Abstract

How far a particle moves along the optical axis in a holographic optical trap is not simply dictated by the programmed motion of the trap, but rather depends on an interplay of the trap’s changing shape and the particle’s material properties. For the particular case of colloidal spheres in optical tweezers, holographic video microscopy reveals that trapped particles tend to move farther along the axial direction than the traps that are moving them and that different kinds of particles move by different amounts. These surprising and sizeable variations in axial placement can be explained by a dipole-order theory for optical forces. Their discovery highlights the need for real-time feedback to achieve precise control of colloidal assemblies in three dimensions and demonstrates that holographic microscopy can meet that need.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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2018 (1)

2017 (1)

A. Yevick, D. J. Evans, and D. G. Grier, “Photokinetic analysis of the forces and torques exerted by optical tweezers carrying angular momentum,” Philos. Trans. R. Soc., A 375(2087), 20150432 (2017).
[Crossref]

2014 (3)

A. Yevick, M. Hannel, and D. G. Grier, “Machine-learning approach to holographic particle characterization,” Opt. Express 22(22), 26884–26890 (2014).
[Crossref]

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82(1), 23–31 (2014).
[Crossref]

M. Lee, G. Gibson, D. Phillips, M. Padgett, and M. Tassieri, “Dynamic stereo microscopy for studying particle sedimentation,” Opt. Express 22(4), 4671–4677 (2014).
[Crossref]

2013 (1)

2012 (1)

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref]

2011 (1)

2010 (2)

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1448 (2010).
[Crossref]

S.-H. Lee, Y. Roichman, and D. G. Grier, “Optical solenoid beams,” Opt. Express 18(7), 6988–6993 (2010).
[Crossref]

2009 (1)

2008 (1)

2007 (3)

2006 (4)

2005 (2)

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref]

2002 (1)

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

1998 (1)

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

1996 (1)

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
[Crossref]

1993 (1)

B. T. Draine and J. Goodman, “Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[Crossref]

1986 (1)

1983 (1)

Abdulali, A.

Abramochkin, E.

Alieva, T.

Amato-Grill, J.

Ashkin, A.

Bell, B. A.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82(1), 23–31 (2014).
[Crossref]

Benito, D.

Bianchi, S.

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1448 (2010).
[Crossref]

Bjorkholm, J. E.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

Carberry, D.

Castro, I.

Chapin, S. C.

Cheong, F. C.

Cholis, I.

Chu, S.

Colen-Landy, A.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82(1), 23–31 (2014).
[Crossref]

Crocker, J. C.

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
[Crossref]

Curtis, J. E.

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

Di Leonardo, R.

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1448 (2010).
[Crossref]

Dixon, L.

Draine, B. T.

B. T. Draine and J. Goodman, “Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[Crossref]

Dreyfus, R.

Dufresne, E. R.

S. C. Chapin, V. Germain, and E. R. Dufresne, “Automated trapping, assembly, and sorting with holographic optical tweezers,” Opt. Express 14(26), 13095–13100 (2006).
[Crossref]

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

Dziedzic, J. M.

Evans, D. J.

A. Yevick, D. J. Evans, and D. G. Grier, “Photokinetic analysis of the forces and torques exerted by optical tweezers carrying angular momentum,” Philos. Trans. R. Soc., A 375(2087), 20150432 (2017).
[Crossref]

Germain, V.

Gibson, G.

Goodman, J.

B. T. Draine and J. Goodman, “Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[Crossref]

Grier, D. G.

M. D. Hannel, A. Abdulali, M. O’Brien, and D. G. Grier, “Machine-learning techniques for fast and accurate feature localization in holograms of colloidal particles,” Opt. Express 26(12), 15221–15231 (2018).
[Crossref]

A. Yevick, D. J. Evans, and D. G. Grier, “Photokinetic analysis of the forces and torques exerted by optical tweezers carrying angular momentum,” Philos. Trans. R. Soc., A 375(2087), 20150432 (2017).
[Crossref]

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82(1), 23–31 (2014).
[Crossref]

A. Yevick, M. Hannel, and D. G. Grier, “Machine-learning approach to holographic particle characterization,” Opt. Express 22(22), 26884–26890 (2014).
[Crossref]

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref]

E. R. Shanblatt and D. G. Grier, “Extended and knotted optical traps in three dimensions,” Opt. Express 19(7), 5833–5838 (2011).
[Crossref]

S.-H. Lee, Y. Roichman, and D. G. Grier, “Optical solenoid beams,” Opt. Express 18(7), 6988–6993 (2010).
[Crossref]

F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17(15), 13071–13079 (2009).
[Crossref]

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

S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15(4), 1505–1512 (2007).
[Crossref]

S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15(26), 18275–18282 (2007).
[Crossref]

Y. Roichman, I. Cholis, and D. G. Grier, “Volumetric imaging of holographic optical traps,” Opt. Express 14(22), 10907–10912 (2006).
[Crossref]

Y. Roichman and D. G. Grier, “Projecting extended optical traps with shape-phase holography,” Opt. Lett. 31(11), 1675–1677 (2006).
[Crossref]

Y. Roichman and D. G. Grier, “Holographic assembly of quasicrystalline photonic heterostructures,” Opt. Express 13(14), 5434–5439 (2005).
[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]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref]

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 optical elements,” Rev. Sci. Instrum. 69(5), 1974–1977 (1998).
[Crossref]

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179(1), 298–310 (1996).
[Crossref]

Hanna, S.

