Abstract

Upon illumination by a circularly polarized plane wave, a nanohelix converts part of the incoming optical spin angular momentum into optical orbital angular momentum. Here, by combining partial wave analysis with band structure and eigenmode calculations, we studied the optical torque and light extinction for a gold nanohelix. It is found that spin-orbital angular momentum conversion is a necessary condition for inducing recoil optical torque, but not for light extinction. In other words, a particle can have a large light extinction cross section but not a strong torque, or vice versa. Our calculation also shows that broad frequency band negative optical torque can also exist in a nanohelix, which possesses screw-axis symmetry.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Spinning and orbiting motion of particles in vortex beams with circular or radial polarizations

Manman Li, Shaohui Yan, Baoli Yao, Yansheng Liang, and Peng Zhang
Opt. Express 24(18) 20604-20612 (2016)

Interaction of light carrying orbital angular momentum with a chiral dipolar scatterer

Paweł Woźniak, Israel De Leon, Katja Höflich, Gerd Leuchs, and Peter Banzer
Optica 6(8) 961-965 (2019)

Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett
Opt. Lett. 22(1) 52-54 (1997)

References

  • View by:
  • |
  • |
  • |

  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986).
    [Crossref] [PubMed]
  2. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
    [Crossref]
  3. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
    [Crossref] [PubMed]
  4. A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
    [Crossref] [PubMed]
  5. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
    [Crossref] [PubMed]
  6. A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95(16), 168102 (2005).
    [Crossref] [PubMed]
  7. A. Kotnala and R. Gordon, “Quantification of high-efficiency trapping of nanoparticles in a double nanohole optical tweezer,” Nano Lett. 14(2), 853–856 (2014).
    [Crossref] [PubMed]
  8. P. C. Chaumet and A. Rahmani, “Dressed for success,” Nat. Nanotechnol. 9(4), 252–253 (2014).
    [Crossref] [PubMed]
  9. A. Rahimzadegan, M. Fruhnert, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Optical force and torque on dipolar dual chiral particles,” Phys. Rev. B 94(12), 125123 (2016).
    [Crossref]
  10. L. M. Zhou, K. W. Xiao, J. Chen, and N. Zhao, “Optical levitation of nanodiamonds by doughnut beams in vacuum,” Laser Photonics Rev. 11(2), 1600284 (2017).
    [Crossref]
  11. A. Rahimzadegan, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Fundamental limits of optical force and torque,” Phys. Rev. B 95(3), 035106 (2017).
    [Crossref]
  12. R. Shaniv and R. Ozeri, “Quantum lock-in force sensing using optical clock Doppler velocimetry,” Nat. Commun. 8, 14157 (2017).
    [Crossref] [PubMed]
  13. J. Li and P. M. Haney, “Optical spin transfer and spin-orbit torques in thin film ferromagnets,” Phys. Rev. B 96(5), 054447 (2017).
    [Crossref] [PubMed]
  14. M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
    [Crossref] [PubMed]
  15. W. Li, N. Li, Y. Shen, Z. Fu, H. Su, and H. Hu, “Dynamic analysis and rotation experiment of an optical-trapped microsphere in air,” Appl. Opt. 57(4), 823–828 (2018).
    [Crossref] [PubMed]
  16. J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
    [Crossref]
  17. D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
    [Crossref] [PubMed]
  18. A. Dogariu, S. Sukhov, and J. Saenz, “Optically induced ‘negative forces’,” Nat. Photonics 7(1), 24–27 (2013).
    [Crossref]
  19. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
    [Crossref] [PubMed]
  20. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
    [Crossref]
  21. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
    [Crossref] [PubMed]
  22. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
    [Crossref] [PubMed]
  23. S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nat. Mater. 4(7), 530–533 (2005).
    [Crossref] [PubMed]
  24. 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]
  25. J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
    [Crossref] [PubMed]
  26. Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4(1), 2374 (2013).
    [Crossref] [PubMed]
  27. L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics Publishing, 2003).
  28. F. Cardano and L. Marrucci, “Spin-orbit photonics,” Nat. Photonics 9(12), 776–778 (2015).
    [Crossref]
  29. K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
    [Crossref]
  30. G. Li, M. Kang, S. Chen, S. Zhang, E. Y. B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
    [Crossref] [PubMed]
  31. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
    [Crossref] [PubMed]
  32. D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8(8), 610–614 (2014).
    [Crossref]
  33. S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A 24(2), 430–443 (2007).
    [Crossref] [PubMed]
  34. J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative optical torque,” Sci. Rep. 4(1), 6386 (2015).
    [Crossref] [PubMed]
  35. H. Magallanes and E. Brasselet, “Macroscopic direct observation of optical spin-dependent lateral forces and left-handed torques,” Nat. Photonics 12(8), 461–464 (2018).
    [Crossref]
  36. M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24(24), 4493–4499 (1985).
    [Crossref] [PubMed]
  37. S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014).
    [Crossref] [PubMed]
  38. K. Ding, J. Ng, L. Zhou, and C. T. Chan, “Realization of optical pulling forces using chirality,” Phys. Rev. A 89(6), 063825 (2014).
    [Crossref]
  39. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
    [Crossref] [PubMed]
  40. R. N. Ji, S. W. Wang, X. X. Liu, H. J. Guo, and W. Lu, “Hybrid helix metamaterials for giant and ultrawide circular dichroism,” ACS Photonics 3(12), 2368–2374 (2016).
    [Crossref]
  41. M. Esposito, V. Tasco, F. Todisco, M. Cuscunà, A. Benedetti, M. Scuderi, G. Nicotra, and A. Passaseo, “Programmable extreme chirality in the visible by helix-shaped metamaterial platform,” Nano Lett. 16(9), 5823–5828 (2016).
    [Crossref] [PubMed]
  42. COMSOL is a finite-element-method electromagnetic solver, see “ www.comsol.com
  43. S. Sensiper, “Electromagnetic wave propagation on helical structures (a review and survey of recent progress),” Proc. IRE43, 149–161 (1955).
  44. C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
    [Crossref] [PubMed]
  45. Y. L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34(21), 4573–4588 (1995).
    [Crossref] [PubMed]
  46. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, 1983).
  47. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002).
  48. M. J. Berg, A. Chakrabarti, and C. M. Sorensen, “General derivation of the total electromagnetic cross sections for an arbitrary particle,” J. Quant. Spectrosc. Radiat. Transf. 110(1-2), 43–50 (2009).
    [Crossref]
  49. M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, “On definition and measurement of extinction cross section,” J. Quant. Spectrosc. Radiat. Transf. 110(4-5), 323–327 (2009).
    [Crossref]
  50. J. Chen, J. Ng, S. Liu, and Z. Lin, “Analytical calculation of axial optical force on a Rayleigh particle illuminated by Gaussian beams beyond the paraxial approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(2), 026607 (2009).
    [Crossref] [PubMed]
  51. A. Dogariu and C. Schwartz, “Conservation of angular momentum of light in single scattering,” Opt. Express 14(18), 8425–8433 (2006).
    [Crossref] [PubMed]
  52. D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
    [Crossref] [PubMed]

