Abstract

We propose and demonstrate trapping and rotation of microparticles and biological samples with a moiré-based rotating optical tweezers. We show that polystyrene beads, as well as Escherichia coli cells, can be rotated with ease, while the speed and direction of rotation are fully controllable by a computer, obviating mechanical movement or phase-sensitive interference. Furthermore, we demonstrate experimentally the generation of white-light propelling beams and arrays, and discuss the possibility of optical tweezing and particle micro-manipulation based on incoherent white-light rotating patterns.

© 2012 OSA

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  24. E. R. Dufresne and D. G. Grier, “Optical tweezer arrays and optical substrates created with diffractive optics,” Rev. Sci. Instrum.69(5), 1974–1977 (1998).
    [CrossRef]
  25. P. Li, K. Shi, and Z. Liu, “Manipulation and spectroscopy of a single particle by use of white-light optical tweezers,” Opt. Lett.30(2), 156–158 (2005).
    [CrossRef] [PubMed]
  26. K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, “Vortex formation in a stirred bose-einstein condensate,” Phys. Rev. Lett.84(5), 806–809 (2000).
    [CrossRef] [PubMed]
  27. Y. Lamhot, A. Barak, C. Rotschild, M. Segev, M. Saraf, E. Lifshitz, A. Marmur, R. El-Ganainy, and D. N. Christodoulides, “Optical control of thermocapillary effects in complex nanofluids,” Phys. Rev. Lett.103(26), 264503 (2009).
    [CrossRef] [PubMed]

2011

2010

2009

Y. Lamhot, A. Barak, C. Rotschild, M. Segev, M. Saraf, E. Lifshitz, A. Marmur, R. El-Ganainy, and D. N. Christodoulides, “Optical control of thermocapillary effects in complex nanofluids,” Phys. Rev. Lett.103(26), 264503 (2009).
[CrossRef] [PubMed]

2008

M. K. Kreysing, T. Kieβling, A. Fritsch, C. Dietrich, J. R. Guck, and J. A. Käs, “The optical cell rotator,” Opt. Express16(21), 16984–16992 (2008).
[CrossRef] [PubMed]

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem.77(1), 205–228 (2008).
[CrossRef] [PubMed]

2005

2004

W. M. Lee and X.-C. Yuan, “Experimental observation of 'pure helical phase' interference using moiré fringes generated from holograms with dislocations,” J. Opt. A, Pure Appl. Opt.6(5), 482–485 (2004).
[CrossRef]

2003

D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett.90(13), 133901 (2003).
[CrossRef] [PubMed]

Z. Bryant, M. D. Stone, J. Gore, S. B. Smith, N. R. Cozzarelli, and C. Bustamante, “Structural transitions and elasticity from torque measurements on DNA,” Nature424(6946), 338–341 (2003).
[CrossRef] [PubMed]

R. Dasgupta, S. K. Mohanty, and P. K. Gupta, “Controlled rotation of biological microscopic objects using optical line tweezers,” Biotechnol. Lett.25(19), 1625–1628 (2003).
[CrossRef] [PubMed]

2002

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science296(5570), 1101–1103 (2002).
[CrossRef] [PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun.201(1-3), 21–28 (2002).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

A. T. O’Neil and M. J. Padgett, “Rotational control within optical tweezers by use of a rotating aperture,” Opt. Lett.27(9), 743–745 (2002).
[CrossRef] [PubMed]

2001

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

L. Sacconi, G. Romano, R. Ballerini, M. Capitanio, M. De Pas, M. Giuntini, D. Dunlap, L. Finzi, and F. S. Pavone, “Three-dimensional magneto-optic trap for micro-object manipulation,” Opt. Lett.26(17), 1359–1361 (2001).
[CrossRef] [PubMed]

2000

K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, “Vortex formation in a stirred bose-einstein condensate,” Phys. Rev. Lett.84(5), 806–809 (2000).
[CrossRef] [PubMed]

1998

E. R. Dufresne and D. G. Grier, “Optical tweezer arrays and optical substrates created with diffractive optics,” Rev. Sci. Instrum.69(5), 1974–1977 (1998).
[CrossRef]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature394(6691), 348–350 (1998).
[CrossRef]

1995

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

1991

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher-order mode Nd: YAG laserbeams,” Electron. Lett.27(20), 1831–1832 (1991).
[CrossRef]

1987

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science235(4795), 1517–1520 (1987).
[CrossRef] [PubMed]

1970

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

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science296(5570), 1101–1103 (2002).
[CrossRef] [PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun.201(1-3), 21–28 (2002).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science235(4795), 1517–1520 (1987).
[CrossRef] [PubMed]

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

Ay, C.

