2007).
[CrossRef] [PubMed]

Chu, S.

S. Chu, "Nobel lecture: The manipulation of neutral particles," Rev. Mod. Phys. 70, 685-706 (1998).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, "Nobel lecture: Manipulating atoms with photons," Rev. Mod. Phys. 70, 707-719 (1998).
[CrossRef]

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, and C. M. Soukoulis, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Drachev, V. P.

V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Economou, E. N.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low loss metamaterials based on classical electromagnetically induced transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Planar designs for electromagnetically induced transparency in metamaterials," Opt. Express 17, 5595-5605 (2009).
[CrossRef] [PubMed]

R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, "Multi-gap individual and coupled split-ring resonator structures," Opt. Express 16, 18131-18144 (2008).
[CrossRef] [PubMed]

J. Zhou, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006).
[CrossRef] [PubMed]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the electric resonance of split-ring resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Elson, J. M.

K. Halterman, J. M. Elson, and S. Singh, "Plasmonic resonances and electromagnetic forces between coupled silver nanowires," Phys. Rev. B 72, 075429 (2005).
[CrossRef]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, and C. M. Soukoulis, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Fedotov, V. A.

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, "A metamaterial analog of electromagnetically induced transparency," Phys. Rev. Lett. 101, 253903 (2008).
[CrossRef] [PubMed]

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

Garcia-Garcia, J.

J. Garcia-Garcia, F. Martin, J. D. Baena, R. Marques, and L. Jelink, "On the resonances and polarizabilities of split-ring resonators," J. Appl. Phys. 98, 033103 (2005).
[CrossRef]

Gay-Balmaz, P.

P. Gay-Balmaz, and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

Giessen, H.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

Gondarenko, A.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, "Controlling photonic structures using optical forces," Nature 462, 633-636 (2009).
[CrossRef]

Hallock, A. J.

A. J. Hallock, P. L. Redmond, and L. E. Brus, "Optical forces between metallic particles," Proc. Natl. Acad. Sci. U.S.A. 102, 1280-1284 (2005).
[CrossRef] [PubMed]

Halterman, K.

K. Halterman, J. M. Elson, and S. Singh, "Plasmonic resonances and electromagnetic forces between coupled silver nanowires," Phys. Rev. B 72, 075429 (2005).
[CrossRef]

Herzig, H. P.

C. Rockstuhl, and H. P. Herzig, "Wavelength-dependent optical force on elliptical silver cylinders at plasmon resonance," Opt. Lett. 29, 2181-2183 (2004).
[CrossRef] [PubMed]

Hochberg, M.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, "Harnessing optical forces in integrated photonic circuits," Nature 456, 480-484 (2008).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Ibanescu, M.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, "Evanescent-wave bonding between optical waveguides," Opt. Lett. 30, 3042-3044 (2005).
[CrossRef] [PubMed]

Jelink, L.

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M. N’Gom, J. Ringnalda, J. F. Mansfield, A. Agarwal, N. Kotov, N. J. Zaluzec, and T. B. Norris, "Single particle plasmon spectroscopy of silver nanowires and gold nanorods," Nano Lett. 8, 3200-3204 (2008).
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H.-S. Park, A. Agarwal, N. A. Kotov, and O. D. Lavrentovich, "Controllable side-by-side and end-to-end assembly of Au nanorods by lyotropic chromonic materials," Langmuir 24, 13833-13837 (2008).
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M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, "Harnessing optical forces in integrated photonic circuits," Nature 456, 480-484 (2008).
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J. Garcia-Garcia, F. Martin, J. D. Baena, R. Marques, and L. Jelink, "On the resonances and polarizabilities of split-ring resonators," J. Appl. Phys. 98, 033103 (2005).
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P. Gay-Balmaz, and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
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M. N’Gom, J. Ringnalda, J. F. Mansfield, A. Agarwal, N. Kotov, N. J. Zaluzec, and T. B. Norris, "Single particle plasmon spectroscopy of silver nanowires and gold nanorods," Nano Lett. 8, 3200-3204 (2008).
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S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
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R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, "Multi-gap individual and coupled split-ring resonator structures," Opt. Express 16, 18131-18144 (2008).
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D. R. Smith, W. J. Padilla, D. C. Vier, D. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
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S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
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N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, "A metamaterial analog of electromagnetically induced transparency," Phys. Rev. Lett. 101, 253903 (2008).
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J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
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M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, "Harnessing optical forces in integrated photonic circuits," Nature 456, 480-484 (2008).
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N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
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N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, "A metamaterial analog of electromagnetically induced transparency," Phys. Rev. Lett. 101, 253903 (2008).
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M. N’Gom, J. Ringnalda, J. F. Mansfield, A. Agarwal, N. Kotov, N. J. Zaluzec, and T. B. Norris, "Single particle plasmon spectroscopy of silver nanowires and gold nanorods," Nano Lett. 8, 3200-3204 (2008).
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J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
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V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
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R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
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D. R. Smith, W. J. Padilla, D. C. Vier, D. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
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Shalaev, V. M.

