Abstract

An optical bottle field containing a three-dimensional intensity null at the focal point can be generated by placing a spatially inhomogeneous birefringent mask at the pupil of an aplanatic high-NA focusing system. We derive the optimal birefringence distribution for which a uniformly polarized input beam is converted into a bottle field with the sharpest possible null in intensity. We show that a stress engineered optical (SEO) window, which has a radially varying retardance, followed by a half-wave plate, performs nearly as well as the optimal solution. Experimental results corroborate that an SEO element can be used to generate a bottle field.

© 2017 Optical Society of America

Full Article  |  PDF Article

Corrections

Anthony Vella, Hippolyte Dourdent, Lukas Novotny, and Miguel A. Alonso, "Birefringent masks that are optimal for generating bottle fields: erratum," Opt. Express 25, 19654-19654 (2017)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-25-16-19654

24 April 2017: Corrections were made to the body text and Refs. 27 and 31.


OSA Recommended Articles
Generation of optical bottle beams by incoherent white-light vortices

Vladlen G. Shvedov, Yana V. Izdebskaya, Andrei V. Rode, Anton Desyatnikov, Wieslaw Krolikowski, and Yuri S. Kivshar
Opt. Express 16(25) 20902-20907 (2008)

Simultaneous rotation, orientation and displacement control of birefringent microparticles in holographic optical tweezers

A. Arias, S. Etcheverry, P. Solano, J. P. Staforelli, M. J. Gallardo, H. Rubinsztein-Dunlop, and C. Saavedra
Opt. Express 21(1) 102-111 (2013)

Trapping and transporting aerosols with a single optical bottle beam generated by moiré techniques

Peng Zhang, Ze Zhang, Jai Prakash, Simon Huang, Daniel Hernandez, Matthew Salazar, Demetrios N. Christodoulides, and Zhigang Chen
Opt. Lett. 36(8) 1491-1493 (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, 288–290 (1986).
    [Crossref] [PubMed]
  2. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
    [Crossref]
  3. A. Ashkin, History of Optical Trapping and Manipulation of Small Neutral Particles, Atoms, and Molecules (SpringerBerlin Heidelberg, 2001), pp. 1–31.
  4. S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
    [Crossref] [PubMed]
  5. A. Ashkin, J. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
    [Crossref] [PubMed]
  6. A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1521 (1987).
    [Crossref] [PubMed]
  7. A. T. O’Neil and M. J. Padgett, “Axial and lateral trapping efficiency of laguerre–gaussian modes in inverted optical tweezers,” Opt. Comm. 193, 45–50 (2001).
    [Crossref]
  8. N. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
    [Crossref]
  9. J. Arlt and M. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25, 191–193 (2000).
    [Crossref]
  10. V. G. Shvedov, C. Hnatovsky, A. V. Rode, and W. Krolikowski, “Robust trapping and manipulation of airborne particles with a bottle beam,” Opt. Expr. 19, 17350–17356 (2011).
    [Crossref]
  11. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780–782 (1994).
    [Crossref] [PubMed]
  12. M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
    [Crossref]
  13. T. Suyama and Y. Zhang, “3d super-resolution fluorescence microscopy using cylindrical vector beams,” Prog. Electromagn. Res. 43, 73–81 (2013).
    [Crossref]
  14. V. G. Shvedov, Y. V. Izdebskaya, A. V. Rode, A. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Generation of optical bottle beams by incoherent white-light vortices,” Opt. Express 16, 20902–20907 (2008).
    [Crossref] [PubMed]
  15. C.-H. Chen, P.-T. Tai, and W.-F. Hsieh, “Bottle beam from a bare laser for single-beam trapping,” Appl. Opt. 43, 6001–6006 (2004).
    [Crossref] [PubMed]
  16. P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, “Trapping and transporting aerosols with a single optical bottle beam generated by moiré techniques,” Opt. Lett. 36, 1491–1493 (2011).
    [Crossref] [PubMed]
  17. Y. V. Loiko, A. Turpin, T. Kalkandjiev, E. Rafailov, and J. Mompart, “Generating a three-dimensional dark focus from a single conically refracted light beam,” Opt. Lett. 38, 4648–4651 (2013).
    [Crossref] [PubMed]
  18. M. Soskin, P. Polyanskii, and O. Arkhelyuk, “Computer-synthesized hologram-based rainbow optical vortices,” New J. Phys. 6, 196 (2004).
    [Crossref]
  19. G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Comm. 222, 117–125 (2003).
    [Crossref]
  20. P. Mahou, N. Curry, D. Pinotsi, G. K. Schierle, and C. Kaminski, “Stimulated emission depletion microscopy to study amyloid fibril formation,” Proc. SPIE 9931, 93310U (2015).
  21. A. K. Spilman and T. G. Brown, “Stress birefringent, space-variant wave plates for vortex illumination,” Appl. Opt. 46, 61–66 (2007).
    [Crossref]
  22. A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full poincaré beams,” Opt. Express 18, 10777–10785 (2010).
    [Crossref] [PubMed]
  23. A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full poincaré beams II: partial polarization,” Opt. Express 20, 9357–9362 (2012).
    [Crossref] [PubMed]
  24. R. D. Ramkhalawon, T. G. Brown, and M. A. Alonso, “Imaging the polarization of a light field,” Opt. Express 21, 4106–4115 (2013).
    [Crossref] [PubMed]
  25. B. G. Zimmerman and T. G. Brown, “Star test image-sampling polarimeter,” Opt. Express 24, 23154–23161 (2016).
    [Crossref] [PubMed]
  26. S. Sivankutty, E. R. Andresen, G. Bouwmans, T. G. Brown, M. A. Alonso, and H. Rigneault, “Single-shot polarimetry imaging of multicore fiber,” Opt. Lett. 41, 2105–2108 (2016).
    [Crossref] [PubMed]
  27. A. K. Spilman and T. G. Brown, “Stress-induced focal splitting,” Opt. Express 15, 8411–8421 (2007).
    [Crossref] [PubMed]
  28. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotechnol. 10, 937–943 (2015).
    [Crossref] [PubMed]
  29. S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1, 030801 (2016).
    [Crossref]
  30. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. ii. structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
    [Crossref]
  31. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006), pp. 56–60.
  32. M. A. Alonso, “The effect of orbital angular momentum and helicity in the uncertainty-type relations between focal spot size and angular spread,” J. Opt. 13, 064016 (2011).
    [Crossref]
  33. K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82, 063825 (2010).
    [Crossref]
  34. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
    [Crossref] [PubMed]
  35. F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
    [Crossref] [PubMed]

