Abstract

We introduce optical solenoid beams, diffractionless solutions of the Helmholtz equation whose diffraction-limited in-plane intensity peak spirals around the optical axis, and whose wavefronts carry an independent helical pitch. Unlike other collimated beams of light, appropriately designed solenoid beams have the noteworthy property of being able to exert forces on illuminated objects that are directed opposite to the direction of the light’s propagation. We demonstrate this through video microscopy observations of a colloidal sphere moving upstream along a holographically projected optical solenoid beam.

© 2010 Optical Society of America

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  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. J. Durnin, "Exact-solutions for nondiffracting beams. 1. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1987).
    [CrossRef]
  3. J. Durnin, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
    [CrossRef] [PubMed]
  4. J. Tervo and J. Turunen, "Rotating scale-invariant electromagnetic fields," Opt. Express 9, 9-15 (2001).
    [CrossRef] [PubMed]
  5. Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
    [CrossRef] [PubMed]
  6. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  7. Y. Roichman and D. G. Grier, "Projecting extended optical traps with shape-phase holography," Opt. Lett. 31, 1675-1677 (2006).
    [CrossRef] [PubMed]
  8. Y. Roichman and D. G. Grier, "Three-dimensional holographic ring traps," Proc. SPIE 6483, 64830F (2007).
    [CrossRef]
  9. A. Vasara, J. Turunen, and A. T. Friberg, "Realization of general nondiffracting beams with computer-generated holograms," J. Opt. Soc. Am. A 6(11), 1748-1754 (1989).
    [CrossRef] [PubMed]
  10. P. L. Overfelt, "Scalar optical beams with helical symmetry," Phys. Rev. A 46, 3516-3522 (1992).
    [CrossRef] [PubMed]
  11. J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
    [CrossRef]
  12. S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, "Nondiffracting beams: travelling, standing, rotating and spiral waves," Opt. Commun. 123, 225-233 (1996).
    [CrossRef]
  13. V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: Rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
    [CrossRef]
  14. P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
    [CrossRef]
  15. Z. Bouchal and J. Kyvalsky, "Controllable 3D spatial localization of light fields synthesized by non-diffracting modes," J. Mod. Opt. 51, 157-176 (2004).
    [CrossRef]
  16. J. Courtial, G. Whyte, Z. Bouchal, and J. Wagner, "Iterative algorithms for holographic shaping of non-diffracting and self-imaging light beams," Opt. Express 14, 2108-2116 (2006).
    [CrossRef] [PubMed]
  17. E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
    [CrossRef]
  18. D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
    [CrossRef] [PubMed]
  19. M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13(15), 5831-5845 (2005).
    [CrossRef] [PubMed]
  20. S.-H. Lee and D. G. Grier, "Robustness of holographic optical traps against phase scaling errors," Opt. Express 13, 7458-7465 (2005).
    [CrossRef] [PubMed]
  21. Y. Roichman, I. Cholis, and D. G. Grier, "Volumetric imaging of holographic optical traps," Opt. Express 14, 10,907-10,912 (2006).
    [CrossRef]
  22. J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
    [CrossRef]
  23. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
    [CrossRef] [PubMed]
  24. T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
    [CrossRef]

2008 (1)

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

2007 (1)

Y. Roichman and D. G. Grier, "Three-dimensional holographic ring traps," Proc. SPIE 6483, 64830F (2007).
[CrossRef]

2006 (4)

Y. Roichman and D. G. Grier, "Projecting extended optical traps with shape-phase holography," Opt. Lett. 31, 1675-1677 (2006).
[CrossRef] [PubMed]

J. Courtial, G. Whyte, Z. Bouchal, and J. Wagner, "Iterative algorithms for holographic shaping of non-diffracting and self-imaging light beams," Opt. Express 14, 2108-2116 (2006).
[CrossRef] [PubMed]

Y. Roichman, I. Cholis, and D. G. Grier, "Volumetric imaging of holographic optical traps," Opt. Express 14, 10,907-10,912 (2006).
[CrossRef]

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

2005 (2)

2004 (1)

Z. Bouchal and J. Kyvalsky, "Controllable 3D spatial localization of light fields synthesized by non-diffracting modes," J. Mod. Opt. 51, 157-176 (2004).
[CrossRef]

2003 (1)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

2002 (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

2001 (2)

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

J. Tervo and J. Turunen, "Rotating scale-invariant electromagnetic fields," Opt. Express 9, 9-15 (2001).
[CrossRef] [PubMed]

1998 (2)

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
[CrossRef]

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

1997 (1)

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: Rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
[CrossRef]

1996 (2)

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, "Nondiffracting beams: travelling, standing, rotating and spiral waves," Opt. Commun. 123, 225-233 (1996).
[CrossRef]

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

1992 (1)

P. L. Overfelt, "Scalar optical beams with helical symmetry," Phys. Rev. A 46, 3516-3522 (1992).
[CrossRef] [PubMed]

1989 (1)

1987 (2)

1986 (1)

Amato-Grill, J.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Arlt, J.