2018 (3)

M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
[Crossref] [PubMed]

W. Li, N. Li, Y. Shen, Z. Fu, H. Su, and H. Hu, “Dynamic analysis and rotation experiment of an optical-trapped microsphere in air,” Appl. Opt. 57(4), 823–828 (2018).
[Crossref] [PubMed]

H. Magallanes and E. Brasselet, “Macroscopic direct observation of optical spin-dependent lateral forces and left-handed torques,” Nat. Photonics 12(8), 461–464 (2018).
[Crossref]

2017 (4)

L. M. Zhou, K. W. Xiao, J. Chen, and N. Zhao, “Optical levitation of nanodiamonds by doughnut beams in vacuum,” Laser Photonics Rev. 11(2), 1600284 (2017).
[Crossref]

A. Rahimzadegan, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Fundamental limits of optical force and torque,” Phys. Rev. B 95(3), 035106 (2017).
[Crossref]

R. Shaniv and R. Ozeri, “Quantum lock-in force sensing using optical clock Doppler velocimetry,” Nat. Commun. 8, 14157 (2017).
[Crossref] [PubMed]

J. Li and P. M. Haney, “Optical spin transfer and spin-orbit torques in thin film ferromagnets,” Phys. Rev. B 96(5), 054447 (2017).
[Crossref] [PubMed]

2016 (3)

A. Rahimzadegan, M. Fruhnert, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Optical force and torque on dipolar dual chiral particles,” Phys. Rev. B 94(12), 125123 (2016).
[Crossref]

R. N. Ji, S. W. Wang, X. X. Liu, H. J. Guo, and W. Lu, “Hybrid helix metamaterials for giant and ultrawide circular dichroism,” ACS Photonics 3(12), 2368–2374 (2016).
[Crossref]

M. Esposito, V. Tasco, F. Todisco, M. Cuscunà, A. Benedetti, M. Scuderi, G. Nicotra, and A. Passaseo, “Programmable extreme chirality in the visible by helix-shaped metamaterial platform,” Nano Lett. 16(9), 5823–5828 (2016).
[Crossref] [PubMed]

2015 (3)

J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative optical torque,” Sci. Rep. 4(1), 6386 (2015).
[Crossref] [PubMed]

