Abstract

We propose nano-optical antennas with asymmetric radiation patterns as light-driven mechanical recoil force generators. Directional antennas are found to generate recoil force efficiently when driven in the spectral proximity of their resonances. It is also shown that the recoil force is equivalent to the Poynting vector integrated over a closed sphere containing the antenna structures.

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References

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  1. A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19(8), 283–335 (1971).
    [CrossRef]
  2. S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57(3), 314–317 (1986).
    [CrossRef] [PubMed]
  3. S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010).
    [CrossRef] [PubMed]
  4. S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
    [CrossRef] [PubMed]
  5. M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5(8), 570–573 (2010).
    [CrossRef] [PubMed]
  6. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2007).
  7. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  8. S. Uda, “Wireless beam of short electric waves,” J. IEE (Japan) 452, 273–282 (1926).
  9. H. Yagi, “Beam transmission of ultra short waves,” in Proceedings of IRE Conference, pp. 715–741.
  10. A. W. Rudge, “Offset-parabolic-reflector antennas: a review,” in Proceedings of IEEE Conference (1978), pp. 1592–1618.
  11. T. Pakizeh and M. Käll, “Unidirectional ultracompact optical nanoantennas,” Nano Lett. 9(6), 2343–2349 (2009).
    [CrossRef] [PubMed]
  12. T. Pakizeh, M. S. Abrishamian, N. Granpayeh, A. Dmitriev, and M. Käll, “Magnetic-field enhancement in gold nanosandwiches,” Opt. Express 14(18), 8240–8246 (2006).
    [CrossRef] [PubMed]
  13. T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical Yagi-Uda antenna,” Opt. Express 16(14), 10858–6 (2008).
    [CrossRef] [PubMed]
  14. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, 1995), Chap. 2.
  15. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
    [CrossRef] [PubMed]
  16. C. A. Balanis, Antenna Theory (John Wiley & Sons, 2005).
  17. T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4(5), 312–315 (2010).
    [CrossRef]

2010 (4)

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010).
[CrossRef] [PubMed]

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
[CrossRef] [PubMed]

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5(8), 570–573 (2010).
[CrossRef] [PubMed]

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4(5), 312–315 (2010).
[CrossRef]

2009 (1)

T. Pakizeh and M. Käll, “Unidirectional ultracompact optical nanoantennas,” Nano Lett. 9(6), 2343–2349 (2009).
[CrossRef] [PubMed]

2008 (1)

2006 (1)

2003 (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

1986 (1)

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57(3), 314–317 (1986).
[CrossRef] [PubMed]

1971 (1)

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19(8), 283–335 (1971).
[CrossRef]

1926 (1)

S. Uda, “Wireless beam of short electric waves,” J. IEE (Japan) 452, 273–282 (1926).

Abrishamian, M. S.

Ashkin, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57(3), 314–317 (1986).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19(8), 283–335 (1971).
[CrossRef]

Bartal, G.

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5(8), 570–573 (2010).
[CrossRef] [PubMed]

Bjorkholm, J. E.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57(3), 314–317 (1986).
[CrossRef] [PubMed]

Cable, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57(3), 314–317 (1986).
[CrossRef] [PubMed]

Chu, S.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57(3), 314–317 (1986).
[CrossRef] [PubMed]

Crozier, K.

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
[CrossRef] [PubMed]

Dmitriev, A.

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19(8), 283–335 (1971).
[CrossRef]

Erickson, D.

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010).
[CrossRef] [PubMed]

Granpayeh, N.

Halas, N. J.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Hofmann, H. F.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4(5), 312–315 (2010).
[CrossRef]

Kadoya, Y.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4(5), 312–315 (2010).
[CrossRef]

Käll, M.

Kosako, T.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4(5), 312–315 (2010).
[CrossRef]

Lin, S.

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
[CrossRef] [PubMed]

Liu, M.

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5(8), 570–573 (2010).
[CrossRef] [PubMed]

Liu, Y.

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5(8), 570–573 (2010).
[CrossRef] [PubMed]

Mandal, S.

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010).
[CrossRef] [PubMed]

Nordlander, P.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Pakizeh, T.

Prodan, E.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Schonbrun, E.

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
[CrossRef] [PubMed]

Serey, X.

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010).
[CrossRef] [PubMed]

Stefani, F. D.

Taminiau, T. H.

Uda, S.

S. Uda, “Wireless beam of short electric waves,” J. IEE (Japan) 452, 273–282 (1926).

van Hulst, N. F.

Zentgraf, T.

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5(8), 570–573 (2010).
[CrossRef] [PubMed]

Zhang, X.

