Abstract

This study proposes a method for creating a light field with controlled distribution of transverse momentum (TM) by displaying a hologram only in an azimuth region that centers at θ0 and has a range of Δθ of a spatial light modulator in holographic optical tweezers. This study utilized ray optics to analyze the TM of the resultant field, revealing that the direction of the TM is determined by the center angle of the azimuth region and that the magnitude of the TM is proportional to sin(Δθ/2), without regarding the intensity. The relationship was verified experimentally. In addition, this study demonstrated moving particles along a designed path and depleting particles by the fields.

© 2011 Optical Society of America

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    [CrossRef]
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2011 (1)

2008 (2)

2007 (1)

2006 (3)

2005 (1)

2004 (3)

2003 (1)

2002 (1)

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

2000 (1)

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[CrossRef]

1999 (1)

1986 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

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]

Ashkin, A.

Bernet, S.

Bjorkholm, J. E.

Chu, S.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28, 872–874 (2003).
[CrossRef] [PubMed]

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

Di Leonardo, R.

Dziedzic, J. M.

Furhapter, S.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 1996).

Grier, D. G.

Haist, T.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
[CrossRef]

Hsu, L.

S. Y. Tseng and L. Hsu, “An intuitive view of the origin of orbital angular momentum in optical vortices,” Proc. SPIE 6326, 63261C (2006).
[CrossRef]

Ianni, F.

Jesacher, A.

Koss, B. A.

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

Ladavac, K.

Liesener, J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[CrossRef]

Lin, J.

Mansuripur, M.

M. Mansuripur, Classical Optics and its Applications(Cambridge University Press, 2002).

Maurer, C.

Mueth, D. M.

Niu, H. B.

Peng, X.

Plewa, J.

Reicherter, M.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
[CrossRef]

Ritsch-Marte, 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, “Projecting extended optical traps with shape-phase holography,” Opt. Lett. 31, 1675–1677(2006).
[CrossRef] [PubMed]

Ruocco, G.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Schwaighofer, A.

Shanblatt, E. R.

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]

Tanner, E.

Tao, S. H.

Tiziani, H. J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
[CrossRef]

Tseng, S. Y.

S. Y. Tseng and L. Hsu, “An intuitive view of the origin of orbital angular momentum in optical vortices,” Proc. SPIE 6326, 63261C (2006).
[CrossRef]

Wagemann, E. U.

Yuan, X. C.

Opt. Commun. (2)

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[CrossRef]

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

Opt. Express (8)

Opt. Lett. (4)

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Phys. Rev. Lett. (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]

Proc. SPIE (1)

S. Y. Tseng and L. Hsu, “An intuitive view of the origin of orbital angular momentum in optical vortices,” Proc. SPIE 6326, 63261C (2006).
[CrossRef]

Other (2)

M. Mansuripur, Classical Optics and its Applications(Cambridge University Press, 2002).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 1996).

Supplementary Material (2)

» Media 1: MOV (281 KB)     
» Media 2: MOV (3676 KB)     

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Figures (6)

Fig. 1
Fig. 1

Schematic illustration of a ray path in HOTs from the SLM plane to the focal plane.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Moving particles along two trap arrays (a number near the trap array indicates the region from which the trap array was created): (a) is the phase pattern for creating two trap arrays; (b) is the corresponding intensity distribution on the focal plane; (c) and (d) are the simulated TM distributions in the x and y directions, respectively; and (e) represents the sequential snapshots of two 9 μm diameter beads moving in the trap arrays.

Fig. 4
Fig. 4

Average moving speed of a 9 μm diameter bead in a trap array at different Δ θ and p total : (a) is the average moving speed at different Δ θ from 60 ° to 300 ° . The solid lines fit the function V max Sin ( Δ θ / 2 ) ; (b) is V max at different incident power p total . The straight line is a linear fit, which does not pass through the origin, indicating that a minimum incident power of approximately 63.2 mW is required to overcome the resistance between the particle and slide surface.

Fig. 5
Fig. 5

Particles moving along a heart-shaped path: (a) is the phase pattern for producing a heart-shaped path; (b) is the corresponding intensity distribution on the focal plane; (c) and (d) are the simulated TM distributions in the x and y directions, respectively; and (e) represents the sequential snapshots of beads moving along the path (Media 1).

Fig. 6
Fig. 6

Depleting 0.5 μm diameter beads by an equally-spaced trap array with TM directing outward (a number near each triangular trap array indicates the azimuth region from which the triangular trap array was created): (a) is the phase pattern for producing an equally-spaced trap array, which forms a hexagon; (b) is the corresponding intensity distribution on the focal plane; (c) and (d) are the simulated TM distributions in the x and y directions, respectively; and (e) represents the sequential snapshots of bead depletion (Media 2).

Equations (5)

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P t , ray = ( n p ray c f obj ) r r = ( n p ray c f obj ) r r [ cos ( θ ) x + sin ( θ ) y ] ,
P t , total p total = 0 R θ 0 Δ θ / 2 θ 0 + Δ θ / 2 N r P t , ray r r d θ d r r = 0 R θ 0 Δ θ / 2 θ 0 + Δ θ / 2 N r ( n c f obj ) ( p total π R 2 N r ) [ cos ( θ ) x + sin ( θ ) y ] r r 2 d θ d r r = ( 2 3 π c ) ( n R f obj ) p total sin ( Δ θ / 2 ) [ cos ( θ 0 ) x + sin ( θ 0 ) y ] ,
J total p total ( x , y ) = P t , total p total I n ( x , y ) ,
I n ( x , y ) = I ( x , y ) I ( x , y ) d x d y ,
J t , total p total ( x , y ) = ( 2 3 π c ) ( n R f obj ) p total sin ( Δ θ / 2 ) [ cos ( θ 0 ) x + sin ( θ 0 ) y ] I n ( x , y ) .

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