Abstract

Complex three-dimensional patterns of multifunctional optical traps can be encoded in phase-only computer-generated holograms and projected with the holographic optical trapping technique. The trap-forming holograms, in turn, are implemented as diffractive optical elements whose phase transfer functions generally do not faithfully reproduce the design. We demonstrate that phase encoding errors reduce the overall intensities of the projected traps but, remarkably, do not affect their positions, relative intensities or mode structure. We exploit this robust performance to implement dual-color holographic optical tweezers with a single hologram.

© 2005 Optical Society of America

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References

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Appl. Opt. (1)

Europhys. Lett. (2)

K. Ladavac and D. G. Grier, �??Colloidal hydrodynamic coupling in concentric optical vortices,�?? Europhys. Lett. 70, 548�??554 (2005).
[CrossRef]

E. R. Dufresne, D. Altman, and D. G. Grier, �??Brownian dynamics of a sphere in a slit pore,�?? Europhys. Lett. 53, 264�??270 (2001).
[CrossRef]

IBM J. Res. Dev. (1)

J.W. Goodman and A. M. Silverstri, �??Some effects of Fourier-domain phase quantization,�?? IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

IBM J. Res. Develop. (1)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, �??The kinoform: A new wavefront reconstruction device,�?? IBM J. Res. Develop. 13, 150�??155 (1969).
[CrossRef]

J. Mod. Opt. (3)

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, �??Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,�?? J. Mod. Opt. 42, 217�??223 (1995).
[CrossRef]

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, P. Perlo, and P. Repetto, �??Design of DOEs for wavelength division and focusing,�?? J. Mod. Opt. 52, 917�??926 (2005).
[CrossRef]

N. B. Simpson, L. Allen, and M. J. Padgett, �??Optical tweezers and optical spanners with Laguerre-Gaussian modes,�?? J. Mod. Opt. 43, 2485�??2491 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nature (1)

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

New J. Phys. (1)

J. Leach and M. J. Padgett, �??Observation of chromatic effects near a white-light vortex,�?? New J. Phys. 5, 154 (2003).
[CrossRef]

Opt. Comm. (3)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, �??Optical micromanipulation using a Bessel light beam,�?? Opt. Comm. 197, 239�??245 (2001).
[CrossRef]

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

J. E. Curtis, B. A. Koss, and D. G. Grier, �??Dynamic holographic optical tweezers,�?? Opt. Comm. 207, 169�??175 (2002).
[CrossRef]

Opt. Express (6)

A. Jesacher, S. Furhpater, S. Bernet, and M. Ritsch-Marte, �??Size selective trapping with optical �??cogwheel�?? tweezers,�?? Opt. Express 12, 4129�??4135 (2004). <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4129">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4129</a>.
[CrossRef] [PubMed]

Y. Roichman and D. G. Grier, �??Holographic assembly of quasicrystalline photonic heterostructures,�?? Opt. Express 13, 5434�??5439 (2005) <a href=. "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-14-5434">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-14-5434</a>.
[CrossRef] [PubMed]

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier, �??Optimized holographic optical traps,�?? Opt. Express 13, 5831�??5845 (2005). <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5831">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5831.
[CrossRef] [PubMed]

P. Fischer, C. T. A. Brown, J. E. Morris, C. López-Mariscal, E. M. Wright, W. Sibbett, and K. Dholakia, �??White light propagation invariant beams,�?? Opt. Express 13, 6657�??6666 (2005) <a href=. "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6657">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6657</a>.
[CrossRef] [PubMed]

K. Ladavac and D. G. Grier, �??Microoptomechanical pump assembled and driven by holographic optical vortex arrays,�?? Opt. Express 12, 1144�??1149 (2004) <a href "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1144">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1144</a>.
[CrossRef] [PubMed]

C.-S. Guo, X. Liu, J.-L. He, and H.-T. Wang, �??Optimal annulus structures of optical vortices,�?? Opt. Express 12, 4625�??4634 (2004) <a href=. "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4625">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4625</a>.
[CrossRef] [PubMed]