Ballerini, R.

Barak, A.

Y. Lamhot, A. Barak, C. Rotschild, M. Segev, M. Saraf, E. Lifshitz, A. Marmur, R. El-Ganainy, and D. N. Christodoulides, “Optical control of thermocapillary effects in complex nanofluids,” Phys. Rev. Lett.103(26), 264503 (2009).
[CrossRef] [PubMed]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Bryant, Z.

Z. Bryant, M. D. Stone, J. Gore, S. B. Smith, N. R. Cozzarelli, and C. Bustamante, “Structural transitions and elasticity from torque measurements on DNA,” Nature424(6946), 338–341 (2003).
[CrossRef] [PubMed]

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem.77(1), 205–228 (2008).
[CrossRef] [PubMed]

Z. Bryant, M. D. Stone, J. Gore, S. B. Smith, N. R. Cozzarelli, and C. Bustamante, “Structural transitions and elasticity from torque measurements on DNA,” Nature424(6946), 338–341 (2003).
[CrossRef] [PubMed]

Capitanio, M.

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem.77(1), 205–228 (2008).
[CrossRef] [PubMed]

Chen, S.

Chen, Z.

Chevy, F.

K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, “Vortex formation in a stirred bose-einstein condensate,” Phys. Rev. Lett.84(5), 806–809 (2000).
[CrossRef] [PubMed]

Christodoulides, D. N.

Cozzarelli, N. R.

Z. Bryant, M. D. Stone, J. Gore, S. B. Smith, N. R. Cozzarelli, and C. Bustamante, “Structural transitions and elasticity from torque measurements on DNA,” Nature424(6946), 338–341 (2003).
[CrossRef] [PubMed]

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett.90(13), 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

Dalibard, J.

K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, “Vortex formation in a stirred bose-einstein condensate,” Phys. Rev. Lett.84(5), 806–809 (2000).
[CrossRef] [PubMed]

Dasgupta, R.

R. Dasgupta, S. K. Mohanty, and P. K. Gupta, “Controlled rotation of biological microscopic objects using optical line tweezers,” Biotechnol. Lett.25(19), 1625–1628 (2003).
[CrossRef] [PubMed]

De Pas, M.

Dholakia, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science296(5570), 1101–1103 (2002).
[CrossRef] [PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun.201(1-3), 21–28 (2002).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Dietrich, C.

Dufresne, E. R.

E. R. Dufresne and D. G. Grier, “Optical tweezer arrays and optical substrates created with diffractive optics,” Rev. Sci. Instrum.69(5), 1974–1977 (1998).
[CrossRef]

Dunlap, D.

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science235(4795), 1517–1520 (1987).
[CrossRef] [PubMed]

Efremidis, N. K.

El-Ganainy, R.

Y. Lamhot, A. Barak, C. Rotschild, M. Segev, M. Saraf, E. Lifshitz, A. Marmur, R. El-Ganainy, and D. N. Christodoulides, “Optical control of thermocapillary effects in complex nanofluids,” Phys. Rev. Lett.103(26), 264503 (2009).
[CrossRef] [PubMed]

Finzi, L.

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature394(6691), 348–350 (1998).
[CrossRef]

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

Fritsch, A.

Giuntini, M.

Gore, J.

Z. Bryant, M. D. Stone, J. Gore, S. B. Smith, N. R. Cozzarelli, and C. Bustamante, “Structural transitions and elasticity from torque measurements on DNA,” Nature424(6946), 338–341 (2003).
[CrossRef] [PubMed]

Grier, D. G.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett.90(13), 133901 (2003).
[CrossRef] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

E. R. Dufresne and D. G. Grier, “Optical tweezer arrays and optical substrates created with diffractive optics,” Rev. Sci. Instrum.69(5), 1974–1977 (1998).
[CrossRef]

Guck, J. R.