2016 (3)

2015 (2)

P. Mahou, N. Curry, D. Pinotsi, G. K. Schierle, and C. Kaminski, “Stimulated emission depletion microscopy to study amyloid fibril formation,” Proc. SPIE 9931, 93310U (2015).

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

2014 (1)

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
[Crossref]

2013 (3)

2012 (2)

2011 (3)

P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, “Trapping and transporting aerosols with a single optical bottle beam generated by moiré techniques,” Opt. Lett. 36, 1491–1493 (2011).
[Crossref] [PubMed]

V. G. Shvedov, C. Hnatovsky, A. V. Rode, and W. Krolikowski, “Robust trapping and manipulation of airborne particles with a bottle beam,” Opt. Expr. 19, 17350–17356 (2011).
[Crossref]

M. A. Alonso, “The effect of orbital angular momentum and helicity in the uncertainty-type relations between focal spot size and angular spread,” J. Opt. 13, 064016 (2011).
[Crossref]

2010 (2)

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82, 063825 (2010).
[Crossref]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full poincaré beams,” Opt. Express 18, 10777–10785 (2010).
[Crossref] [PubMed]

2008 (1)

2007 (2)

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

2004 (2)

M. Soskin, P. Polyanskii, and O. Arkhelyuk, “Computer-synthesized hologram-based rainbow optical vortices,” New J. Phys. 6, 196 (2004).
[Crossref]

C.-H. Chen, P.-T. Tai, and W.-F. Hsieh, “Bottle beam from a bare laser for single-beam trapping,” Appl. Opt. 43, 6001–6006 (2004).
[Crossref] [PubMed]

2003 (1)

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Comm. 222, 117–125 (2003).
[Crossref]

2001 (1)

A. T. O’Neil and M. J. Padgett, “Axial and lateral trapping efficiency of laguerre–gaussian modes in inverted optical tweezers,” Opt. Comm. 193, 45–50 (2001).
[Crossref]

2000 (1)

1998 (1)

N. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[Crossref]

1994 (1)

1987 (2)

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

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1521 (1987).
[Crossref] [PubMed]

1986 (2)

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[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, 288–290 (1986).
[Crossref] [PubMed]

1970 (1)

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

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. ii. structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[Crossref]

Aiello, A.

