Abstract

Conical refraction occurs when a beam of light travels through an appropriately cut biaxial crystal. By focusing the conically refracted beam through a high numerical aperture microscope objective, conical refraction optical tweezers can be created, allowing for particle manipulation in both Raman spots, and in the Lloyd/Poggendorff rings. We present a thorough quantification of the trapping properties of such a beam, focusing on the trap stiffness, and how this varies with trap power and trapped particle location. We show that the lower Raman spot can be thought of as a single-beam optical gradient force trap, while radiation pressure dominates in the upper Raman spot, leading to optical levitation rather than trapping. Particles in the Lloyd/Poggendorff rings experience a lower trap stiffness than particles in the lower Raman spot, but benefit from rotational control.

© 2014 Optical Society of America

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References

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2014 (1)

2013 (3)

2012 (3)

D. P. O’Dwyer, K. E. Ballantine, C. F. Phelan, J. G. Lunney, and J. F. Donegan, Opt. Express 20, 9908 (2012).

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).

M. Esseling, P. Rose, C. Alpmann, and C. Denz, Appl. Phys. Lett. 101, 131115 (2012).
[Crossref]

2010 (1)

2006 (1)

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, Proc. Roy. Soc. A 462, 1629 (2006).
[Crossref]

2004 (2)

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[Crossref]

K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
[Crossref]

2002 (1)

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[Crossref]

2001 (2)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[Crossref]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[Crossref]

1998 (1)

A. Pralle, E. Florin, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S71 (1998).
[Crossref]

1994 (1)

1993 (1)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[Crossref]

1986 (1)

1837 (1)

W. R. Hamilton, Trans. Roy. Irish Acad. 17, 1 (1837).

Abdolvand, A.

Alpmann, C.

M. Esseling, P. Rose, C. Alpmann, and C. Denz, Appl. Phys. Lett. 101, 131115 (2012).
[Crossref]

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[Crossref]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[Crossref]

Ashkin, A.

Ballantine, K. E.

D. P. O’Dwyer, K. E. Ballantine, C. F. Phelan, J. G. Lunney, and J. F. Donegan, Opt. Express 20, 9908 (2012).

D. P. O’Dwyer, C. F. Phelan, K. E. Ballantine, Y. P. Rakovich, J. G. Lunney, and J. F. Donegan, Opt. Express 18, 27319 (2010).
[Crossref]

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[Crossref]

Berry, M. V.

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, Proc. Roy. Soc. A 462, 1629 (2006).
[Crossref]

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
[Crossref]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[Crossref]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[Crossref]

Carnegie, D. J.

G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, Opt. Express 21, 11125 (2013).
[Crossref]

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).

Chu, S.

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[Crossref]

Denz, C.

M. Esseling, P. Rose, C. Alpmann, and C. Denz, Appl. Phys. Lett. 101, 131115 (2012).
[Crossref]

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[Crossref]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[Crossref]

Donegan, J. F.

D. P. O’Dwyer, K. E. Ballantine, C. F. Phelan, J. G. Lunney, and J. F. Donegan, Opt. Express 20, 9908 (2012).

D. P. O’Dwyer, C. F. Phelan, K. E. Ballantine, Y. P. Rakovich, J. G. Lunney, and J. F. Donegan, Opt. Express 18, 27319 (2010).
[Crossref]

Dziedzic, J. M.

Esseling, M.

M. Esseling, P. Rose, C. Alpmann, and C. Denz, Appl. Phys. Lett. 101, 131115 (2012).
[Crossref]

Florin, E.

A. Pralle, E. Florin, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S71 (1998).
[Crossref]

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[Crossref]

Garces-Chavez, V.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[Crossref]

Gillespie, W. A.

Grant, S. D.

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[Crossref]

Hamilton, W. R.

W. R. Hamilton, Trans. Roy. Irish Acad. 17, 1 (1837).

Hell, S. W.

Henderson, R.

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).

Hnatovsky, C.

Hörber, J. K. H.

A. Pralle, E. Florin, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S71 (1998).
[Crossref]

Jeffrey, M. R.

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, Proc. Roy. Soc. A 462, 1629 (2006).
[Crossref]

Kalkandjiev, T. K.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[Crossref]

Krolikowski, W.

Loiko, Y. V.

Lunney, J. G.

D. P. O’Dwyer, K. E. Ballantine, C. F. Phelan, J. G. Lunney, and J. F. Donegan, Opt. Express 20, 9908 (2012).

D. P. O’Dwyer, C. F. Phelan, K. E. Ballantine, Y. P. Rakovich, J. G. Lunney, and J. F. Donegan, Opt. Express 18, 27319 (2010).
[Crossref]

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, Proc. Roy. Soc. A 462, 1629 (2006).
[Crossref]

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[Crossref]

McDougall, C.

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).

McGloin, D.

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).

Mompart, J.

Neuman, K. C.

K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
[Crossref]

O’Dwyer, D. P.

