Abstract

We use holographic video microscopy to track the three-dimensional translational and rotational diffusion of copper oxide nanorods suspended in water. Rayleigh-Sommerfeld back-propagation of a single holographic snapshot yields a volumetric reconstruction of the nanorod’s optical scattering pattern, from which we estimate both its dimensions and also its instantaneous position and orientation. Analyzing a video sequence yields measurements of the freely diffusing nanorod’s dynamics, from which we estimate the technique’s resolution.

© 2010 Optical Society of America

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  1. J. Plewa, E. Tanner, D. M. Mueth, and D. G. Grier, "Processing carbon nanotubes with holographic optical tweezers," Opt. Express 12(9), 1978-1981 (2004).
    [CrossRef] [PubMed]
  2. T. Yu, F.-C. Cheong, and C.-H. Sow, "The manipulation and assembly of CuO nanorods with line optical tweezers," Nanotechnology 15, 1732-1736 (2004).
    [CrossRef]
  3. R. Agarwal, K. Ladavac, Y. Roichman, G. Yu, C. M. Lieber, and D. G. Grier, "Manipulation and assembly of nanowires with holographic optical traps," Opt. Express 13, 8906-8912 (2005).
    [CrossRef] [PubMed]
  4. Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, and P. D. Yang, "Tunable nanowire nonlinear optical probe," Nature 447, 1098-1101 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. 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, 18275-18282 (2007).
    [CrossRef] [PubMed]
  8. F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, "Holographic microrheology of polysaccharides from Streptococcus mutans biofilms," Rheol. Acta 48, 109-115 (2009).
    [CrossRef]
  9. Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, "Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability," Phys. Rev. Lett. 101, 128301 (2008).
    [CrossRef] [PubMed]
  10. F. C. Cheong, B. Sun, R. Dreyfus, Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, "Flow visualization and flow cytometry with holographic video microscopy," Opt. Express 17, 13071-13079 (2009).
    [CrossRef] [PubMed]
  11. F. C. Cheong, K. Xiao, and D. G. Grier, "Characterization of individual milk fat globules with holographic video microscopy," J. Dairy Sci. 92, 95-99 (2009).
    [CrossRef]
  12. Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, "Brownian motion of an ellipsoid," Science 314, 626-630 (2009).
    [CrossRef]
  13. D. Mukhija and M. J. Solomon, "Translational and rotational dynamics of colloidal rods by direct visualization with confocal microscopy," J. Colloid Interface Sci. 314, 98-106 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  21. T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, "Patterning and fusion of CuO nanorods with a focused laser beam," Nanotechnology 16, 1238-1244 (2005).
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    [CrossRef]

2009

F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, "Holographic microrheology of polysaccharides from Streptococcus mutans biofilms," Rheol. Acta 48, 109-115 (2009).
[CrossRef]

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

F. C. Cheong, K. Xiao, and D. G. Grier, "Characterization of individual milk fat globules with holographic video microscopy," J. Dairy Sci. 92, 95-99 (2009).
[CrossRef]

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, "Brownian motion of an ellipsoid," Science 314, 626-630 (2009).
[CrossRef]

B. D. Marshall, V. A. Davis, D. C. Lee, and B. A. Korgel, "Rotational and translational diffusivities of germanium nanowires," Rheol. Acta 48, 589-596 (2009).
[CrossRef]

2008

B. Bhaduri, A. Neild, and T.W. Ng, "Directional Brownian diffusion dynamics with variable magnitudes," Appl. Phys. Lett. 92, 084105 (2008).
[CrossRef]

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, "Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability," Phys. Rev. Lett. 101, 128301 (2008).
[CrossRef] [PubMed]

2007

S.-H. Lee and D. G. Grier, "Holographic microscopy of holographically trapped three-dimensional structures," Opt. Express 15, 1505-1512 (2007).
[CrossRef] [PubMed]

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, 18275-18282 (2007).
[CrossRef] [PubMed]

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, and P. D. Yang, "Tunable nanowire nonlinear optical probe," Nature 447, 1098-1101 (2007).
[CrossRef] [PubMed]

D. Mukhija and M. J. Solomon, "Translational and rotational dynamics of colloidal rods by direct visualization with confocal microscopy," J. Colloid Interface Sci. 314, 98-106 (2007).
[CrossRef] [PubMed]