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82, 063825 (2010).
[Crossref]

Allen, L.

N. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[Crossref]

Alonso, M. A.

Andresen, E. R.

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Arkhelyuk, O.

M. Soskin, P. Polyanskii, and O. Arkhelyuk, “Computer-synthesized hologram-based rainbow optical vortices,” New J. Phys. 6, 196 (2004).
[Crossref]

Arlt, J.

Ashkin, A.

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

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1521 (1987).
[Crossref] [PubMed]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[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, 288–290 (1986).
[Crossref] [PubMed]

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

A. Ashkin, History of Optical Trapping and Manipulation of Small Neutral Particles, Atoms, and Molecules (SpringerBerlin Heidelberg, 2001), pp. 1–31.

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Beckley, A. M.

Bjorkholm, J. E.

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, 288–290 (1986).
[Crossref] [PubMed]

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

Bliokh, K. Y.

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82, 063825 (2010).
[Crossref]

Bouwmans, G.

Brown, A. C.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
[Crossref]

Brown, T. G.

Cable, A.

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

Cardano, F.

Chen, C.-H.

Chen, Z.

Christodoulides, D. N.

Chu, S.

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, 288–290 (1986).
[Crossref] [PubMed]

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

Clegg, J. H.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
[Crossref]

Curry, N.

P. Mahou, N. Curry, D. Pinotsi, G. K. Schierle, and C. Kaminski, “Stimulated emission depletion microscopy to study amyloid fibril formation,” Proc. SPIE 9931, 93310U (2015).

Davis, D. M.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
[Crossref]

de Lisio, C.

Desyatnikov, A.

Dholakia, K.

N. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[Crossref]

Dunsby, C.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
[Crossref]

Dziedzic, J.

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1521 (1987).
[Crossref] [PubMed]

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

Dziedzic, J. M.

Faraon, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

French, P. M.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
[Crossref]

Gbur, G.

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Comm. 222, 117–125 (2003).
[Crossref]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006), pp. 56–60.

Hell, S. W.

Hernandez, D.

Hnatovsky, C.

V. G. Shvedov, C. Hnatovsky, A. V. Rode, and W. Krolikowski, “Robust trapping and manipulation of airborne particles with a bottle beam,” Opt. Expr. 19, 17350–17356 (2011).
[Crossref]

Hopkins, B.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1, 030801 (2016).
[Crossref]

Horie, Y.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Hsieh, W.-F.

Huang, S.

Izdebskaya, Y. V.

Kalkandjiev, T.

Kaminski, C.

P. Mahou, N. Curry, D. Pinotsi, G. K. Schierle, and C. Kaminski, “Stimulated emission depletion microscopy to study amyloid fibril formation,” Proc. SPIE 9931, 93310U (2015).

Karimi, E.

Kivshar, Y. S.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1, 030801 (2016).
[Crossref]

V. G. Shvedov, Y. V. Izdebskaya, A. V. Rode, A. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Generation of optical bottle beams by incoherent white-light vortices,” Opt. Express 16, 20902–20907 (2008).
[Crossref] [PubMed]

Kravchenko, I. I.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1, 030801 (2016).
[Crossref]

Krolikowski, W.

V. G. Shvedov, C. Hnatovsky, A. V. Rode, and W. Krolikowski, “Robust trapping and manipulation of airborne particles with a bottle beam,” Opt. Expr. 19, 17350–17356 (2011).
[Crossref]

V. G. Shvedov, Y. V. Izdebskaya, A. V. Rode, A. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Generation of optical bottle beams by incoherent white-light vortices,” Opt. Express 16, 20902–20907 (2008).
[Crossref] [PubMed]

Kruk, S.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1, 030801 (2016).
[Crossref]

Lenz, M. O.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
[Crossref]

Loiko, Y. V.

