Abstract

We demonstrate an optical tweezers using a laser beam on which is imprinted a focusing phase profile generated by a Devil’s staircase fractal structure (Cantor set). We show that a beam shaped in this way is capable of stably trapping a variety of micron- and submicron-sized particles and calibrate the optical trap as a function of the control parameters of the fractal structure, and explain the observed variation as arising from radiation pressure exerted by unfocused parts of the beam in the region of the optical trap. Experimental results are complemented by calculation of the structure of the focus in the regime of high numerical aperture.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Devil’s vortex-lenses

Walter D. Furlan, Fernando Giménez, Arnau Calatayud, and Juan A. Monsoriu
Opt. Express 17(24) 21891-21896 (2009)

Devil’s lenses

Juan A. Monsoriu, Walter D. Furlan, Genaro Saavedra, and Fernando Giménez
Opt. Express 15(21) 13858-13864 (2007)

Self-similar focusing with generalized devil’s lenses

Cristina Casanova, Walter D. Furlan, Laura Remón, Arnau Calatayud, Juan A. Monsoriu, and Omel Mendoza-Yero
J. Opt. Soc. Am. A 28(2) 210-213 (2011)

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. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004). URL http://scitation.aip.org/content/aip/journal/rsi/75/9/10.1063/1.1785844 .
    [Crossref]
  3. K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37, 42–55 (2008).
    [Crossref] [PubMed]
  4. O. M. Maragó, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013). URL http://www.nature.com/nnano/journal/v8/n11/full/nnano.2013.208.html .
    [Crossref] [PubMed]
  5. F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5, 318–321 (2011). URL http://www.nature.com/nphoton/journal/v5/n6/full/nphoton.2011.100.html .
    [Crossref] [PubMed]
  6. O. M. Maragó, P. G. Gucciardi, P. H. Jones, R. Saija, F. Borghese, P. Denti, and M. A. Iatì, “Optical trapping of carbon nanotubes,” Physica E: Low-dimensional Systems and Nanostructures 40(7), 2347–2351 (2008). URL http://www.sciencedirect.com/science/article/pii/S1386947707007308 .
    [Crossref]
  7. O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
    [Crossref] [PubMed]
  8. H. Zhang and K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5(24), 671–690 (2008). URL http://rsif.royalsocietypublishing.org/content/5/24/671.full .
    [Crossref] [PubMed]
  9. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
    [Crossref] [PubMed]
  10. P. H. Jones, M. Rashid, M. Makita, and O. M. Maragó, “Sagnac interferometer method for synthesis of fractional polarization vortices,” Opt. Lett. 34(17), 2560–2562 (2009).
    [Crossref] [PubMed]
  11. K. T. Gahagan and G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21(11), 827–829 (1996).
    [Crossref] [PubMed]
  12. M. G. Donato, S. Vasi, R. Sayed, P. H. Jones, F. Bonaccorso, A. C. Ferrari, P. G. Gucciardi, and O. M. Maragó, “Optical trapping of nanotubes with cylindrical vector beams,” Opt. Lett. 37(16), 3381–3383 (2012).
    [Crossref]
  13. S. E. Skelton, M. Sergides, R. Saija, M. A. Iatì, O. M. Maragó, and P. H. Jones, “Trapping volume control in optical tweezers using cylindrical vector beams,” Opt. Lett. 38(1), 28–30 (2013).
    [Crossref] [PubMed]
  14. B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).
  15. M. Segev, M. Soljaic, and J. M. Dudley, “Fractal optics and beyond,” Nat. Photonics 6, 201–209 (2012). URL http://www.nature.com/nphoton/journal/v6/n4/full/nphoton.2012.71.html .
    [Crossref]
  16. G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28(12), 971–973 (2003).
    [Crossref] [PubMed]
  17. J. A. Davis, L. Ramirez, J. A. R. Martín-Romo, T. Alieva, and M. Calvo, “Focusing properties of fractal zone plates: experimental implementation with a liquid-crystal display,” Opt. Lett. 29(12), 1321–1323 (2004).
    [Crossref] [PubMed]
  18. S. H. Tao, X.-C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006). URL http://link.aip.org/link/?APL/89/031105/1 .
    [Crossref]
  19. D. Wu, L.-G. Niu, Q.-D. Chen, R. Wang, and H.-B. Sun, “High efficiency multilevel phase-type fractal zone plates,” Opt. Lett. 33(24), 2913–2915 (2008).
    [Crossref] [PubMed]
  20. J. A. Monsoriu, C. J. Zapata-Rodrguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun. 263(1), 1–5 (2006). URL http://www.sciencedirect.com/science/article/pii/S0030401806000484 .
    [Crossref]
  21. J. A. Monsoriu, W. D. Furlan, G. Saavedra, and F. Giménez, “Devil’s lenses,” Opt. Express 15(21), 13858–13864 (2007).
    [Crossref] [PubMed]
  22. W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devil’s vortex-lenses,” Opt. Express 17(24), 21891–21896 (2009).
    [Crossref] [PubMed]
  23. M. Mitry, D. C. Doughty, J. L. Chaloupka, and M. E. Anderson, “Experimental realization of the devil’s vortex Fresnel lens with a programmable spatial light modulator,” Appl. Opt. 51(18), 4103–4108 (2012).
    [Crossref] [PubMed]
  24. G. Volpe, G. Volpe, and R. Quidant, “Fractal plasmonics: subdiffraction focusing and broadband spectral response by a Sierpinski nanocarpet,” Opt. Express 19(4), 3612–3618 (2011).
    [Crossref] [PubMed]
  25. W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010). URL https://www.jeos.org/index.php/jeos_rp/article/view/10037s .
    [Crossref]
  26. G. Cantor, “De la puissance des ansembles parfaits de points,” Acta Math. 4, 381–392 (1884).
    [Crossref]
  27. B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. Royal Soc. London A. 253(1274), 358–379 (1959). URL http://rspa.royalsocietypublishing.org/content/253/1274/358 .
    [Crossref]
  28. P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
    [Crossref] [PubMed]
  29. F. Borghese, P. Denti, R. Saija, and M. A. Iatì, “Optical trapping of nonspherical particles in the T-matrix formalism,” Opt. Express 15(19), 11984–11998 (2007).
    [Crossref] [PubMed]