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Ashkin, A.

Bjorkholm, J. E.

Bouchal, Z.

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

J. Courtial, G. Whyte, Z. Bouchal, and J. Wagner, "Iterative algorithms for holographic shaping of non-diffracting and self-imaging light beams," Opt. Express 14, 2108-2116 (2006).
[CrossRef] [PubMed]

Z. Bouchal and J. Kyvalsky, "Controllable 3D spatial localization of light fields synthesized by non-diffracting modes," J. Mod. Opt. 51, 157-176 (2004).
[CrossRef]

Chávez-Cerda, S.

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, "Nondiffracting beams: travelling, standing, rotating and spiral waves," Opt. Commun. 123, 225-233 (1996).
[CrossRef]

Cholis, I.

Y. Roichman, I. Cholis, and D. G. Grier, "Volumetric imaging of holographic optical traps," Opt. Express 14, 10,907-10,912 (2006).
[CrossRef]

Chu, S.

Cižmár, T.

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

Courtial, J.

Crocker, J. C.

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

Dholakia, K.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Dufresne, E. R.

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Durnin, J.

Dziedzic, J. M.

Friberg, A. T.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
[CrossRef]

A. Vasara, J. Turunen, and A. T. Friberg, "Realization of general nondiffracting beams with computer-generated holograms," J. Opt. Soc. Am. A 6(11), 1748-1754 (1989).
[CrossRef] [PubMed]

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Grier, D. G.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Y. Roichman and D. G. Grier, "Three-dimensional holographic ring traps," Proc. SPIE 6483, 64830F (2007).
[CrossRef]

Y. Roichman and D. G. Grier, "Projecting extended optical traps with shape-phase holography," Opt. Lett. 31, 1675-1677 (2006).
[CrossRef] [PubMed]

Y. Roichman, I. Cholis, and D. G. Grier, "Volumetric imaging of holographic optical traps," Opt. Express 14, 10,907-10,912 (2006).
[CrossRef]

S.-H. Lee and D. G. Grier, "Robustness of holographic optical traps against phase scaling errors," Opt. Express 13, 7458-7465 (2005).
[CrossRef] [PubMed]

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13(15), 5831-5845 (2005).
[CrossRef] [PubMed]

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

Honkanen, M.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
[CrossRef]

Khonina, S. N.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
[CrossRef]

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: Rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
[CrossRef]

Kollárová, V.

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

Kotlyar, V. V.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
[CrossRef]

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: Rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
[CrossRef]

Kuittinen, M.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
[CrossRef]

Kyvalsky, J.

Z. Bouchal and J. Kyvalsky, "Controllable 3D spatial localization of light fields synthesized by non-diffracting modes," J. Mod. Opt. 51, 157-176 (2004).
[CrossRef]

Ladavac, K.

Lautanen, J.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
[CrossRef]

Lee, S.-H.

McDonald, G. S.

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, "Nondiffracting beams: travelling, standing, rotating and spiral waves," Opt. Commun. 123, 225-233 (1996).
[CrossRef]

McGloin, D.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

New, G. H. C.

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, "Nondiffracting beams: travelling, standing, rotating and spiral waves," Opt. Commun. 123, 225-233 (1996).
[CrossRef]

Overfelt, P. L.

P. L. Overfelt, "Scalar optical beams with helical symmetry," Phys. Rev. A 46, 3516-3522 (1992).
[CrossRef] [PubMed]

Pääkkönen, P.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
[CrossRef]

Polin, M.

Roichman, Y.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Y. Roichman and D. G. Grier, "Three-dimensional holographic ring traps," Proc. SPIE 6483, 64830F (2007).
[CrossRef]

Y. Roichman and D. G. Grier, "Projecting extended optical traps with shape-phase holography," Opt. Lett. 31, 1675-1677 (2006).
[CrossRef] [PubMed]

Y. Roichman, I. Cholis, and D. G. Grier, "Volumetric imaging of holographic optical traps," Opt. Express 14, 10,907-10,912 (2006).
[CrossRef]

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13(15), 5831-5845 (2005).
[CrossRef] [PubMed]

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Soifer, V. A.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
[CrossRef]

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: Rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
[CrossRef]

Sun, B.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Tervo, J.