Mahou, P.

P. Mahou, N. Curry, D. Pinotsi, G. K. Schierle, and C. Kaminski, “Stimulated emission depletion microscopy to study amyloid fibril formation,” Proc. SPIE 9931, 93310U (2015).

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Marrucci, L.

McGloin, D.

N. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[Crossref]

Miroshnichenko, A.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1, 030801 (2016).
[Crossref]

Mompart, J.

Neil, M. A.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
[Crossref]

Neshev, D. N.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1, 030801 (2016).
[Crossref]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006), pp. 56–60.

O’Neil, A. T.

A. T. O’Neil and M. J. Padgett, “Axial and lateral trapping efficiency of laguerre–gaussian modes in inverted optical tweezers,” Opt. Comm. 193, 45–50 (2001).
[Crossref]

Ostrovskaya, E. A.

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82, 063825 (2010).
[Crossref]

Padgett, M.

J. Arlt and M. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25, 191–193 (2000).
[Crossref]

N. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[Crossref]

Padgett, M. J.

A. T. O’Neil and M. J. Padgett, “Axial and lateral trapping efficiency of laguerre–gaussian modes in inverted optical tweezers,” Opt. Comm. 193, 45–50 (2001).
[Crossref]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Pinotsi, D.

P. Mahou, N. Curry, D. Pinotsi, G. K. Schierle, and C. Kaminski, “Stimulated emission depletion microscopy to study amyloid fibril formation,” Proc. SPIE 9931, 93310U (2015).

Polyanskii, P.

M. Soskin, P. Polyanskii, and O. Arkhelyuk, “Computer-synthesized hologram-based rainbow optical vortices,” New J. Phys. 6, 196 (2004).
[Crossref]

Prakash, J.

Rafailov, E.

Ramkhalawon, R. D.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. ii. structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[Crossref]

Rigneault, H.

Rode, A. V.

V. G. Shvedov, C. Hnatovsky, A. V. Rode, and W. Krolikowski, “Robust trapping and manipulation of airborne particles with a bottle beam,” Opt. Expr. 19, 17350–17356 (2011).
[Crossref]

V. G. Shvedov, Y. V. Izdebskaya, A. V. Rode, A. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Generation of optical bottle beams by incoherent white-light vortices,” Opt. Express 16, 20902–20907 (2008).
[Crossref] [PubMed]

Salazar, M.

Santamato, E.

Savell, A.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
[Crossref]

Schierle, G. K.

P. Mahou, N. Curry, D. Pinotsi, G. K. Schierle, and C. Kaminski, “Stimulated emission depletion microscopy to study amyloid fibril formation,” Proc. SPIE 9931, 93310U (2015).

Shvedov, V. G.

V. G. Shvedov, C. Hnatovsky, A. V. Rode, and W. Krolikowski, “Robust trapping and manipulation of airborne particles with a bottle beam,” Opt. Expr. 19, 17350–17356 (2011).
[Crossref]

V. G. Shvedov, Y. V. Izdebskaya, A. V. Rode, A. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Generation of optical bottle beams by incoherent white-light vortices,” Opt. Express 16, 20902–20907 (2008).
[Crossref] [PubMed]

Simpson, N.

N. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[Crossref]

Sinclair, H. G.

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
[Crossref]

Sivankutty, S.

Slussarenko, S.

Soskin, M.

M. Soskin, P. Polyanskii, and O. Arkhelyuk, “Computer-synthesized hologram-based rainbow optical vortices,” New J. Phys. 6, 196 (2004).
[Crossref]

Spilman, A. K.

Suyama, T.

T. Suyama and Y. Zhang, “3d super-resolution fluorescence microscopy using cylindrical vector beams,” Prog. Electromagn. Res. 43, 73–81 (2013).
[Crossref]

Tai, P.-T.

Turpin, A.

Visser, T. D.

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Comm. 222, 117–125 (2003).
[Crossref]

Wichmann, J.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. ii. structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[Crossref]

Yamane, T.