2013 (2)

O. M. Maragó, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013). URL http://www.nature.com/nnano/journal/v8/n11/full/nnano.2013.208.html .
[Crossref] [PubMed]

S. E. Skelton, M. Sergides, R. Saija, M. A. Iatì, O. M. Maragó, and P. H. Jones, “Trapping volume control in optical tweezers using cylindrical vector beams,” Opt. Lett. 38(1), 28–30 (2013).
[Crossref] [PubMed]

2012 (3)

2011 (2)

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5, 318–321 (2011). URL http://www.nature.com/nphoton/journal/v5/n6/full/nphoton.2011.100.html .
[Crossref] [PubMed]

G. Volpe, G. Volpe, and R. Quidant, “Fractal plasmonics: subdiffraction focusing and broadband spectral response by a Sierpinski nanocarpet,” Opt. Express 19(4), 3612–3618 (2011).
[Crossref] [PubMed]

2010 (2)

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010). URL https://www.jeos.org/index.php/jeos_rp/article/view/10037s .
[Crossref]

2009 (3)

2008 (4)

D. Wu, L.-G. Niu, Q.-D. Chen, R. Wang, and H.-B. Sun, “High efficiency multilevel phase-type fractal zone plates,” Opt. Lett. 33(24), 2913–2915 (2008).
[Crossref] [PubMed]

H. Zhang and K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5(24), 671–690 (2008). URL http://rsif.royalsocietypublishing.org/content/5/24/671.full .
[Crossref] [PubMed]