Hannel, M.

Hannel, M. D.

Hasebe, P.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82(1), 23–31 (2014).
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

Jones, J. R.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82(1), 23–31 (2014).
[Crossref]

Katz, J.

Kim, S.-H.

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]

Krishnatreya, B. J.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82(1), 23–31 (2014).
[Crossref]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, 2001).

Ladavac, K.

Lee, M.

Lee, S.-H.

Malkiel, E.

Miles, M.

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, 2001).

O’Brien, M.

Padgett, M.

Phillips, D.

Polin, M.

Rarity, J.

Rodrigo, J. A.

Roichman, Y.

Ruffner, D. B.

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref]

Self, S. A.

Shanblatt, E. R.

Sheng, J.

Simpson, S.

Sun, B.

Sunda-Meya, A.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82(1), 23–31 (2014).
[Crossref]

Tassieri, M.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, 2001).

van Blaaderen, A.

van Oostrum, P.

Xiao, K.

Yang, S.-M.

Yevick, A.

A. Yevick, D. J. Evans, and D. G. Grier, “Photokinetic analysis of the forces and torques exerted by optical tweezers carrying angular momentum,” Philos. Trans. R. Soc., A 375(2087), 20150432 (2017).
[Crossref]

A. Yevick, M. Hannel, and D. G. Grier, “Machine-learning approach to holographic particle characterization,” Opt. Express 22(22), 26884–26890 (2014).
[Crossref]

Yi, G.-R.

Am. J. Phys. (1)

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82(1), 23–31 (2014).
[Crossref]

Appl. Opt. (2)

Astrophys. J. (1)

B. T. Draine and J. Goodman, “Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[Crossref]

Comput. Phys. Commun. (1)

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1448 (2010).
[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(1), 298–310 (1996).
[Crossref]

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (14)

Y. Roichman, I. Cholis, and D. G. Grier, “Volumetric imaging of holographic optical traps,” Opt. Express 14(22), 10907–10912 (2006).
[Crossref]

S. C. Chapin, V. Germain, and E. R. Dufresne, “Automated trapping, assembly, and sorting with holographic optical tweezers,” Opt. Express 14(26), 13095–13100 (2006).
[Crossref]

S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15(4), 1505–1512 (2007).
[Crossref]

S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15(26), 18275–18282 (2007).
[Crossref]

D. Benito, D. Carberry, S. Simpson, G. Gibson, M. Padgett, J. Rarity, M. Miles, and S. Hanna, “Constructing 3D crystal templates for photonic band gap materials using holographic optical tweezers,” Opt. Express 16(17), 13005–13015 (2008).
[Crossref]

F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17(15), 13071–13079 (2009).
[Crossref]

S.-H. Lee, Y. Roichman, and D. G. Grier, “Optical solenoid beams,” Opt. Express 18(7), 6988–6993 (2010).
[Crossref]

E. R. Shanblatt and D. G. Grier, “Extended and knotted optical traps in three dimensions,” Opt. Express 19(7), 5833–5838 (2011).
[Crossref]

J. A. Rodrigo, T. Alieva, E. Abramochkin, and I. Castro, “Shaping of light beams along curves in three dimensions,” Opt. Express 21(18), 20544–20555 (2013).
[Crossref]

M. Lee, G. Gibson, D. Phillips, M. Padgett, and M. Tassieri, “Dynamic stereo microscopy for studying particle sedimentation,” Opt. Express 22(4), 4671–4677 (2014).
[Crossref]

A. Yevick, M. Hannel, and D. G. Grier, “Machine-learning approach to holographic particle characterization,” Opt. Express 22(22), 26884–26890 (2014).
[Crossref]

M. D. Hannel, A. Abdulali, M. O’Brien, and D. G. Grier, “Machine-learning techniques for fast and accurate feature localization in holograms of colloidal particles,” Opt. Express 26(12), 15221–15231 (2018).
[Crossref]

Y. Roichman and D. G. Grier, “Holographic assembly of quasicrystalline photonic heterostructures,” Opt. Express 13(14), 5434–5439 (2005).
[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]

Opt. Lett. (2)

Philos. Trans. R. Soc., A (1)

A. Yevick, D. J. Evans, and D. G. Grier, “Photokinetic analysis of the forces and torques exerted by optical tweezers carrying angular momentum,” Philos. Trans. R. Soc., A 375(2087), 20150432 (2017).
[Crossref]

Phys. Rev. Lett. (1)

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109(16), 163903 (2012).
[Crossref]

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(5), 1974–1977 (1998).
[Crossref]

Other (2)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, 2001).