Gupta, P. K.

R. Dasgupta, S. K. Mohanty, and P. K. Gupta, “Controlled rotation of biological microscopic objects using optical line tweezers,” Biotechnol. Lett.25(19), 1625–1628 (2003).
[CrossRef] [PubMed]

He, H.

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

Heckenberg, N. R.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature394(6691), 348–350 (1998).
[CrossRef]

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

Hernandez, D.

Hu, Y.

Huang, S.

Inaba, H.

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher-order mode Nd: YAG laserbeams,” Electron. Lett.27(20), 1831–1832 (1991).
[CrossRef]

Ishigure, M.

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher-order mode Nd: YAG laserbeams,” Electron. Lett.27(20), 1831–1832 (1991).
[CrossRef]

Käs, J. A.

Kießling, T.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

Kreysing, M. K.

Lamhot, Y.

Y. Lamhot, A. Barak, C. Rotschild, M. Segev, M. Saraf, E. Lifshitz, A. Marmur, R. El-Ganainy, and D. N. Christodoulides, “Optical control of thermocapillary effects in complex nanofluids,” Phys. Rev. Lett.103(26), 264503 (2009).
[CrossRef] [PubMed]

Lan, T. K.

Lee, W. M.

W. M. Lee and X.-C. Yuan, “Experimental observation of 'pure helical phase' interference using moiré fringes generated from holograms with dislocations,” J. Opt. A, Pure Appl. Opt.6(5), 482–485 (2004).
[CrossRef]

Li, P.

Lifshitz, E.

Y. Lamhot, A. Barak, C. Rotschild, M. Segev, M. Saraf, E. Lifshitz, A. Marmur, R. El-Ganainy, and D. N. Christodoulides, “Optical control of thermocapillary effects in complex nanofluids,” Phys. Rev. Lett.103(26), 264503 (2009).
[CrossRef] [PubMed]

Lin, Y. C.

Liu, Z.

MacDonald, M. P.

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun.201(1-3), 21–28 (2002).
[CrossRef]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science296(5570), 1101–1103 (2002).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Madison, K. W.

K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, “Vortex formation in a stirred bose-einstein condensate,” Phys. Rev. Lett.84(5), 806–809 (2000).
[CrossRef] [PubMed]

Marmur, A.

Y. Lamhot, A. Barak, C. Rotschild, M. Segev, M. Saraf, E. Lifshitz, A. Marmur, R. El-Ganainy, and D. N. Christodoulides, “Optical control of thermocapillary effects in complex nanofluids,” Phys. Rev. Lett.103(26), 264503 (2009).
[CrossRef] [PubMed]

McGloin, D.

D. McGloin and J. P. Reid, “40 years of optical manipulation,” Opt. Photonics News21(3), 20–26 (2010).
[CrossRef]

Mills, M. S.

Moffitt, J. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem.77(1), 205–228 (2008).
[CrossRef] [PubMed]

Mohanty, S. K.

R. Dasgupta, S. K. Mohanty, and P. K. Gupta, “Controlled rotation of biological microscopic objects using optical line tweezers,” Biotechnol. Lett.25(19), 1625–1628 (2003).
[CrossRef] [PubMed]

Nieminen, T. A.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature394(6691), 348–350 (1998).
[CrossRef]

O’Neil, A. T.

Padgett, M. J.

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science296(5570), 1101–1103 (2002).
[CrossRef] [PubMed]

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun.201(1-3), 21–28 (2002).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Pavone, F. S.

Prakash, J.

Reid, J. P.

D. McGloin and J. P. Reid, “40 years of optical manipulation,” Opt. Photonics News21(3), 20–26 (2010).
[CrossRef]

Romano, G.

Rotschild, C.