O. M. Maragó, P. G. Gucciardi, P. H. Jones, R. Saija, F. Borghese, P. Denti, and M. A. Iatì, “Optical trapping of carbon nanotubes,” Physica E: Low-dimensional Systems and Nanostructures 40(7), 2347–2351 (2008). URL http://www.sciencedirect.com/science/article/pii/S1386947707007308 .
[Crossref]

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

2007 (2)

2006 (2)

J. A. Monsoriu, C. J. Zapata-Rodrguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun. 263(1), 1–5 (2006). URL http://www.sciencedirect.com/science/article/pii/S0030401806000484 .
[Crossref]

S. H. Tao, X.-C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006). URL http://link.aip.org/link/?APL/89/031105/1 .
[Crossref]

2004 (2)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004). URL http://scitation.aip.org/content/aip/journal/rsi/75/9/10.1063/1.1785844 .
[Crossref]

J. A. Davis, L. Ramirez, J. A. R. Martín-Romo, T. Alieva, and M. Calvo, “Focusing properties of fractal zone plates: experimental implementation with a liquid-crystal display,” Opt. Lett. 29(12), 1321–1323 (2004).
[Crossref] [PubMed]

2003 (1)

1996 (1)

1992 (1)

1986 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. Royal Soc. London A. 253(1274), 358–379 (1959). URL http://rspa.royalsocietypublishing.org/content/253/1274/358 .
[Crossref]

1884 (1)

G. Cantor, “De la puissance des ansembles parfaits de points,” Acta Math. 4, 381–392 (1884).
[Crossref]

Alieva, T.

Anderson, M. E.

Ashkin, A.

Bjorkholm, J. E.

Block, S. M.

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5, 318–321 (2011). URL http://www.nature.com/nphoton/journal/v5/n6/full/nphoton.2011.100.html .
[Crossref] [PubMed]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004). URL http://scitation.aip.org/content/aip/journal/rsi/75/9/10.1063/1.1785844 .
[Crossref]

Bonaccorso, F.

M. G. Donato, S. Vasi, R. Sayed, P. H. Jones, F. Bonaccorso, A. C. Ferrari, P. G. Gucciardi, and O. M. Maragó, “Optical trapping of nanotubes with cylindrical vector beams,” Opt. Lett. 37(16), 3381–3383 (2012).
[Crossref]

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[Crossref] [PubMed]

Borghese, F.

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

O. M. Maragó, P. G. Gucciardi, P. H. Jones, R. Saija, F. Borghese, P. Denti, and M. A. Iatì, “Optical trapping of carbon nanotubes,” Physica E: Low-dimensional Systems and Nanostructures 40(7), 2347–2351 (2008). URL http://www.sciencedirect.com/science/article/pii/S1386947707007308 .
[Crossref]

F. Borghese, P. Denti, R. Saija, and M. A. Iatì, “Optical trapping of nonspherical particles in the T-matrix formalism,” Opt. Express 15(19), 11984–11998 (2007).
[Crossref] [PubMed]

Burge, R. E.

S. H. Tao, X.-C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006). URL http://link.aip.org/link/?APL/89/031105/1 .
[Crossref]

Calatayud, A.

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010). URL https://www.jeos.org/index.php/jeos_rp/article/view/10037s .
[Crossref]

W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devil’s vortex-lenses,” Opt. Express 17(24), 21891–21896 (2009).
[Crossref] [PubMed]

Calogero, G.

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[Crossref] [PubMed]

Calvo, M.

Cantor, G.

G. Cantor, “De la puissance des ansembles parfaits de points,” Acta Math. 4, 381–392 (1884).
[Crossref]

Chaloupka, J. L.

Chen, Q.-D.

Chu, S.

Davis, J. A.

Denti, P.