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Figures (3)

Fig. 1.
Fig. 1. (a) Schematic representation of the combined instrument for holographic optical trapping and in-line holographic video microscopy. Holographic traps are projected into the sample cell by imprinting a phase hologram onto the wavefronts of an infrared laser beam and relaying the hologram to the input pupil of an objective lens with a dichroic beamsplitter. In-line holograms of trapped particles are recorded with a blue laser beam that passes through the dichroic to a video camera. (b) Typical holograms of a polystyrene sphere (PS) and a silica sphere (SiO$_2$) displaced to specified axial positions, $z_j$, by adjusting the phase hologram. (c) Measured axial positions, $z_p(z_j)$, of a polystyrene sphere (PS) and a silica sphere (SiO$_2$) as a function of specified trap position, $z_j$. Large circles depict the holographically measured radii, $a_p$, of the two spheres and are positioned at the measured plateau heights of their trajectories. The two particles thus agree on the height, $z_{\textrm{wall}}$, of the upper glass wall of their sample cell. Shading between the traces emphasizes the spheres’ increasing axial separation.
Fig. 2.
Fig. 2. (a) Axial displacements of colloidal spheres in holographic optical traps, including polystyrene (PS), 3-(trimethoxysilyl)propyl methacrylate (TPM) and silica (SiO$_2$). Data for polystyrene and TPM are displaced upward for clarity. Each composition is represented by data from multiple spheres (11 for PS, 10 for SiO$_2$ and 4 for TPM) of nominally identical radii measured in different sample cells. (b) Residuals of displacements from linear fits for each of the three classes of spheres. (c) Experimental measurements of particles’ axial scale factors, $m_p(a_p)$, as a function of radius, $a_p$, for spheres made of polystyrene, silica and TPM. Values from (a) are plotted as crosses.
Fig. 3.
Fig. 3. Particle position, $z_0$, within an optical trap as a function of the trap’s axial displacement, $z_j$ for 120 nm-diameter polystyrene (PS, magenta, upper) and silica (SiO$_2$, yellow, lower) spheres dispersed in water and trapped in a diffration-limited optical tweezer at $\lambda _0 = 1064\;\textrm{nm}$. Colored contours reveal how the trap’s intensity profile, $\left \vert {\boldsymbol {E}(\boldsymbol {r})} \right \vert ^{2}$, broadens and elongates with increasing $z_j$. The polystyrene sphere rises in the trap, while the silica sphere sinks.

Equations (17)

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E ( ρ ) = j = 1 N E j exp ( i k f r j ρ ) exp ( i k 2 f 2 z j ρ 2 ) ,
P = 1 2 Ω n m c ϵ 0 j = 1 N | E j | 2 ,
φ ( ρ ) = k 2 f 2 z j ρ 2 mod 2 π ,
E 0 ( r , t ) = E 0 e i q z e i ω t x ^ ,
E s ( r , t ) = E 0 e i q z p f s ( q ( r r p ) ) ,
b ( r ) = I ( r ) | E 0 | 2 = | x ^ + e i q z p f s ( q ( r r p ) ) | 2 .
m p d z p d z j .
| E ( r ) | 2 = | E j | 2 z R 2 z 2 + z R 2 exp ( 2 r 2 w 0 2 z 2 z 2 + z R 2 ) ,
F e ( r ) = 1 2 k α e | E j | 2 [ r z R r ^ + z z 0 k z R 2 z ^ ] ,
z 0 = α e α e z R ( k z R 1 ) ,
z R ( z j ) = z R ( 0 ) ( 1 + z j f ) 2 ,
z p ( z j ) = z j + z 0 ( z j ) .
m p 1 + 2 α e α e z R ( 0 ) f [ 2 k z R ( 0 ) 1 ] .
α e = α e ( 0 ) 1 i 6 π ϵ 0 n m 2 k 3 α e ( 0 ) ,
α e ( 0 ) = 4 π ϵ 0 n m 2 a p 3 n p 2 n m 2 n p 2 + 2 n m 2 .
α e α e 2 3 ( k a p ) 3 n p 2 n m 2 n p 2 + 2 n m 2 .
Δ z 0 ( z j ) = 8 3 π a p 3 ( ρ p ρ m ) g z R 2 ( z j ) α e | E j | 2 ,

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