F. Cardano and L. Marrucci, “Spin-orbit photonics,” Nat. Photonics 9(12), 776–778 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

2014 (6)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8(8), 610–614 (2014).
[Crossref]

A. Kotnala and R. Gordon, “Quantification of high-efficiency trapping of nanoparticles in a double nanohole optical tweezer,” Nano Lett. 14(2), 853–856 (2014).
[Crossref] [PubMed]

P. C. Chaumet and A. Rahmani, “Dressed for success,” Nat. Nanotechnol. 9(4), 252–253 (2014).
[Crossref] [PubMed]

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014).
[Crossref] [PubMed]

K. Ding, J. Ng, L. Zhou, and C. T. Chan, “Realization of optical pulling forces using chirality,” Phys. Rev. A 89(6), 063825 (2014).
[Crossref]

2013 (3)

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4(1), 2374 (2013).
[Crossref] [PubMed]

A. Dogariu, S. Sukhov, and J. Saenz, “Optically induced ‘negative forces’,” Nat. Photonics 7(1), 24–27 (2013).
[Crossref]

2012 (1)

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

2011 (1)

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

2010 (3)

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]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref] [PubMed]

2009 (5)

M. J. Berg, A. Chakrabarti, and C. M. Sorensen, “General derivation of the total electromagnetic cross sections for an arbitrary particle,” J. Quant. Spectrosc. Radiat. Transf. 110(1-2), 43–50 (2009).
[Crossref]

M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, “On definition and measurement of extinction cross section,” J. Quant. Spectrosc. Radiat. Transf. 110(4-5), 323–327 (2009).
[Crossref]

J. Chen, J. Ng, S. Liu, and Z. Lin, “Analytical calculation of axial optical force on a Rayleigh particle illuminated by Gaussian beams beyond the paraxial approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(2), 026607 (2009).
[Crossref] [PubMed]

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[Crossref] [PubMed]

2007 (1)

2006 (1)

2005 (2)

S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nat. Mater. 4(7), 530–533 (2005).
[Crossref] [PubMed]

A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95(16), 168102 (2005).
[Crossref] [PubMed]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

2002 (1)

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref] [PubMed]

2001 (1)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

1998 (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
[Crossref]

1995 (2)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

Y. L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34(21), 4573–4588 (1995).
[Crossref] [PubMed]

1987 (2)

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[Crossref] [PubMed]

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[Crossref] [PubMed]

1986 (1)

1985 (1)

1970 (1)

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

Alaee, R.

A. Rahimzadegan, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Fundamental limits of optical force and torque,” Phys. Rev. B 95(3), 035106 (2017).
[Crossref]

A. Rahimzadegan, M. Fruhnert, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Optical force and torque on dipolar dual chiral particles,” Phys. Rev. B 94(12), 125123 (2016).
[Crossref]

Alexander, R. W.

Arita, Y.

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4(1), 2374 (2013).
[Crossref] [PubMed]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[Crossref] [PubMed]

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[Crossref] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986).
[Crossref] [PubMed]

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

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

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]

Bell, R. J.

Benedetti, A.

M. Esposito, V. Tasco, F. Todisco, M. Cuscunà, A. Benedetti, M. Scuderi, G. Nicotra, and A. Passaseo, “Programmable extreme chirality in the visible by helix-shaped metamaterial platform,” Nano Lett. 16(9), 5823–5828 (2016).
[Crossref] [PubMed]

Berg, M. J.

M. J. Berg, A. Chakrabarti, and C. M. Sorensen, “General derivation of the total electromagnetic cross sections for an arbitrary particle,” J. Quant. Spectrosc. Radiat. Transf. 110(1-2), 43–50 (2009).
[Crossref]

M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, “On definition and measurement of extinction cross section,” J. Quant. Spectrosc. Radiat. Transf. 110(4-5), 323–327 (2009).
[Crossref]

Bjorkholm, J. E.

Bliokh, K. Y.

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Brasselet, E.

H. Magallanes and E. Brasselet, “Macroscopic direct observation of optical spin-dependent lateral forces and left-handed torques,” Nat. Photonics 12(8), 461–464 (2018).
[Crossref]

D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8(8), 610–614 (2014).
[Crossref]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Cardano, F.

F. Cardano and L. Marrucci, “Spin-orbit photonics,” Nat. Photonics 9(12), 776–778 (2015).
[Crossref]

Chakrabarti, A.

M. J. Berg, A. Chakrabarti, and C. M. Sorensen, “General derivation of the total electromagnetic cross sections for an arbitrary particle,” J. Quant. Spectrosc. Radiat. Transf. 110(1-2), 43–50 (2009).
[Crossref]

Chan, C. T.