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5(8), 570–573 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19(8), 283–335 (1971).
[CrossRef]

J. IEE (Japan) (1)

S. Uda, “Wireless beam of short electric waves,” J. IEE (Japan) 452, 273–282 (1926).

Nano Lett. (3)

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010).
[CrossRef] [PubMed]

S. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
[CrossRef] [PubMed]

T. Pakizeh and M. Käll, “Unidirectional ultracompact optical nanoantennas,” Nano Lett. 9(6), 2343–2349 (2009).
[CrossRef] [PubMed]

Nat. Nanotechnol. (1)

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5(8), 570–573 (2010).
[CrossRef] [PubMed]

Nat. Photonics (1)

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4(5), 312–315 (2010).
[CrossRef]

Opt. Express (2)

Phys. Rev. Lett. (1)

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57(3), 314–317 (1986).
[CrossRef] [PubMed]

Science (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Other (6)

C. A. Balanis, Antenna Theory (John Wiley & Sons, 2005).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, 1995), Chap. 2.

H. Yagi, “Beam transmission of ultra short waves,” in Proceedings of IRE Conference, pp. 715–741.

A. W. Rudge, “Offset-parabolic-reflector antennas: a review,” in Proceedings of IEEE Conference (1978), pp. 1592–1618.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2007).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

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Figures (4)

Fig. 1
Fig. 1

Calculations of the recoil force on a radiator (a) by integrating Maxwell’s stress tensor over an enclosing surface “∂V” and (b) by vector summation of Poynting vectors over the far-field sphere “∂Vfar”.

Fig. 2
Fig. 2

The far-field radiation patterns of (a) y-directed electric dipole oscillator and (b) z-directed magnetic dipole oscillator and (c) the combination of y-directed electric dipole and z-directed magnetic dipole oscillators. The dashed black circles indicate the equator (θ = π/2). (d) The coordinate for the far-field radiation pattern plots. νx and νy are directional cosines in x and y directions, respectively. The radius from the center indicates the polar angle (0≤θ≤π/2) between the observation point P and the z-axis. The angle (ϕ) is the azimuthal angle of the observation point P. The black arrows at the sides of far-field pattern indicate the electric field direction.

Fig. 3
Fig. 3

(a) Schematic of coupled nano-disk structure. The diameter and the thickness of gold nano-disks are 90 nm and 20 nm, respectively. The surrounding media (including the middle gap between the two nano-disks) is the air (ε = 1). (b) Resonance spectrum of coupled nano-disk structure (red line) and a single nano-disk (black line). (c) Electric field profile and far-field radiation pattern of symmetric mode and anti-symmetric mode of coupled nano-disk structure. (d) Schematic of optical Yagi-Uda antenna in the air. The length of five elements are 200 nm (reflector), 160 nm (feed), and 144 nm (3 directors), respectively and the radius of the elements is 20 nm. Each elements have hemi-spherical ends. Reflector-feed distance is 130 nm and feed-director distance is 143 nm. (e) Electric field profile of optical Yagi-Uda antenna at resonance.

Fig. 4
Fig. 4

(a) Far-field radiation pattern of coupled nano-disk structure. (b) Far-field radiation pattern of optical Yagi-Uda antenna. (c) Force conversion efficiency (lines with symbols) of coupled nano-disk structure and optical Yagi-Uda antenna. Also shown is the resonance spectra of coupled nano-disk (dashed-line in red) and optical Yagi-Uda antenna (dashed-line in black). λres = λanti-symmetric = 665 nm for coupled nano-disk structure. λres = 600 nm for optical Yagi-Uda antenna.

Equations (14)

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T = ε 0 E E + μ 0 H H 1 2 ( ε 0 | E | 2 + μ 0 | H | 2 ) I ,
F ( r , t ) = V T ( r , t ) n ^ ( r ) d a .
e ^ ( r , t ) h ^ ( r , t ) ,
E = E ( r , t ) e ^ ( r , t ) ,
H = H ( r , t ) h ^ ( r , t ) ,
s ^ ( r ^ , t ) = e ^ ( r , t ) × h ^ ( r , t ) ,
T = [ ε 0 E 2 2 μ 0 H 2 2 0 0 0 ε 0 E 2 2 + μ 0 H 2 2 0 0 0 ε 0 E 2 2 μ 0 H 2 2 ] .
e ^ e ^ = [ 1 0 0 0 0 0 0 0 0 ] ,     h ^ h ^ = [ 0 0 0 0 1 0 0 0 0 ] ,     s ^ s ^ = [ 0 0 0 0 0 0 0 0 1 ] .
T = [ 0 0 0 0 0 0 0 0 ε 0 E 2 + μ 0 H 2 2 ] = | E × H | s ^ s ^ c = S c s ^ s ^ .
F ( r , t ) = V f a r S c s ^ s ^ n ^ d a = V f a r S c d a .
η i = V f a r S i ^ d a V f a r S n ^ d a ,
F = 1 c V f a r S d a = 1 c ( η x x ^ + η y y ^ + η z z ^ ) V f a r S n ^ d a .
S ( θ , ϕ ) = 3 8 π ( sin θ cos ϕ + 1 ) 2 ,
D = λ λ r e s λ r e s

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