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

Zhang, P.

Zhang, Y.

T. Suyama and Y. Zhang, “3d super-resolution fluorescence microscopy using cylindrical vector beams,” Prog. Electromagn. Res. 43, 73–81 (2013).
[Crossref]

Zhang, Z.

Zimmerman, B. G.

APL Photonics (1)

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1, 030801 (2016).
[Crossref]

Appl. Opt. (3)

J. Biophotonics (1)

M. O. Lenz, H. G. Sinclair, A. Savell, J. H. Clegg, A. C. Brown, D. M. Davis, C. Dunsby, M. A. Neil, and P. M. French, “3-d stimulated emission depletion microscopy with programmable aberration correction,” J. Biophotonics 7, 29–36 (2014).
[Crossref]

J. Mod. Opt. (1)

N. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[Crossref]

J. Opt. (1)

M. A. Alonso, “The effect of orbital angular momentum and helicity in the uncertainty-type relations between focal spot size and angular spread,” J. Opt. 13, 064016 (2011).
[Crossref]

Nature (1)

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

Nature Nanotechnol. (1)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

New J. Phys. (1)

M. Soskin, P. Polyanskii, and O. Arkhelyuk, “Computer-synthesized hologram-based rainbow optical vortices,” New J. Phys. 6, 196 (2004).
[Crossref]

Opt. Comm. (2)

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Comm. 222, 117–125 (2003).
[Crossref]

A. T. O’Neil and M. J. Padgett, “Axial and lateral trapping efficiency of laguerre–gaussian modes in inverted optical tweezers,” Opt. Comm. 193, 45–50 (2001).
[Crossref]

Opt. Expr. (1)

V. G. Shvedov, C. Hnatovsky, A. V. Rode, and W. Krolikowski, “Robust trapping and manipulation of airborne particles with a bottle beam,” Opt. Expr. 19, 17350–17356 (2011).
[Crossref]

Opt. Express (6)

Opt. Lett. (6)

Phys. Rev. A (1)

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82, 063825 (2010).
[Crossref]

Phys. Rev. Lett. (3)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

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

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

Proc. R. 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. R. Soc. London A 253, 358–379 (1959).
[Crossref]

Proc. SPIE (1)

P. Mahou, N. Curry, D. Pinotsi, G. K. Schierle, and C. Kaminski, “Stimulated emission depletion microscopy to study amyloid fibril formation,” Proc. SPIE 9931, 93310U (2015).

Prog. Electromagn. Res. (1)

T. Suyama and Y. Zhang, “3d super-resolution fluorescence microscopy using cylindrical vector beams,” Prog. Electromagn. Res. 43, 73–81 (2013).
[Crossref]

Science (1)

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1521 (1987).
[Crossref] [PubMed]

Other (2)

A. Ashkin, History of Optical Trapping and Manipulation of Small Neutral Particles, Atoms, and Molecules (SpringerBerlin Heidelberg, 2001), pp. 1–31.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006), pp. 56–60.

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 (9)

Fig. 1
Fig. 1

Schematic of system layout for bottle field generation, in which a thin birefringent mask is placed in the pupil plane of an aplanatic lens. The coordinate in the pupil plane is specified in terms of the focus angle η.

Fig. 2
Fig. 2

Illustration of the geometrical meaning of δj (u). Dashed lines are drawn to indicate a sample point u0 on the elliptic curve (left) and the corresponding point on the retardance distribution (right).

Fig. 3
Fig. 3

Numerical solutions for (a) each pair of optimized coefficients gj and hj and (b) the lowest-order stress parameter b0 required to produce a bottle field.

Fig. 4
Fig. 4

Comparison of optimized and linear retardance distributions for generating a bottle field, shown for six different NA values as indicated on the plots. From top to bottom at the right edge of each plot, the curves appear in the following order: δ2, δ4, δ3, δL, δ1.

Fig. 5
Fig. 5

Logarithm of the transverse (left) and longitudinal (right) widths of the bottle fields generated by each solution, normalized by factors of NA3 and NA4, respectively. The longitudinal width of the beam produced by δ1 is not shown because it is infinite.