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

O. M. Maragó, P. G. Gucciardi, P. H. Jones, R. Saija, F. Borghese, P. Denti, and M. A. Iatì, “Optical trapping of carbon nanotubes,” Physica E: Low-dimensional Systems and Nanostructures 40(7), 2347–2351 (2008). URL http://www.sciencedirect.com/science/article/pii/S1386947707007308 .
[Crossref]

F. Borghese, P. Denti, R. Saija, and M. A. Iatì, “Optical trapping of nonspherical particles in the T-matrix formalism,” Opt. Express 15(19), 11984–11998 (2007).
[Crossref] [PubMed]

Dholakia, K.

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

Donato, M. G.

Doughty, D. C.

Dudley, J. M.

M. Segev, M. Soljaic, and J. M. Dudley, “Fractal optics and beyond,” Nat. Photonics 6, 201–209 (2012). URL http://www.nature.com/nphoton/journal/v6/n4/full/nphoton.2012.71.html .
[Crossref]

Dziedzic, J. M.

Fazal, F. M.

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5, 318–321 (2011). URL http://www.nature.com/nphoton/journal/v5/n6/full/nphoton.2011.100.html .
[Crossref] [PubMed]

Ferrari, A. C.

O. M. Maragó, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013). URL http://www.nature.com/nnano/journal/v8/n11/full/nnano.2013.208.html .
[Crossref] [PubMed]

M. G. Donato, S. Vasi, R. Sayed, P. H. Jones, F. Bonaccorso, A. C. Ferrari, P. G. Gucciardi, and O. M. Maragó, “Optical trapping of nanotubes with cylindrical vector beams,” Opt. Lett. 37(16), 3381–3383 (2012).
[Crossref]

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[Crossref] [PubMed]

Furlan, W. D.

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010). URL https://www.jeos.org/index.php/jeos_rp/article/view/10037s .
[Crossref]

W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devil’s vortex-lenses,” Opt. Express 17(24), 21891–21896 (2009).
[Crossref] [PubMed]

J. A. Monsoriu, W. D. Furlan, G. Saavedra, and F. Giménez, “Devil’s lenses,” Opt. Express 15(21), 13858–13864 (2007).
[Crossref] [PubMed]

J. A. Monsoriu, C. J. Zapata-Rodrguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun. 263(1), 1–5 (2006). URL http://www.sciencedirect.com/science/article/pii/S0030401806000484 .
[Crossref]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28(12), 971–973 (2003).
[Crossref] [PubMed]

Gahagan, K. T.

Gimenez, F.

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010). URL https://www.jeos.org/index.php/jeos_rp/article/view/10037s .
[Crossref]

Giménez, F.

Gu, M.

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

Gucciardi, P. G.

O. M. Maragó, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013). URL http://www.nature.com/nnano/journal/v8/n11/full/nnano.2013.208.html .
[Crossref] [PubMed]

M. G. Donato, S. Vasi, R. Sayed, P. H. Jones, F. Bonaccorso, A. C. Ferrari, P. G. Gucciardi, and O. M. Maragó, “Optical trapping of nanotubes with cylindrical vector beams,” Opt. Lett. 37(16), 3381–3383 (2012).
[Crossref]

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[Crossref] [PubMed]

O. M. Maragó, P. G. Gucciardi, P. H. Jones, R. Saija, F. Borghese, P. Denti, and M. A. Iatì, “Optical trapping of carbon nanotubes,” Physica E: Low-dimensional Systems and Nanostructures 40(7), 2347–2351 (2008). URL http://www.sciencedirect.com/science/article/pii/S1386947707007308 .
[Crossref]

Heckenberg, N. R.

Iatì, M. A.