V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
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R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
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K. Halterman, J. M. Elson, and S. Singh, "Plasmonic resonances and electromagnetic forces between coupled silver nanowires," Phys. Rev. B 72, 075429 (2005).
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R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
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D. R. Smith, W. J. Padilla, D. C. Vier, D. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Smythe, E. J.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, "Evanescent-wave bonding between optical waveguides," Opt. Lett. 30, 3042-3044 (2005).
[CrossRef] [PubMed]

Soukoulis, C. M.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low loss metamaterials based on classical electromagnetically induced transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Planar designs for electromagnetically induced transparency in metamaterials," Opt. Express 17, 5595-5605 (2009).
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R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, "Multi-gap individual and coupled split-ring resonator structures," Opt. Express 16, 18131-18144 (2008).
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J. Zhou, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006).
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N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the electric resonance of split-ring resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef] [PubMed]

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J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
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Tang, H. X.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, "Harnessing optical forces in integrated photonic circuits," Nature 456, 480-484 (2008).
[CrossRef]

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P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low loss metamaterials based on classical electromagnetically induced transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Planar designs for electromagnetically induced transparency in metamaterials," Opt. Express 17, 5595-5605 (2009).
[CrossRef] [PubMed]

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T. J. Kippenberg, and K. J. Vahala, "Cavity optomechanics: Back-action at the mesoscale," Science 321, 1172-1176 (2008).
[CrossRef] [PubMed]

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D. Van Thourhout, and J. Roels, "Optomechanical device actuation through the optical gradient force," Nat. Photonics 4, 211-217 (2010).
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D. R. Smith, W. J. Padilla, D. C. Vier, D. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
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G. Dolling, C. Enkrich, M. Wegener, and C. M. Soukoulis, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

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N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

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G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, "Controlling photonic structures using optical forces," Nature 462, 633-636 (2009).
[CrossRef]

Xiong, C.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, "Harnessing optical forces in integrated photonic circuits," Nature 456, 480-484 (2008).
[CrossRef]

Yuan, H. K.

V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

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M. N’Gom, J. Ringnalda, J. F. Mansfield, A. Agarwal, N. Kotov, N. J. Zaluzec, and T. B. Norris, "Single particle plasmon spectroscopy of silver nanowires and gold nanorods," Nano Lett. 8, 3200-3204 (2008).
[CrossRef]

Zhang, L.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low loss metamaterials based on classical electromagnetically induced transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Planar designs for electromagnetically induced transparency in metamaterials," Opt. Express 17, 5595-5605 (2009).
[CrossRef] [PubMed]

Zhang, S.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Zheludev, N. I.

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, "A metamaterial analog of electromagnetically induced transparency," Phys. Rev. Lett. 101, 253903 (2008).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the electric resonance of split-ring resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

J. Appl. Phys.

J. Garcia-Garcia, F. Martin, J. D. Baena, R. Marques, and L. Jelink, "On the resonances and polarizabilities of split-ring resonators," J. Appl. Phys. 98, 033103 (2005).
[CrossRef]

P. Gay-Balmaz, and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

J. Phys. Condens. Matter

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Langmuir

H.-S. Park, A. Agarwal, N. A. Kotov, and O. D. Lavrentovich, "Controllable side-by-side and end-to-end assembly of Au nanorods by lyotropic chromonic materials," Langmuir 24, 13833-13837 (2008).
[CrossRef] [PubMed]

Nano Lett.

M. N’Gom, J. Ringnalda, J. F. Mansfield, A. Agarwal, N. Kotov, N. J. Zaluzec, and T. B. Norris, "Single particle plasmon spectroscopy of silver nanowires and gold nanorods," Nano Lett. 8, 3200-3204 (2008).
[CrossRef]

Nat. Mater.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
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Figures (11)

Fig. 1
Fig. 1

The nanowire pair that is considered in this article for the purpose of studying the optical force in metamaterials. The propagation direction and polarization of the incident electromagnetic wave is indicated.