D. P. O’Dwyer, K. E. Ballantine, C. F. Phelan, J. G. Lunney, and J. F. Donegan, Opt. Express 20, 9908 (2012).

D. P. O’Dwyer, C. F. Phelan, K. E. Ballantine, Y. P. Rakovich, J. G. Lunney, and J. F. Donegan, Opt. Express 18, 27319 (2010).
[Crossref]

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[Crossref]

Peet, V.

V. Peet, Opt. Commun. 311, 150 (2013).
[Crossref]

Phelan, C. F.

D. P. O’Dwyer, K. E. Ballantine, C. F. Phelan, J. G. Lunney, and J. F. Donegan, Opt. Express 20, 9908 (2012).

D. P. O’Dwyer, C. F. Phelan, K. E. Ballantine, Y. P. Rakovich, J. G. Lunney, and J. F. Donegan, Opt. Express 18, 27319 (2010).
[Crossref]

Pralle, A.

A. Pralle, E. Florin, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S71 (1998).
[Crossref]

Rafailov, E. U.

G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, Opt. Express 21, 11125 (2013).
[Crossref]

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).

Rakovich, Y. P.

Rose, P.

M. Esseling, P. Rose, C. Alpmann, and C. Denz, Appl. Phys. Lett. 101, 131115 (2012).
[Crossref]

Schmidt, C. F.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[Crossref]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[Crossref]

Shvedov, V.

Sibbett, W.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[Crossref]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[Crossref]

Sokolovskii, G. S.

G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, Opt. Express 21, 11125 (2013).
[Crossref]

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).

Stelzer, E. H. K.

A. Pralle, E. Florin, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S71 (1998).
[Crossref]

Svoboda, K.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[Crossref]

Turpin, A.

Wichmann, J.

Zolotovskaya, S. A.

Appl. Phys. A (1)

A. Pralle, E. Florin, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S71 (1998).
[Crossref]

Appl. Phys. Lett. (1)

M. Esseling, P. Rose, C. Alpmann, and C. Denz, Appl. Phys. Lett. 101, 131115 (2012).
[Crossref]

Nature (1)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[Crossref]

Opt. Commun. (3)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[Crossref]

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[Crossref]

V. Peet, Opt. Commun. 311, 150 (2013).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Proc. Roy. Soc. A (1)

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, Proc. Roy. Soc. A 462, 1629 (2006).
[Crossref]

Proc. SPIE (1)

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).

Rev. Sci. Instrum. (2)

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[Crossref]

K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
[Crossref]

Science (1)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[Crossref]

Trans. Roy. Irish Acad. (1)

W. R. Hamilton, Trans. Roy. Irish Acad. 17, 1 (1837).

Other (1)

M. V. Berry, M. R. Jeffrey, and E. Wolf, eds., Progress of Optics (Elsevier, 2007), Vol. 2, Chap. 2.

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Figures (5)

Fig. 1.
Fig. 1. Experimental setup for conical refraction tweezers; DIC, dichroic mirror; L#, lens; M#, mirror; OBJ 1, Nikon 0.9 NA 50× oil immersion objective; OBJ 2, Nikon 1.25 NA 100× oil immersion objective; PBS, polarizing beam splitting cube; λ/2WP, half-wave plate; λ/4WP, quarter-wave plate; not shown, sample stage was positioned on a Newport xyz-translation stage; OBJ 2, L8, L9, 50:50 splitter, and CCD camera were positioned on a second Newport xyz-translation stage; QPD was positioned on another Newport xyz-translation stage; inset shows Lloyd/Poggendorff rings; (a) circular incident beam polarizartion; (b) linear incident beam polarizations; out of focus light is visible within (and surrounding) the Lloyd/Poggendorff rings, due to the depth of field of the imaging system.
Fig. 2.
Fig. 2. Circularly polarized, conically refracted beam, 75.5 μm long, propagating from left to right, focused with a 0.9 NA objective; (a) empty trap; (b) 2.56 μm bead in upper Raman spot, identifiable by increased scatter; slight asymmetry in the images is due to the projection method used; (c) lower Raman spot cross section; (d) Lloyd/Poggendorff rings cross section; (e) upper Raman spot cross section; all three cross sections shown for an empty trap.
Fig. 3.
Fig. 3. Trap stiffness versus power; (a) 5.2 μm bead (trapped in lower Raman spot); (d) 2.56 μm bead (trapped in lower Raman spot); (b) 5.2 μm bead (trapped in Lloyd/Poggendorff rings); (e) 2.56 μm bead (trapped in Lloyd/Poggendorff rings); (c) 5.2 μm bead (trapped in upper Raman spot); kx circ, trap stiffness in X for circular polarized light; kx lin, trap stiffness in X for linearly polarized light; ky circ, trap stiffness in Y for circular polarized light; ky lin, trap stiffness in Y for linearly polarized light; (f) power spectrum for a 2.56 μm bead (trapped in upper Raman spot).
Fig. 4.
Fig. 4. 5.2 μm bead in upper Raman spot, height above Lloyd/Poggendorff ring plane, versus trap power.
Fig. 5.
Fig. 5. Power spectrum for a 5.2 μm bead, trapped with 137±6mW, in a Gaussian trap.

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