J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative optical torque,” Sci. Rep. 4(1), 6386 (2015).
[Crossref] [PubMed]

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014).
[Crossref] [PubMed]

K. Ding, J. Ng, L. Zhou, and C. T. Chan, “Realization of optical pulling forces using chirality,” Phys. Rev. A 89(6), 063825 (2014).
[Crossref]

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref] [PubMed]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

Chaumet, P. C.

P. C. Chaumet and A. Rahmani, “Dressed for success,” Nat. Nanotechnol. 9(4), 252–253 (2014).
[Crossref] [PubMed]

Cheah, K. W.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Chen, J.

L. M. Zhou, K. W. Xiao, J. Chen, and N. Zhao, “Optical levitation of nanodiamonds by doughnut beams in vacuum,” Laser Photonics Rev. 11(2), 1600284 (2017).
[Crossref]

J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative optical torque,” Sci. Rep. 4(1), 6386 (2015).
[Crossref] [PubMed]

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

J. Chen, J. Ng, S. Liu, and Z. Lin, “Analytical calculation of axial optical force on a Rayleigh particle illuminated by Gaussian beams beyond the paraxial approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(2), 026607 (2009).
[Crossref] [PubMed]

Chen, S.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Chu, S.

Cuscunà, M.

M. Esposito, V. Tasco, F. Todisco, M. Cuscunà, A. Benedetti, M. Scuderi, G. Nicotra, and A. Passaseo, “Programmable extreme chirality in the visible by helix-shaped metamaterial platform,” Nano Lett. 16(9), 5823–5828 (2016).
[Crossref] [PubMed]

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Dholakia, K.

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4(1), 2374 (2013).
[Crossref] [PubMed]

S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nat. Mater. 4(7), 530–533 (2005).
[Crossref] [PubMed]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Ding, K.

J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative optical torque,” Sci. Rep. 4(1), 6386 (2015).
[Crossref] [PubMed]

K. Ding, J. Ng, L. Zhou, and C. T. Chan, “Realization of optical pulling forces using chirality,” Phys. Rev. A 89(6), 063825 (2014).
[Crossref]

Dogariu, A.

A. Dogariu, S. Sukhov, and J. Saenz, “Optically induced ‘negative forces’,” Nat. Photonics 7(1), 24–27 (2013).
[Crossref]

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[Crossref] [PubMed]

A. Dogariu and C. Schwartz, “Conservation of angular momentum of light in single scattering,” Opt. Express 14(18), 8425–8433 (2006).
[Crossref] [PubMed]

Donato, M. G.

M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
[Crossref] [PubMed]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[Crossref] [PubMed]

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[Crossref] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986).
[Crossref] [PubMed]

Esposito, M.

M. Esposito, V. Tasco, F. Todisco, M. Cuscunà, A. Benedetti, M. Scuderi, G. Nicotra, and A. Passaseo, “Programmable extreme chirality in the visible by helix-shaped metamaterial platform,” Nano Lett. 16(9), 5823–5828 (2016).
[Crossref] [PubMed]

Fernandez-Corbaton, I.

A. Rahimzadegan, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Fundamental limits of optical force and torque,” Phys. Rev. B 95(3), 035106 (2017).
[Crossref]

A. Rahimzadegan, M. Fruhnert, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Optical force and torque on dipolar dual chiral particles,” Phys. Rev. B 94(12), 125123 (2016).
[Crossref]

Foti, A.

M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
[Crossref] [PubMed]

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
[Crossref]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

Fruhnert, M.

A. Rahimzadegan, M. Fruhnert, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Optical force and torque on dipolar dual chiral particles,” Phys. Rev. B 94(12), 125123 (2016).
[Crossref]

Fu, Z.

Fung, K. H.

J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative optical torque,” Sci. Rep. 4(1), 6386 (2015).
[Crossref] [PubMed]

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Gordon, R.

A. Kotnala and R. Gordon, “Quantification of high-efficiency trapping of nanoparticles in a double nanohole optical tweezer,” Nano Lett. 14(2), 853–856 (2014).
[Crossref] [PubMed]

Grier, D. G.

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Gucciardi, P. G.

M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
[Crossref] [PubMed]

Guo, H. J.

R. N. Ji, S. W. Wang, X. X. Liu, H. J. Guo, and W. Lu, “Hybrid helix metamaterials for giant and ultrawide circular dichroism,” ACS Photonics 3(12), 2368–2374 (2016).
[Crossref]

Haefner, D.

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[Crossref] [PubMed]

Hakobyan, D.

D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8(8), 610–614 (2014).
[Crossref]

Haney, P. M.