S. E. Skelton, M. Sergides, R. Saija, M. A. Iatì, O. M. Maragó, and P. H. Jones, “Trapping volume control in optical tweezers using cylindrical vector beams,” Opt. Lett. 38(1), 28–30 (2013).
[Crossref] [PubMed]

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

O. M. Maragó, P. G. Gucciardi, P. H. Jones, R. Saija, F. Borghese, P. Denti, and M. A. Iatì, “Optical trapping of carbon nanotubes,” Physica E: Low-dimensional Systems and Nanostructures 40(7), 2347–2351 (2008). URL http://www.sciencedirect.com/science/article/pii/S1386947707007308 .
[Crossref]

F. Borghese, P. Denti, R. Saija, and M. A. Iatì, “Optical trapping of nonspherical particles in the T-matrix formalism,” Opt. Express 15(19), 11984–11998 (2007).
[Crossref] [PubMed]

Jones, P. H.

S. E. Skelton, M. Sergides, R. Saija, M. A. Iatì, O. M. Maragó, and P. H. Jones, “Trapping volume control in optical tweezers using cylindrical vector beams,” Opt. Lett. 38(1), 28–30 (2013).
[Crossref] [PubMed]

O. M. Maragó, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013). URL http://www.nature.com/nnano/journal/v8/n11/full/nnano.2013.208.html .
[Crossref] [PubMed]

M. G. Donato, S. Vasi, R. Sayed, P. H. Jones, F. Bonaccorso, A. C. Ferrari, P. G. Gucciardi, and O. M. Maragó, “Optical trapping of nanotubes with cylindrical vector beams,” Opt. Lett. 37(16), 3381–3383 (2012).
[Crossref]

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[Crossref] [PubMed]

P. H. Jones, M. Rashid, M. Makita, and O. M. Maragó, “Sagnac interferometer method for synthesis of fractional polarization vortices,” Opt. Lett. 34(17), 2560–2562 (2009).
[Crossref] [PubMed]

O. M. Maragó, P. G. Gucciardi, P. H. Jones, R. Saija, F. Borghese, P. Denti, and M. A. Iatì, “Optical trapping of carbon nanotubes,” Physica E: Low-dimensional Systems and Nanostructures 40(7), 2347–2351 (2008). URL http://www.sciencedirect.com/science/article/pii/S1386947707007308 .
[Crossref]

Lin, J.

S. H. Tao, X.-C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006). URL http://link.aip.org/link/?APL/89/031105/1 .
[Crossref]

Liu, K.

H. Zhang and K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5(24), 671–690 (2008). URL http://rsif.royalsocietypublishing.org/content/5/24/671.full .
[Crossref] [PubMed]

Makita, M.

Mandelbrot, B. B.

B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).

Maragó, O. M.

O. M. Maragó, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013). URL http://www.nature.com/nnano/journal/v8/n11/full/nnano.2013.208.html .
[Crossref] [PubMed]

S. E. Skelton, M. Sergides, R. Saija, M. A. Iatì, O. M. Maragó, and P. H. Jones, “Trapping volume control in optical tweezers using cylindrical vector beams,” Opt. Lett. 38(1), 28–30 (2013).
[Crossref] [PubMed]

M. G. Donato, S. Vasi, R. Sayed, P. H. Jones, F. Bonaccorso, A. C. Ferrari, P. G. Gucciardi, and O. M. Maragó, “Optical trapping of nanotubes with cylindrical vector beams,” Opt. Lett. 37(16), 3381–3383 (2012).
[Crossref]

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[Crossref] [PubMed]

P. H. Jones, M. Rashid, M. Makita, and O. M. Maragó, “Sagnac interferometer method for synthesis of fractional polarization vortices,” Opt. Lett. 34(17), 2560–2562 (2009).
[Crossref] [PubMed]

O. M. Maragó, P. G. Gucciardi, P. H. Jones, R. Saija, F. Borghese, P. Denti, and M. A. Iatì, “Optical trapping of carbon nanotubes,” Physica E: Low-dimensional Systems and Nanostructures 40(7), 2347–2351 (2008). URL http://www.sciencedirect.com/science/article/pii/S1386947707007308 .
[Crossref]

Martín-Romo, J. A. R.

McDuff, R.