Turunen, J.

J. Tervo and J. Turunen, "Rotating scale-invariant electromagnetic fields," Opt. Express 9, 9-15 (2001).
[CrossRef] [PubMed]

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
[CrossRef]

A. Vasara, J. Turunen, and A. T. Friberg, "Realization of general nondiffracting beams with computer-generated holograms," J. Opt. Soc. Am. A 6(11), 1748-1754 (1989).
[CrossRef] [PubMed]

Vasara, A.

Wagner, J.

Whyte, G.

Zemánek, P.

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

J. Colloid Interface Sci. (1)

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

J. Mod. Opt. (3)

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: Rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
[CrossRef]

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. T. Friberg, "Rotating optical fields: experimental demonstration with diffractive optics," J. Mod. Opt. 45, 2355-2369 (1998).
[CrossRef]

Z. Bouchal and J. Kyvalsky, "Controllable 3D spatial localization of light fields synthesized by non-diffracting modes," J. Mod. Opt. 51, 157-176 (2004).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature (2)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

New J. Phys. (1)

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New J. Phys. 8, 43 (2006).
[CrossRef]

Opt. Commun. (2)

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, "Nondiffracting beams: travelling, standing, rotating and spiral waves," Opt. Commun. 123, 225-233 (1996).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. A (1)

P. L. Overfelt, "Scalar optical beams with helical symmetry," Phys. Rev. A 46, 3516-3522 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

J. Durnin, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Proc. SPIE (1)

Y. Roichman and D. G. Grier, "Three-dimensional holographic ring traps," Proc. SPIE 6483, 64830F (2007).
[CrossRef]

Rev. Sci. Instrum. (1)

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Supplementary Material (2)

» Media 1: MOV (246 KB)     
» Media 2: MOV (1075 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

(a) Calculated three-dimensional intensity distribution of a solenoid beam propagating in the ẑ direction. (b) Volumetric rendering of the measured intensity in an experimental realization. Media 1 shows a rotating view of this static beam.

Fig. 2.
Fig. 2.

Retrograde forces in a helical solenoid beam. The local wave vector k is normal to the light’s wavefronts, with a component in the ẑ direction. (a) ℓ = +40: k is directed along the solenoid, resulting in a downstream phase-gradient force. (b) ℓ = 0: Wavefronts are parallel to the solenoid so that k is everywhere normal to the spiral. Particles trapped by intensity-gradient forces experience no net force. (c) ℓ= -40: A component of k is directed back down the spiral. A particle confined to the spiral therefore moves upstream.

Fig. 3.
Fig. 3.

Three-dimensional trajectory of a colloidal sphere moving along one turn of an optical solenoid beam together with a multiply-exposed image of the sphere at six points in its motion (Media 2). Alternating between ℓ = ±30 switches the direction of the particle’s motion relative to the propagation direction, ẑ. Arrows indicate the direction of motion for the downstream (blue) and retrograde upstream (red) trajectories.

Equations (10)

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A ( r , z , t ) = u ( r , z ) e iωt ε ̂ ,
u 0 ( r ) = ( u h z ) ( r ) dz , where
h z ( r ) = 1 2 π z ( e ik r 2 + z 2 r 2 + z 2 )
( u h z ) ( r ) = u ( r , z ) h z ( r r ) d 2 r .
u p ( r , z ) = ( u 0 h z ) ( r ) .
u ( r , z ) = { a ( z ) δ ( r r 0 ( z ) ) e ( z ) , z 1 z z 2 0 , otherwise .
u ˜ 0 ( q ) = z 1 z 2 a ( z ) e ( z ) e i q · r 0 ( z ) e iz ( k 2 q 2 ) 1 / 2 dz .
u 0 ( r ) = β J 0 ( ( k 2 β 2 ) 1 / 2 r )
u γ , ( r , z ) = m = [ γk ] [ ] m γ 2 J m ( q m R ) e i ( m ) γ z e imθ J m ( q m r ) ,
u γ , * ( r , z ) u γ , ( r , z ) d 2 rdz = δ ℓℓ δ ( γ γ ) ,

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