J. Li and P. M. Haney, “Optical spin transfer and spin-orbit torques in thin film ferromagnets,” Phys. Rev. B 96(5), 054447 (2017).
[Crossref] [PubMed]

Hanna, S.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

Heckenberg, N. R.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
[Crossref]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

Hu, H.

Iatì, M. A.

M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
[Crossref] [PubMed]

Ji, R. N.

R. N. Ji, S. W. Wang, X. X. Liu, H. J. Guo, and W. Lu, “Hybrid helix metamaterials for giant and ultrawide circular dichroism,” ACS Photonics 3(12), 2368–2374 (2016).
[Crossref]

Jones, P. H.

M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
[Crossref] [PubMed]

Kang, M.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Kotnala, A.

A. Kotnala and R. Gordon, “Quantification of high-efficiency trapping of nanoparticles in a double nanohole optical tweezer,” Nano Lett. 14(2), 853–856 (2014).
[Crossref] [PubMed]

Krauss, T. F.

S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nat. Mater. 4(7), 530–533 (2005).
[Crossref] [PubMed]

Li, G.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Li, H.

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref] [PubMed]

Li, J.

J. Li and P. M. Haney, “Optical spin transfer and spin-orbit torques in thin film ferromagnets,” Phys. Rev. B 96(5), 054447 (2017).
[Crossref] [PubMed]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Li, N.

Li, W.

Lin, Z.

J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative optical torque,” Sci. Rep. 4(1), 6386 (2015).
[Crossref] [PubMed]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

J. Chen, J. Ng, S. Liu, and Z. Lin, “Analytical calculation of axial optical force on a Rayleigh particle illuminated by Gaussian beams beyond the paraxial approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(2), 026607 (2009).
[Crossref] [PubMed]

Lin, Z. F.

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Linden, S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[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, S.

J. Chen, J. Ng, S. Liu, and Z. Lin, “Analytical calculation of axial optical force on a Rayleigh particle illuminated by Gaussian beams beyond the paraxial approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(2), 026607 (2009).
[Crossref] [PubMed]

Liu, X. X.

R. N. Ji, S. W. Wang, X. X. Liu, H. J. Guo, and W. Lu, “Hybrid helix metamaterials for giant and ultrawide circular dichroism,” ACS Photonics 3(12), 2368–2374 (2016).
[Crossref]

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]

Long, L. L.

Lu, W.

R. N. Ji, S. W. Wang, X. X. Liu, H. J. Guo, and W. Lu, “Hybrid helix metamaterials for giant and ultrawide circular dichroism,” ACS Photonics 3(12), 2368–2374 (2016).
[Crossref]

MacDonald, M. P.

S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nat. Mater. 4(7), 530–533 (2005).
[Crossref] [PubMed]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Magallanes, H.

H. Magallanes and E. Brasselet, “Macroscopic direct observation of optical spin-dependent lateral forces and left-handed torques,” Nat. Photonics 12(8), 461–464 (2018).
[Crossref]

Maragò, O. M.

M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
[Crossref] [PubMed]

Marrucci, L.

F. Cardano and L. Marrucci, “Spin-orbit photonics,” Nat. Photonics 9(12), 776–778 (2015).
[Crossref]

Mazilu, M.

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4(1), 2374 (2013).
[Crossref] [PubMed]

Messina, E.

M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
[Crossref] [PubMed]

Mishchenko, M. I.

M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, “On definition and measurement of extinction cross section,” J. Quant. Spectrosc. Radiat. Transf. 110(4-5), 323–327 (2009).
[Crossref]

Neale, S. L.

S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nat. Mater. 4(7), 530–533 (2005).
[Crossref] [PubMed]

Ng, J.

J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative optical torque,” Sci. Rep. 4(1), 6386 (2015).
[Crossref] [PubMed]

K. Ding, J. Ng, L. Zhou, and C. T. Chan, “Realization of optical pulling forces using chirality,” Phys. Rev. A 89(6), 063825 (2014).
[Crossref]

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

J. Chen, J. Ng, S. Liu, and Z. Lin, “Analytical calculation of axial optical force on a Rayleigh particle illuminated by Gaussian beams beyond the paraxial approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(2), 026607 (2009).
[Crossref] [PubMed]

Nicotra, G.

M. Esposito, V. Tasco, F. Todisco, M. Cuscunà, A. Benedetti, M. Scuderi, G. Nicotra, and A. Passaseo, “Programmable extreme chirality in the visible by helix-shaped metamaterial platform,” Nano Lett. 16(9), 5823–5828 (2016).
[Crossref] [PubMed]

Nieminen, T. A.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
[Crossref]

Nori, F.

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Ordal, M. A.

Ozeri, R.

R. Shaniv and R. Ozeri, “Quantum lock-in force sensing using optical clock Doppler velocimetry,” Nat. Commun. 8, 14157 (2017).
[Crossref] [PubMed]

Passaseo, A.