Y. W. Zhu, T. Yu, F. C. Cheong, X. J. Xui, C. T. Lim, V. B. C. Tan, J. T. L. Thong, and C. H. Sow, "Large-scale synthesis and field emission properties of vertically oriented CuO nanowire films," Nanotechnology 16, 88-92 (2007).
[CrossRef]

2006

2005

R. Agarwal, K. Ladavac, Y. Roichman, G. Yu, C. M. Lieber, and D. G. Grier, "Manipulation and assembly of nanowires with holographic optical traps," Opt. Express 13, 8906-8912 (2005).
[CrossRef] [PubMed]

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, "Patterning and fusion of CuO nanorods with a focused laser beam," Nanotechnology 16, 1238-1244 (2005).
[CrossRef]

T. Savin and P. S. Doyle, "Static and dynamic errors in particle tracking microrheology," Biophys. J. 88, 623-638 (2005).
[CrossRef]

2004

J. Plewa, E. Tanner, D. M. Mueth, and D. G. Grier, "Processing carbon nanotubes with holographic optical tweezers," Opt. Express 12(9), 1978-1981 (2004).
[CrossRef] [PubMed]

T. Yu, F.-C. Cheong, and C.-H. Sow, "The manipulation and assembly of CuO nanorods with line optical tweezers," Nanotechnology 15, 1732-1736 (2004).
[CrossRef]

2002

U. Schnars and W. P. O. Jüptner, "Digital recording and reconstruction of holograms," Meas. Sci. Tech. 13, R85-R101 (2002).
[CrossRef]

1999

G. Borgefors, I. Nyström, and G. Sanniti Di Baja, "Computing skeletons in three dimensions," Pattern Recognition 32, 1225-1236 (1999).
[CrossRef]

1996

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

1967

Agarwal, R.

Alsayed, A. M.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, "Brownian motion of an ellipsoid," Science 314, 626-630 (2009).
[CrossRef]

Amato-Grill, R.

Bhaduri, B.

B. Bhaduri, A. Neild, and T.W. Ng, "Directional Brownian diffusion dynamics with variable magnitudes," Appl. Phys. Lett. 92, 084105 (2008).
[CrossRef]

Borgefors, G.

G. Borgefors, I. Nyström, and G. Sanniti Di Baja, "Computing skeletons in three dimensions," Pattern Recognition 32, 1225-1236 (1999).
[CrossRef]

Cheong, F. C.

F. C. Cheong, K. Xiao, and D. G. Grier, "Characterization of individual milk fat globules with holographic video microscopy," J. Dairy Sci. 92, 95-99 (2009).
[CrossRef]

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

F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, "Holographic microrheology of polysaccharides from Streptococcus mutans biofilms," Rheol. Acta 48, 109-115 (2009).
[CrossRef]

Y. W. Zhu, T. Yu, F. C. Cheong, X. J. Xui, C. T. Lim, V. B. C. Tan, J. T. L. Thong, and C. H. Sow, "Large-scale synthesis and field emission properties of vertically oriented CuO nanowire films," Nanotechnology 16, 88-92 (2007).
[CrossRef]

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, "Patterning and fusion of CuO nanorods with a focused laser beam," Nanotechnology 16, 1238-1244 (2005).
[CrossRef]

Cheong, F.-C.

T. Yu, F.-C. Cheong, and C.-H. Sow, "The manipulation and assembly of CuO nanorods with line optical tweezers," Nanotechnology 15, 1732-1736 (2004).
[CrossRef]

Chin, K. C.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, "Patterning and fusion of CuO nanorods with a focused laser beam," Nanotechnology 16, 1238-1244 (2005).
[CrossRef]

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]

Davis, V. A.

B. D. Marshall, V. A. Davis, D. C. Lee, and B. A. Korgel, "Rotational and translational diffusivities of germanium nanowires," Rheol. Acta 48, 589-596 (2009).
[CrossRef]

Doyle, P. S.

T. Savin and P. S. Doyle, "Static and dynamic errors in particle tracking microrheology," Biophys. J. 88, 623-638 (2005).
[CrossRef]

Dreyfus, R.

Duarte, S.

F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, "Holographic microrheology of polysaccharides from Streptococcus mutans biofilms," Rheol. Acta 48, 109-115 (2009).
[CrossRef]

Gantimahapatruni, A.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, "Patterning and fusion of CuO nanorods with a focused laser beam," Nanotechnology 16, 1238-1244 (2005).
[CrossRef]

Grier, D. G.