Fig. 2
Fig. 2

(a) The common and (b) the relative optical force exerted on a pair of nanowires by an incident field of 50 mW / μm2. The length of the nanowires is L = 100 nm, their diameter is D = 25 nm, and the distance between the nanowires is d = 25 nm. The relative force exhibits two resonances: the magnetic dipole resonance with an attractive force and the electric dipole resonance with a repulsive force.

Fig. 3
Fig. 3

Electric (a) and magnetic (b) dipole moment of the charge distribution in an isolated nanowire pair with length L = 100 nm, diameter D = 25 nm, and interwire distance D = 25 nm. The insets show the charge and current distributions of the eigenmodes at 445 THz (electric dipole resonance) and at 410 THz (magnetic dipole resonance).

Fig. 4
Fig. 4

The relative optical force in an isolated nanowire pair as a function of length. All nanowires have diameter D = 25 nm and interwire distance d = 25 nm. Note that the force in the longer rods is exponentially larger than the force in the shortest sample (which has L = D = 25 nm and is therefore actually a pair of nanospheres).

Fig. 5
Fig. 5

(a) The relative optical force in an isolated nanowire pair as a function of frequency for different interwire distances. All nanowires have diameter D = 25 nm and length L = 100 nm. (b) The relative optical force at the resonance frequency as a function of the interwire distance.

Fig. 6
Fig. 6

Schematic of the array of nanowires studied in Sec. 4.

Fig. 7
Fig. 7

(a) The common and (b) the relative optical force exerted on a pair of nanowires in a 2D periodic array with unit cell 100 nm × 200 nm when illuminated by a laser field of 50 mW/μm2. The length of the nanowires is L = 100 nm, their diameter is D = 25 nm, and the distance between the nanowires is d = 25 nm. The relative force exhibits two resonances: the magnetic dipole resonance with an attractive force and the electric dipole resonance with a repulsive force.

Fig. 8
Fig. 8

Electric (a) and magnetic (b) dipole moment of the charge distribution in a 2D periodic nanowire pair metamaterial with unit cell 100 nm × 200 nm. The length of the nanowires is L = 100 nm, their diameter D = 25 nm, and the interwire distance equals D = 25 nm.

Fig. 9
Fig. 9

The relative optical force in a periodic nanowire pair metamaterial as a function of the unit cell size height h (for smaller unit cell height, the ends of the nanowires in neighbouring cells come closer). All nanowires have length L = 100 nm, diameter D = 25 nm, and interwire distance d = 25 nm. The unit cell size is 100 nm × h. Note that the optical force decreases significantly for metamaterials with smaller unit cell height.

Fig. 10
Fig. 10

The relative optical force in a periodic nanowire pair metamaterial as a function of the unit cell size height h (for smaller unit cell height, the ends of the nanowires in neighbouring cells come closer). All nanowires have length L = 200 nm, diameter D = 50 nm, and interwire distance d = 50 nm. The unit cell size is 200 nm × h. Note that the optical force reverses from attractive to repulsive for metamaterials with smaller unit cell height. The arrows mark the position of the magnetic dipole resonance.

Fig. 11
Fig. 11

Charge and current distribution in the nanowire pair metamaterial. (a) If the height of the unit cell is substantially larger than the length of the nanowires, the force at the magnetic dipole resonance frequency has the nature of a Coulomb force between the charges at the ends of the wires and is attractive for the magnetic dipole resonance. (b) If the height of the unit cell is only slightly larger than the length of the nanowires, the force at the magnetic dipole resonance frequency has the nature of an electric dipole-dipole interaction; the repulsive Lorentz force between the currents flowing in opposite directions can now be of comparable size or even dominate the optical force.

Equations (6)

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F i = V ( ρ E i + ɛ ijk J j B k ) d V ,
F i = ɛ 0 μ 0 V S i t d V + V T ij x j d V ,
T ij = ɛ 0 ( E i E j 1 2 δ ij E 2 ) + 1 μ 0 ( B i B i 1 2 δ ij B 2 ) ,
F i = S T i j n i d S .
p z = V P z d V = V ( D z ɛ 0 E z ) d V .
m y = V ( z P x t x P z t ) d V = i ω V [ z ( D x ɛ 0 E x ) x ( D z ɛ 0 E z ) ] d V .

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