M. Esposito, V. Tasco, F. Todisco, M. Cuscunà, A. Benedetti, M. Scuderi, G. Nicotra, and A. Passaseo, “Programmable extreme chirality in the visible by helix-shaped metamaterial platform,” Nano Lett. 16(9), 5823–5828 (2016).
[Crossref] [PubMed]

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Pun, E. Y. B.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Querry, M. R.

Rahimzadegan, A.

A. Rahimzadegan, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Fundamental limits of optical force and torque,” Phys. Rev. B 95(3), 035106 (2017).
[Crossref]

A. Rahimzadegan, M. Fruhnert, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Optical force and torque on dipolar dual chiral particles,” Phys. Rev. B 94(12), 125123 (2016).
[Crossref]

Rahmani, A.

P. C. Chaumet and A. Rahmani, “Dressed for success,” Nat. Nanotechnol. 9(4), 252–253 (2014).
[Crossref] [PubMed]

Rill, M. S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Rockstuhl, C.

A. Rahimzadegan, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Fundamental limits of optical force and torque,” Phys. Rev. B 95(3), 035106 (2017).
[Crossref]

A. Rahimzadegan, M. Fruhnert, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Optical force and torque on dipolar dual chiral particles,” Phys. Rev. B 94(12), 125123 (2016).
[Crossref]

Rodriguez-Fortuno, F. J.

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Rohrbach, A.

A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95(16), 168102 (2005).
[Crossref] [PubMed]

Rubinsztein-Dunlop, H.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
[Crossref]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

Ruffner, D. B.

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

Saenz, J.

A. Dogariu, S. Sukhov, and J. Saenz, “Optically induced ‘negative forces’,” Nat. Photonics 7(1), 24–27 (2013).
[Crossref]

Saija, R.

M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
[Crossref] [PubMed]

Saile, V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Schwartz, C.

Scuderi, M.

M. Esposito, V. Tasco, F. Todisco, M. Cuscunà, A. Benedetti, M. Scuderi, G. Nicotra, and A. Passaseo, “Programmable extreme chirality in the visible by helix-shaped metamaterial platform,” Nano Lett. 16(9), 5823–5828 (2016).
[Crossref] [PubMed]

Sensiper, S.

S. Sensiper, “Electromagnetic wave propagation on helical structures (a review and survey of recent progress),” Proc. IRE43, 149–161 (1955).

Shaniv, R.

R. Shaniv and R. Ozeri, “Quantum lock-in force sensing using optical clock Doppler velocimetry,” Nat. Commun. 8, 14157 (2017).
[Crossref] [PubMed]

Shen, Y.

Sibbett, W.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Simpson, S. H.

Smart, T. J.

M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
[Crossref] [PubMed]

Sorensen, C. M.

M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, “On definition and measurement of extinction cross section,” J. Quant. Spectrosc. Radiat. Transf. 110(4-5), 323–327 (2009).
[Crossref]

M. J. Berg, A. Chakrabarti, and C. M. Sorensen, “General derivation of the total electromagnetic cross sections for an arbitrary particle,” J. Quant. Spectrosc. Radiat. Transf. 110(1-2), 43–50 (2009).
[Crossref]

Su, H.

Sukhov, S.

A. Dogariu, S. Sukhov, and J. Saenz, “Optically induced ‘negative forces’,” Nat. Photonics 7(1), 24–27 (2013).
[Crossref]

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[Crossref] [PubMed]

Tasco, V.

M. Esposito, V. Tasco, F. Todisco, M. Cuscunà, A. Benedetti, M. Scuderi, G. Nicotra, and A. Passaseo, “Programmable extreme chirality in the visible by helix-shaped metamaterial platform,” Nano Lett. 16(9), 5823–5828 (2016).
[Crossref] [PubMed]

Thiel, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Todisco, F.

M. Esposito, V. Tasco, F. Todisco, M. Cuscunà, A. Benedetti, M. Scuderi, G. Nicotra, and A. Passaseo, “Programmable extreme chirality in the visible by helix-shaped metamaterial platform,” Nano Lett. 16(9), 5823–5828 (2016).
[Crossref] [PubMed]

van der Mee, C. V. M.

M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, “On definition and measurement of extinction cross section,” J. Quant. Spectrosc. Radiat. Transf. 110(4-5), 323–327 (2009).
[Crossref]

Volke-Sepulveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref] [PubMed]

von Freymann, G.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Wang, S. B.

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014).
[Crossref] [PubMed]

Wang, S. W.