Mitry, M.

Monsoriu, J. A.

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010). URL https://www.jeos.org/index.php/jeos_rp/article/view/10037s .
[Crossref]

W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devil’s vortex-lenses,” Opt. Express 17(24), 21891–21896 (2009).
[Crossref] [PubMed]

J. A. Monsoriu, W. D. Furlan, G. Saavedra, and F. Giménez, “Devil’s lenses,” Opt. Express 15(21), 13858–13864 (2007).
[Crossref] [PubMed]

J. A. Monsoriu, C. J. Zapata-Rodrguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun. 263(1), 1–5 (2006). URL http://www.sciencedirect.com/science/article/pii/S0030401806000484 .
[Crossref]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28(12), 971–973 (2003).
[Crossref] [PubMed]

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004). URL http://scitation.aip.org/content/aip/journal/rsi/75/9/10.1063/1.1785844 .
[Crossref]

Nicolosi, V.

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

Niu, L.-G.

Palmisano, F.

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[Crossref] [PubMed]

Privitera, G.

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

Quidant, R.

Ramirez, L.

Rashid, M.

Reece, P.

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

Remon, L.

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010). URL https://www.jeos.org/index.php/jeos_rp/article/view/10037s .
[Crossref]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. Royal Soc. London A. 253(1274), 358–379 (1959). URL http://rspa.royalsocietypublishing.org/content/253/1274/358 .
[Crossref]

Saavedra, G.

Saija, R.

S. E. Skelton, M. Sergides, R. Saija, M. A. Iatì, O. M. Maragó, and P. H. Jones, “Trapping volume control in optical tweezers using cylindrical vector beams,” Opt. Lett. 38(1), 28–30 (2013).
[Crossref] [PubMed]

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

O. M. Maragó, P. G. Gucciardi, P. H. Jones, R. Saija, F. Borghese, P. Denti, and M. A. Iatì, “Optical trapping of carbon nanotubes,” Physica E: Low-dimensional Systems and Nanostructures 40(7), 2347–2351 (2008). URL http://www.sciencedirect.com/science/article/pii/S1386947707007308 .
[Crossref]

F. Borghese, P. Denti, R. Saija, and M. A. Iatì, “Optical trapping of nonspherical particles in the T-matrix formalism,” Opt. Express 15(19), 11984–11998 (2007).
[Crossref] [PubMed]

Sayed, R.

Segev, M.

M. Segev, M. Soljaic, and J. M. Dudley, “Fractal optics and beyond,” Nat. Photonics 6, 201–209 (2012). URL http://www.nature.com/nphoton/journal/v6/n4/full/nphoton.2012.71.html .
[Crossref]

Sergides, M.

Skelton, S. E.

Smith, C. P.

Soljaic, M.

M. Segev, M. Soljaic, and J. M. Dudley, “Fractal optics and beyond,” Nat. Photonics 6, 201–209 (2012). URL http://www.nature.com/nphoton/journal/v6/n4/full/nphoton.2012.71.html .
[Crossref]

Sun, H.-B.

Swartzlander, G. A.

Tao, S. H.

S. H. Tao, X.-C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006). URL http://link.aip.org/link/?APL/89/031105/1 .
[Crossref]

Vasi, S.

Volpe, G.

Wang, R.

White, A. G.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. Royal Soc. London A. 253(1274), 358–379 (1959). URL http://rspa.royalsocietypublishing.org/content/253/1274/358 .
[Crossref]

Wu, D.

Yuan, X.-C.

S. H. Tao, X.-C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006). URL http://link.aip.org/link/?APL/89/031105/1 .
[Crossref]

Zapata-Rodrguez, C. J.

J. A. Monsoriu, C. J. Zapata-Rodrguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun. 263(1), 1–5 (2006). URL http://www.sciencedirect.com/science/article/pii/S0030401806000484 .
[Crossref]

Zhang, H.