Y. Lamhot, A. Barak, C. Rotschild, M. Segev, M. Saraf, E. Lifshitz, A. Marmur, R. El-Ganainy, and D. N. Christodoulides, “Optical control of thermocapillary effects in complex nanofluids,” Phys. Rev. Lett.103(26), 264503 (2009).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature394(6691), 348–350 (1998).
[CrossRef]

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

Sacconi, L.

Salazar, M.

Saraf, M.

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Z. Bryant, M. D. Stone, J. Gore, S. B. Smith, N. R. Cozzarelli, and C. Bustamante, “Structural transitions and elasticity from torque measurements on DNA,” Nature424(6946), 338–341 (2003).
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M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun.201(1-3), 21–28 (2002).
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Y. Lamhot, A. Barak, C. Rotschild, M. Segev, M. Saraf, E. Lifshitz, A. Marmur, R. El-Ganainy, and D. N. Christodoulides, “Optical control of thermocapillary effects in complex nanofluids,” Phys. Rev. Lett.103(26), 264503 (2009).
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[CrossRef] [PubMed]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science296(5570), 1101–1103 (2002).
[CrossRef] [PubMed]

Supplementary Material (11)

» Media 1: AVI (6133 KB)     
» Media 2: AVI (2375 KB)     
» Media 3: AVI (1869 KB)     
» Media 4: AVI (1461 KB)     
» Media 5: AVI (4094 KB)     
» Media 6: AVI (4348 KB)     
» Media 7: AVI (1620 KB)     
» Media 8: AVI (5420 KB)     
» Media 9: AVI (6082 KB)     
» Media 10: AVI (5622 KB)     
» Media 11: AVI (3491 KB)     

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Figures (6)

Fig.
                        1
Fig. 1

(a) Experimental setup for moiré-based rotating optical tweezers. SLM: spatial light modulator; BS: beam splitter; L: lens; O: objective lens; WLS: white light source; CCD: charge-coupled device.

Fig.
                        2
Fig. 2

(a) Moiré pattern used for generating 3-blade rotating beams by overlapping (b) a straight-line grating and (c) a fork-type vortex grating of topological charge m = 3. (d) Illustration of beam focusing and propagation of the Gaussian (solid) and vortex (dashed) components exiting from (a). (e)-(g) Numerical (top) and experimental (bottom) transverse intensity patterns taken at different longitudinal positions marked in (d), as retrieved from (a) with a single input Gaussian beam.

Fig.
                        3
Fig. 3

(a) Moiré pattern used for generating 3-blade rotating beams by overlapping (b) a curved fork-type vortex grating (m = 3) with the straight-line grating shown in Fig. 2(b). (c) Illustration of beam focusing and propagation of the Gaussian (solid) and vortex (dashed) components exiting from (a). (d)-(e) Numerically (top) and experimentally (bottom) retrieved moiré patterns with a single input Gaussian beam at different longitudinal positions marked in (c).

Fig.
                        4
Fig. 4

Trapping and rotation of 2-μm polystyrene beads. Left column: generated multi-blade propelling beams (Media 1, Media 2, and Media 3); right columns: snapshots of trapped beads as driven by the rotating tweezers. (a) to (c) correspond to tweezing with propelling beams of 2-blades (Media 4), 3-blades (Media 5), and 4-blades (Media 6), respectively.

Fig.
                        5
Fig. 5

Experimental demonstration of optical trapping and rotation of an E. coli bacterium (Media 7). (a)-(h) show snapshots of the E. coli cell in different orientations during rotation. The bacterium is about 2 μm in length and 1 μm in width. The white dashed line serves as a visual guide for the orientation of the bacterium, and the white arrow shows the direction of rotation.

Fig.
                        6
Fig. 6

(a-d) Generation of optical propelling beam arrays with coherent light. (a) shows the grating design corresponding to a desired optical vortex array; (b) moiré pattern created by overlapping the grating in (a) with a straight-line grating as shown in Fig. 2(b); (c, d) Numerically (Media 8) and experimentally (Media 9) reconstructed array of rotating beams. (e-h) Experimental demonstration of (e, f) a single optical propelling beam and (g, h) an array of such beams with incoherent white light, where (e) and (g) are the moiré patterns, and (f) and (h) show one snapshot of the generated rotating beams (Media 10 and 11).

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