Fig. 6
Fig. 6

Ratio of longitudinal to transverse widths of the bottle fields generated by each solution. The ratio for δ1 is not shown because it is infinite.

Fig. 7
Fig. 7

Simulated cross-sections over the xz plane of the focused intensity distributions generated by each solution. The results obtained using the optimized solutions δ1 through δ4 (a–p) and the linear solution δL (q–t) are each shown for four different numerical apertures. The solid green curves show the intensity profiles in the x (vertical) and z (horizontal) dimensions. The dashed yellow circle is added for scale, with a radius of one wavelength.

Fig. 8
Fig. 8

Schematic of experimental setup for bottle field generation. (LP = linear polarizer, λ/4 = quarter-wave plate, λ/2 = half-wave plate.)

Fig. 9
Fig. 9

Evolution through focus of the optical bottle beam’s transverse intensity profile over a 2 cm distance along the propagation axis. The intensity distribution at focus has a diameter of 50 μm, matching simulations.

Tables (2)

Tables Icon

Table 1 Constraints for optimality of each merit function.

Tables Icon

Table 2 Constraints for optimality of each merit function for the m = 3 case.

Equations (45)

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

𝕄 lens = cos η [ sin 2 ϕ + cos 2 ϕ cos η sin ϕ cos ϕ ( cos η 1 ) sin ϕ cos ϕ ( cos η 1 ) sin 2 ϕ cos η + cos 2 ϕ cos ϕ sin η sin ϕ sin η ] .
𝕁 ( u ) = exp [ i Γ ( u ) ] { exp [ i δ ( u ) ] p 1 ( u ) p 1 * ( u ) + exp [ i δ ( u ) ] p 2 ( u ) p 2 * ( u ) } ,
p 1 ( u ) = [ cos ( Φ / 2 ) sin ( Φ / 2 ) sin ( Φ / 2 ) cos ( Φ / 2 ) ] [ cos ( Θ / 2 ) i sin ( Θ / 2 ) ] , p 2 ( u ) = [ 0 1 1 0 ] p 1 * ( u ) ,
𝕁 ( u ) = [ cos δ + i sin δ cos Θ cos Φ sin δ ( sin Θ + i cos Θ sin Φ ) sin δ ( sin Θ + icos Θ sin Φ ) cos δ i sin δ cos Θ cos Φ ] exp ( i Γ ) .
I ( r ) = 1 ( π k ) 2 A ( u ) 𝕄 lens 𝕁 ( u ) E 0 exp [ i k ( u r ) ] d 2 u 2 ,
I x i x i | r = 0 = 2 π 2 A 𝕄 lens 𝕁 E 0 u x i d 2 u 2 .
𝕄 lens 𝕁 E 0 = cos η [ cos δ [ cos η cos ϕ + i sin ϕ ] e i ϕ + i sin δ [ cos η cos ϕ i sin ϕ ] e i ( ϕ Φ ) cos δ [ cos η sin ϕ i cos ϕ ] e i ϕ + i sin δ [ cos η sin ϕ + i cos ϕ ] e i ( ϕ Φ ) sin η [ cos δ e i ϕ + i sin δ e i ( ϕ Φ ) ] ] .
Φ = m ϕ ,
I x x = I y y = 2 0 NA A [ 1 2 ξ 211 sin δ 1 2 ξ 211 sin δ ξ 310 cos δ ] d u 2 , I z z = 2 0 NA A [ ξ 131 cos δ ξ 131 cos δ 0 ] d u 2 ,