H. Zhang and K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5(24), 671–690 (2008). URL http://rsif.royalsocietypublishing.org/content/5/24/671.full .
[Crossref] [PubMed]

ACS Nano (2)

O. M. Maragó, F. Bonaccorso, R. Saija, G. Privitera, P. G. Gucciardi, M. A. Iatì, G. Calogero, P. H. Jones, F. Borghese, P. Denti, V. Nicolosi, and A. C. Ferrari, “Brownian motion of graphene,” ACS Nano 4(12), 7515–7523 (2010).
[Crossref] [PubMed]

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[Crossref] [PubMed]

Acta Math. (1)

G. Cantor, “De la puissance des ansembles parfaits de points,” Acta Math. 4, 381–392 (1884).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. H. Tao, X.-C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006). URL http://link.aip.org/link/?APL/89/031105/1 .
[Crossref]

Chem. Soc. Rev. (1)

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

J. Eur. Opt. Soc. Rap. Pub. (1)

W. D. Furlan, F. Gimenez, A. Calatayud, L. Remon, and J. A. Monsoriu, “Volumetric multiple optical traps produced by Devil’s lenses,” J. Eur. Opt. Soc. Rap. Pub. 5, 10037s (2010). URL https://www.jeos.org/index.php/jeos_rp/article/view/10037s .
[Crossref]

J. R. Soc. Interface (1)

H. Zhang and K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5(24), 671–690 (2008). URL http://rsif.royalsocietypublishing.org/content/5/24/671.full .
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

O. M. Maragó, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013). URL http://www.nature.com/nnano/journal/v8/n11/full/nnano.2013.208.html .
[Crossref] [PubMed]

Nat. Photonics (2)

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5, 318–321 (2011). URL http://www.nature.com/nphoton/journal/v5/n6/full/nphoton.2011.100.html .
[Crossref] [PubMed]

M. Segev, M. Soljaic, and J. M. Dudley, “Fractal optics and beyond,” Nat. Photonics 6, 201–209 (2012). URL http://www.nature.com/nphoton/journal/v6/n4/full/nphoton.2012.71.html .
[Crossref]

Opt. Commun. (1)

J. A. Monsoriu, C. J. Zapata-Rodrguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun. 263(1), 1–5 (2006). URL http://www.sciencedirect.com/science/article/pii/S0030401806000484 .
[Crossref]

Opt. Express (4)

Opt. Lett. (9)

D. Wu, L.-G. Niu, Q.-D. Chen, R. Wang, and H.-B. Sun, “High efficiency multilevel phase-type fractal zone plates,” Opt. Lett. 33(24), 2913–2915 (2008).
[Crossref] [PubMed]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28(12), 971–973 (2003).
[Crossref] [PubMed]

J. A. Davis, L. Ramirez, J. A. R. Martín-Romo, T. Alieva, and M. Calvo, “Focusing properties of fractal zone plates: experimental implementation with a liquid-crystal display,” Opt. Lett. 29(12), 1321–1323 (2004).
[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]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[Crossref] [PubMed]

P. H. Jones, M. Rashid, M. Makita, and O. M. Maragó, “Sagnac interferometer method for synthesis of fractional polarization vortices,” Opt. Lett. 34(17), 2560–2562 (2009).
[Crossref] [PubMed]

K. T. Gahagan and G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21(11), 827–829 (1996).
[Crossref] [PubMed]

M. G. Donato, S. Vasi, R. Sayed, P. H. Jones, F. Bonaccorso, A. C. Ferrari, P. G. Gucciardi, and O. M. Maragó, “Optical trapping of nanotubes with cylindrical vector beams,” Opt. Lett. 37(16), 3381–3383 (2012).
[Crossref]

S. E. Skelton, M. Sergides, R. Saija, M. A. Iatì, O. M. Maragó, and P. H. Jones, “Trapping volume control in optical tweezers using cylindrical vector beams,” Opt. Lett. 38(1), 28–30 (2013).
[Crossref] [PubMed]