R. N. Ji, S. W. Wang, X. X. Liu, H. J. Guo, and W. Lu, “Hybrid helix metamaterials for giant and ultrawide circular dichroism,” ACS Photonics 3(12), 2368–2374 (2016).
[Crossref]

Wegener, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Wei, Z.

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref] [PubMed]

Wu, C.

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref] [PubMed]

Xiao, K. W.

L. M. Zhou, K. W. Xiao, J. Chen, and N. Zhao, “Optical levitation of nanodiamonds by doughnut beams in vacuum,” Laser Photonics Rev. 11(2), 1600284 (2017).
[Crossref]

Xu, Y. L.

Yamane, T.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[Crossref] [PubMed]

Yu, N.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Yu, X.

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref] [PubMed]

Zayats, A. V.

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

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, S.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[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]

Zhao, N.

L. M. Zhou, K. W. Xiao, J. Chen, and N. Zhao, “Optical levitation of nanodiamonds by doughnut beams in vacuum,” Laser Photonics Rev. 11(2), 1600284 (2017).
[Crossref]

Zhou, L.

K. Ding, J. Ng, L. Zhou, and C. T. Chan, “Realization of optical pulling forces using chirality,” Phys. Rev. A 89(6), 063825 (2014).
[Crossref]

Zhou, L. M.

L. M. Zhou, K. W. Xiao, J. Chen, and N. Zhao, “Optical levitation of nanodiamonds by doughnut beams in vacuum,” Laser Photonics Rev. 11(2), 1600284 (2017).
[Crossref]

ACS Photonics (1)

R. N. Ji, S. W. Wang, X. X. Liu, H. J. Guo, and W. Lu, “Hybrid helix metamaterials for giant and ultrawide circular dichroism,” ACS Photonics 3(12), 2368–2374 (2016).
[Crossref]

Appl. Opt. (3)

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

J. Quant. Spectrosc. Radiat. Transf. (2)

M. J. Berg, A. Chakrabarti, and C. M. Sorensen, “General derivation of the total electromagnetic cross sections for an arbitrary particle,” J. Quant. Spectrosc. Radiat. Transf. 110(1-2), 43–50 (2009).
[Crossref]

M. I. Mishchenko, M. J. Berg, C. M. Sorensen, and C. V. M. van der Mee, “On definition and measurement of extinction cross section,” J. Quant. Spectrosc. Radiat. Transf. 110(4-5), 323–327 (2009).
[Crossref]

Laser Photonics Rev. (1)

L. M. Zhou, K. W. Xiao, J. Chen, and N. Zhao, “Optical levitation of nanodiamonds by doughnut beams in vacuum,” Laser Photonics Rev. 11(2), 1600284 (2017).
[Crossref]

Nano Lett. (3)

A. Kotnala and R. Gordon, “Quantification of high-efficiency trapping of nanoparticles in a double nanohole optical tweezer,” Nano Lett. 14(2), 853–856 (2014).
[Crossref] [PubMed]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

M. Esposito, V. Tasco, F. Todisco, M. Cuscunà, A. Benedetti, M. Scuderi, G. Nicotra, and A. Passaseo, “Programmable extreme chirality in the visible by helix-shaped metamaterial platform,” Nano Lett. 16(9), 5823–5828 (2016).
[Crossref] [PubMed]

Nanoscale (1)

M. G. Donato, E. Messina, A. Foti, T. J. Smart, P. H. Jones, M. A. Iatì, R. Saija, P. G. Gucciardi, and O. M. Maragò, “Optical trapping and optical force positioning of two-dimensional materials,” Nanoscale 10(3), 1245–1255 (2018).
[Crossref] [PubMed]

Nat. Commun. (3)

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014).
[Crossref] [PubMed]

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4(1), 2374 (2013).
[Crossref] [PubMed]

R. Shaniv and R. Ozeri, “Quantum lock-in force sensing using optical clock Doppler velocimetry,” Nat. Commun. 8, 14157 (2017).
[Crossref] [PubMed]

Nat. Mater. (2)

S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nat. Mater. 4(7), 530–533 (2005).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Nat. Nanotechnol. (2)

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]

P. C. Chaumet and A. Rahmani, “Dressed for success,” Nat. Nanotechnol. 9(4), 252–253 (2014).
[Crossref] [PubMed]

Nat. Photonics (6)

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

A. Dogariu, S. Sukhov, and J. Saenz, “Optically induced ‘negative forces’,” Nat. Photonics 7(1), 24–27 (2013).
[Crossref]

D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8(8), 610–614 (2014).
[Crossref]

F. Cardano and L. Marrucci, “Spin-orbit photonics,” Nat. Photonics 9(12), 776–778 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

H. Magallanes and E. Brasselet, “Macroscopic direct observation of optical spin-dependent lateral forces and left-handed torques,” Nat. Photonics 12(8), 461–464 (2018).
[Crossref]