Opt. Lett. (6)

Opt. Quantum Elect. (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J.Wegener, �??Laser beams with phase singularities,�?? Opt. Quantum Elect. 24, S951�??S962 (1992).
[CrossRef]

Optica Acta (1)

J. P. Riley and F. N. Birkett, �??A reflection kinoform for use with a CO2 laser,�?? Optica Acta 24, 999�??1009 (1977).
[CrossRef]

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, �??Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,�?? Phys. Rev. A 45, 8185�??8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. E (1)

K. Ladavac, K. Kasza, and D. G. Grier, �??Sorting by periodic potential energy landscapes: Optical fractionation,�?? Phys. Rev. E 70, 010901(R) (2004).
[CrossRef]

Phys. Rev. Lett. (1)

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

Rev. Sci. Instr. (1)

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

Other (1)

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

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the geometry of an optimized holographic trapping system. Light in the input pupil Ω is focused by a strongly converging lens of focal length f to form an optical trap at r, which is shown trapping a particle.

Fig. 2.
Fig. 2.

Experimentally realized generalized conjugate images, I 0(r) and I -1(r), to a planar arrangements of optical traps, I 1(r).

Fig. 3.
Fig. 3.

(a) Interference between an on-axis optical vortex and its first-order conjugate creates 2ℓ-fold modulation of the principal ring’s intensity. Here an ℓ = 30 optical vortex is projected on axis in a standard holographic optical trapping geometry. The bright central spot marks the position of the optical axis in the field of view. The ℓ-fold radial striations result from the finite spatial resolution of the DOE. (b) Displacing the vortex away from the optical axis lifts the superposition of conjugate fields and eliminates the circumferential modulation.

Fig. 4.
Fig. 4.

Simultaneous projection of red (685 nm) and green (532 nm) holographic optical trapping patterns with a single computer-generated DOE.

Equations (15)

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E ( r ) = 1 λf Ω u 0 ( ρ ) exp ( i φ 0 ( ρ ) ) exp ( i Φ ( ρ ) ) exp ( i k ρ 2 2 f 2 z ) exp ( i kr ρ f ) d 2 ρ ,
φ 0 ( ρ ) = k ρ 2 2 f 2 z 0 ,
exp ( i Φ ( ρ ) ) = n = a n exp ( i n φ ( ρ ) )
a n = 1 2 π 0 2 π exp ( i f ( x ) ) exp ( inx ) dx .
E n ( r ) = 1 λf Ω u 0 ( ρ ) exp ( i φ 0 ( ρ ) ) exp ( in φ ( ρ ) ) exp ( i k ρ 2 2 f 2 z ) exp ( i kr ρ f ) d 2 ρ .
E ( r ) = n = a n E n ( r ) .
a n = exp ( i π ( n γ ) ) sin ( π ( n γ ) ) π ( n γ ) .
f ( x ) = { 0 x a b a < x 2 π ,
a n = 2 i n π exp ( i na 2 ) exp ( i b 2 ) sin ( na 2 ) sin ( b 2 ) .
I ( r ) = m , n = a n a m * E n ( r ) E m * ( r )
φ z ( ρ , z 1 ) = k ρ 2 z 1 2 f 2 ,
E ( r ) a 1 E 1 ( r ) + a 0 E 0 ( r ) + a 1 E 1 ( r ) .
E 1 ( r ) = E 1 * ( r ) = ( 1 ) u ( r ) exp ( iℓθ ) .
I ( r ) = A 0 ( r ) + A 1 cos ( ℓθ + θ 1 ) + A 2 ( r ) cos ( 2 ℓθ + θ 2 ) ,
tan θ 1 = a 1 sin ( β 1 β 0 ) + ( 1 ) a 1 sin ( β 0 β 1 ) a 1 sin ( β 1 β 0 ) + ( 1 ) a 1 sin ( β 0 β 1 ) .

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