α n m , c = 0 NA A ξ n m cos δ d u , α n m , s = 0 NA A ξ n m sin δ d u ,
I x x = I y y = α 211 , s 2 + 2 α 310 , c 2 ,
I z z = 4 α 131 , c 2 .
I ( 0 ) = 1 k 2 0 NA A [ ξ 111 cos δ ξ 111 cos δ 0 ] d u 2 = 2 k 2 α 111 , c 2 = 0 .
δ M j = Λ S α 111 , c ,
α 111 , c = 0 ,
δ j ( u ) = arctan ( ξ 101 c j ξ 001 + d j ξ 200 + e j ξ 021 ) = arctan ( u ( 1 + 1 u 2 ) c j ( 1 + 1 u 2 ) + d j u 2 + e j 1 u 2 ( 1 + 1 u 2 ) ) ,
δ j ( u ) = arctan ( u g j + h j 1 u 2 ) ,
δ α n m , c = A ξ n m sin δ , δ α n m , s = A ξ n m cos δ .
S [ I x x + I y y + I z z ] = Λ δ α 111 , c .
4 A [ ξ 211 α 211 , s cos δ 2 ( ξ 310 α 310 , c + ξ 131 α 131 , c ) sin δ ] = Λ A ξ 111 α 111 , c sin δ .
2 δ I x x I x x 2 δ I z z I z z 2 = Λ δ α 111 , c
2 [ 2 α 211 , s A ξ 211 cos δ 4 α 310 , c A ξ 310 sin δ ] ( α 211 , s 2 + 2 α 310 , c 2 ) 2 2 α 131 , c A ξ 131 sin δ α 131 , c 4 = Λ A ξ 111 sin δ .
2 I x x I z z δ I x x + I x x 2 δ I z z = Λ δ α 111 , c
α 131 , c ( 2 α 211 , s A ξ 211 cos δ 4 α 310 , c A ξ 310 sin δ ) ( α 211 , s 2 + 2 α 210 , c 2 ) A ξ 131 sin δ = Λ A ξ 111 sin δ ,
I z z δ I x x + I x x δ I z z = Λ δ α 111 , c .
0 NA A ( u ) u ( 1 u 2 ) 1 / 4 ( 1 + 1 u 2 ) cos ( b u ) d u = 0 .
σ x i 1 I x i x i .
I x x = 2 0 NA A [ ξ 230 sin δ ξ 210 sin δ ξ 310 cos δ ] d u 2 ,
I y y = 2 0 NA A [ ξ 210 sin δ ξ 230 sin δ ξ 310 cos δ ] d u 2 ,
I z z = 2 0 NA A [ ξ 131 cos δ ξ 131 cos δ 2 ξ 230 sin δ ] d u 2 ,
I x x = I y y = 2 0 NA A [ 1 2 Δ 3 m ξ ¯ 211 sin δ 1 2 Δ 3 m ξ ¯ 211 sin δ ξ 310 [ cos δ + i ( Δ 0 m + Δ 2 m ) sin δ ] ] d u 2 ,
I z z = 2 0 NA A [ ξ 131 cos δ i ( Δ 2 m ξ ¯ 131 Δ 0 m ξ 131 ) sin δ ξ 131 cos δ i ( Δ 2 m ξ ¯ 131 + Δ 0 m ξ 131 ) sin δ 0 ] d u 2 ,
I x x = I y y = α ¯ 211 , s 2 + α 310 , c 2 ,
I z z = 4 α 131 , c 2 ,
α ¯ n m , s = 0 NA A ξ ¯ n m sin δ d u .
I ( 0 ) = 1 k 2 0 NA A [ ξ 111 cos δ i ( Δ 2 m ξ ¯ 111 Δ 0 m ξ 111 ) sin δ ξ 111 cos δ i ( Δ 2 m ξ ¯ 111 + Δ 0 m ξ 111 ) sin δ 2 Δ 1 m ξ 210 sin δ ] d u 2 = 0 .
δ j ( u ) = arctan ( ξ ¯ 101 c j ξ 001 + d j ξ 200 + e j ξ 021 ) = arctan ( u ( 1 1 u 2 ) c j ( 1 + 1 u 2 ) + d j u 2 + e j 1 u 2 ( 1 + 1 u 2 ) ) ,
ξ 111 = 2 u + 𝒪 ( u 3 ) ,
ξ 310 = u 3 + 𝒪 ( u 5 ) ,
ξ 131 = 2 u 2 u 3 + 𝒪 ( u 5 ) ,
ξ 211 = 2 u 2 + 𝒪 ( u 4 )
α 111 , c 0 NA 2 u cos δ d u ,
α 310 , c 0 NA u 3 cos δ d u ,
α 131 , c 0 NA ( 2 u 2 u 3 ) cos δ d u ,
α 211 , s 0 NA 2 u 2 sin δ d u .

Metrics