Nature (3)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
[Crossref]

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987).
[Crossref] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

K. Ding, J. Ng, L. Zhou, and C. T. Chan, “Realization of optical pulling forces using chirality,” Phys. Rev. A 89(6), 063825 (2014).
[Crossref]

Phys. Rev. B (3)

A. Rahimzadegan, M. Fruhnert, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Optical force and torque on dipolar dual chiral particles,” Phys. Rev. B 94(12), 125123 (2016).
[Crossref]

A. Rahimzadegan, R. Alaee, I. Fernandez-Corbaton, and C. Rockstuhl, “Fundamental limits of optical force and torque,” Phys. Rev. B 95(3), 035106 (2017).
[Crossref]

J. Li and P. M. Haney, “Optical spin transfer and spin-orbit torques in thin film ferromagnets,” Phys. Rev. B 96(5), 054447 (2017).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

J. Chen, J. Ng, S. Liu, and Z. Lin, “Analytical calculation of axial optical force on a Rayleigh particle illuminated by Gaussian beams beyond the paraxial approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(2), 026607 (2009).
[Crossref] [PubMed]

Phys. Rev. Lett. (7)

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[Crossref] [PubMed]

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref] [PubMed]

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

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

A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95(16), 168102 (2005).
[Crossref] [PubMed]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

Sci. Rep. (1)

J. Chen, J. Ng, K. Ding, K. H. Fung, Z. Lin, and C. T. Chan, “Negative optical torque,” Sci. Rep. 4(1), 6386 (2015).
[Crossref] [PubMed]

Science (4)

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002).
[Crossref] [PubMed]

Other (5)

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics Publishing, 2003).

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

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002).

COMSOL is a finite-element-method electromagnetic solver, see “ www.comsol.com

S. Sensiper, “Electromagnetic wave propagation on helical structures (a review and survey of recent progress),” Proc. IRE43, 149–161 (1955).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 (a) A schematic of the nanohelix is drawn to scale. The inner and outer radii are r = 50 nm and R = 100 nm, respectively. The pitch length is p = 300 nm. The incident plane wave propagates along z direction with intensity of 1 mW/ μm 2 . Optical torque exerted on the RH helix made of PEC/gold under different polarizations versus frequencies and also their corresponding wavelength are shown in (b).
Fig. 2
Fig. 2 Optical torque exerted on the lossless RH gold helices with different pitch number N under the incidence of a LH polarized plane wave.
Fig. 3
Fig. 3 The recoil torque, the interception torque, and the total optical torque are shown, respectively, for a RH gold/PEC helix under LH polarization [(a), (c)] and RH polarization [(b), (d)].
Fig. 4
Fig. 4 Optical torque exerted on a RH gold helix contributed by individual partial wave channels under the LH polarization [(a)-(c)] and the RH polarization [(d)-(f)].
Fig. 5
Fig. 5 Partial wave analysis of light extinction and scattered power. (a) and (d): the extinction power (the total energy intercepted) of a RH gold helix under LH and RH polarization. (b) and (e): the energy scattered into different partial wave channels. (c) and (f): the percentage of intercepted energy scattered into each different channels.
Fig. 6
Fig. 6 Band structure for an infinitely long periodic PEC helix. The lines denote the results of the analytical tape helix theory while the circles denote the full-wave results computed with COMSOL assuming a periodic array of helix on the xy plane with a large period of d = 4 μm. The gray area defines the light cone. The sold lines denote non-radiating guided modes while the dashed lines denote radiating modes.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Γ z,tot = 2π ε 0 | E 0 | 2 k 3 l=1 m=l l mRe[ p ml a ml + q ml b ml ( | a ml | 2 + | b ml | 2 ) ] ,
Γ z,int = 2π ε 0 | E 0 | 2 k 3 l=1 m=l l mRe[ p ml a ml + q ml b ml ] = m i m i ω W ext ( m i ) ,
Γ z,sca = 2π ε 0 | E 0 | 2 k 3 l=1 m=l l m( | a ml | 2 + | b ml | 2 ) = m m ω W sca ( m ) ,
Γ z,tot = Γ z,int + Γ z,sca = m i m i ω W ext ( m i ) m m ω W sca ( m )
l [ ( k z 2 R 2 k 2 R 2 + l 2 k 2 τ l 2 cot 2 ψ ) K l ( τ l R ) I l ( τ l R )+ k 2 R 2 cot 2 ψ K l ( τ l R ) I l ( τ l R ) ] J l =0,
S z =σ= ω W Ω S e z + S m z dA= ω W Re [ Ω ε 0 4ωi E ×E+ μ 0 4ωi H ×HdA ] z ,

Metrics