Physica E: Low-dimensional Systems and Nanostructures (1)

O. M. Maragó, P. G. Gucciardi, P. H. Jones, R. Saija, F. Borghese, P. Denti, and M. A. Iatì, “Optical trapping of carbon nanotubes,” Physica E: Low-dimensional Systems and Nanostructures 40(7), 2347–2351 (2008). URL http://www.sciencedirect.com/science/article/pii/S1386947707007308 .
[Crossref]

Proc. Royal Soc. London A. (1)

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. Royal Soc. London A. 253(1274), 358–379 (1959). URL http://rspa.royalsocietypublishing.org/content/253/1274/358 .
[Crossref]

Rev. Sci. Instrum. (1)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004). URL http://scitation.aip.org/content/aip/journal/rsi/75/9/10.1063/1.1785844 .
[Crossref]

Other (1)

B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).

Supplementary Material (4)

» Media 1: MOV (289 KB)     
» Media 2: MOV (257 KB)     
» Media 3: MOV (223 KB)     
» Media 4: MOV (223 KB)     

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) Illustration of the generation of the triadic Cantor set, starting from the initiator, S = 0 to the stage S = 3; (b) the Cantor function FS(x) for S = 3; (c) the phase profile of a “Devil’s Lens”, ΦS = 2S+1πFS(ξ), ξ = (r/a)2; (d) phase retardation pattern for a Devil’s Lens with S = 2; (e) phase retardation pattern for a Devil’s Lens with S = 3; (f) phase retardation pattern for a Devil’s Vortex Lens with S = 3, m = 3. In the experiments an additional linear phase term is included to separate the phase retarded beam from the zero order.
Fig. 2
Fig. 2 Calculated intensity distributions in the z = 0 plane transverse to the optic axis (left column), and in a longitudinal (y = 0) plane (right column) for Devil’s lenses of order (a) S = 0; (b) S = 1; (c) S = 2; (d) S = 3. In each plot the intensity is normalised to the maximum intensity in the plot.
Fig. 3
Fig. 3 Calculated intensity distributions in the z = 0 plane transverse to the optic axis (left column), and in a longitudinal (y = 0) plane (right column) for Devil’s vortex lenses with topological charge m = 1 of order (a) S = 0; (b) S = 1; (c) S = 2; (d) S = 3. In each plot the intensity is normalised to the maximum intensity in the plot.
Fig. 4
Fig. 4 Diagram of the optical tweezers experimental apparatus. The Spatial Light Modulator (SLM) is used to display the Devil’s lens phase retardation pattern which is applied to the Nd:YAG trapping laser beam before injecting into the inverted microscope optical tweezers. Quantitative measurements are made by observing a trapped particle’s Brownian motion using the light backscattered from a helium-neon probe laser beam onto a quadrant photodiode (QPD).
Fig. 5
Fig. 5 Demonstration of optical trapping in a Devil’s lens optical tweezers. (a) A 1.5 μm diameter silica sphere, S = 2 (see also Media 1); (b) A 1.0 μm diameter silica sphere, S = 2 (see also Media 2); (c) An aggregate of gold nanorods, S = 2 (see also Media 3); (d) An aggregate of gold nanorods in a Devil’s vortex lens optical trap. S = 2, m = 1 (see also Media 4). In each panel the trapped particle is circled.
Fig. 6
Fig. 6 Measured optical trap parameters for topological charges m = 0 and m = 1 with increasing order of the Cantor function, S. (a) transverse spring constant; (b) axial spring constant. Data are an average of between 2 and 4 repeats with a fractional uncertainty of better than 0.001.

Equations (2)

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

F S ( x ) = { l 2 S if p S , l x q S , l 1 2 S x q S , l p S , l + 1 q S , l if q S , l x q S , l + 1 .
Φ S = 2 S + 1 π F S ( ξ )

Metrics