F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, "Holographic microrheology of polysaccharides from Streptococcus mutans biofilms," Rheol. Acta 48, 109-115 (2009).
[CrossRef]

F. C. Cheong, K. Xiao, and D. G. Grier, "Characterization of individual milk fat globules with holographic video microscopy," J. Dairy Sci. 92, 95-99 (2009).
[CrossRef]

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, "Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability," Phys. Rev. Lett. 101, 128301 (2008).
[CrossRef] [PubMed]

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, 18275-18282 (2007).
[CrossRef] [PubMed]

S.-H. Lee and D. G. Grier, "Holographic microscopy of holographically trapped three-dimensional structures," Opt. Express 15, 1505-1512 (2007).
[CrossRef] [PubMed]

R. Agarwal, K. Ladavac, Y. Roichman, G. Yu, C. M. Lieber, and D. G. Grier, "Manipulation and assembly of nanowires with holographic optical traps," Opt. Express 13, 8906-8912 (2005).
[CrossRef] [PubMed]

J. Plewa, E. Tanner, D. M. Mueth, and D. G. Grier, "Processing carbon nanotubes with holographic optical tweezers," Opt. Express 12(9), 1978-1981 (2004).
[CrossRef] [PubMed]

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

Han, Y.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, "Brownian motion of an ellipsoid," Science 314, 626-630 (2009).
[CrossRef]

Jüptner, W. P. O.

U. Schnars and W. P. O. Jüptner, "Digital recording and reconstruction of holograms," Meas. Sci. Tech. 13, R85-R101 (2002).
[CrossRef]

Katz, J.

Kim, S.-H.

Korgel, B. A.

B. D. Marshall, V. A. Davis, D. C. Lee, and B. A. Korgel, "Rotational and translational diffusivities of germanium nanowires," Rheol. Acta 48, 589-596 (2009).
[CrossRef]

Ladavac, K.

Lee, D. C.

B. D. Marshall, V. A. Davis, D. C. Lee, and B. A. Korgel, "Rotational and translational diffusivities of germanium nanowires," Rheol. Acta 48, 589-596 (2009).
[CrossRef]

Lee, S.-H.

Lieber, C. M.

Lim, C. T.

Y. W. Zhu, T. Yu, F. C. Cheong, X. J. Xui, C. T. Lim, V. B. C. Tan, J. T. L. Thong, and C. H. Sow, "Large-scale synthesis and field emission properties of vertically oriented CuO nanowire films," Nanotechnology 16, 88-92 (2007).
[CrossRef]

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, "Patterning and fusion of CuO nanorods with a focused laser beam," Nanotechnology 16, 1238-1244 (2005).
[CrossRef]

Lubensky, T. C.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, "Brownian motion of an ellipsoid," Science 314, 626-630 (2009).
[CrossRef]

Malkiel, E.

Marshall, B. D.

B. D. Marshall, V. A. Davis, D. C. Lee, and B. A. Korgel, "Rotational and translational diffusivities of germanium nanowires," Rheol. Acta 48, 589-596 (2009).
[CrossRef]

Mueth, D. M.

Mukhija, D.

D. Mukhija and M. J. Solomon, "Translational and rotational dynamics of colloidal rods by direct visualization with confocal microscopy," J. Colloid Interface Sci. 314, 98-106 (2007).
[CrossRef] [PubMed]

Nakayama, Y.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, and P. D. Yang, "Tunable nanowire nonlinear optical probe," Nature 447, 1098-1101 (2007).
[CrossRef] [PubMed]

Neild, A.

B. Bhaduri, A. Neild, and T.W. Ng, "Directional Brownian diffusion dynamics with variable magnitudes," Appl. Phys. Lett. 92, 084105 (2008).
[CrossRef]

Ng, T.W.

B. Bhaduri, A. Neild, and T.W. Ng, "Directional Brownian diffusion dynamics with variable magnitudes," Appl. Phys. Lett. 92, 084105 (2008).
[CrossRef]

Nobili, M.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, "Brownian motion of an ellipsoid," Science 314, 626-630 (2009).
[CrossRef]

Nyström, I.

G. Borgefors, I. Nyström, and G. Sanniti Di Baja, "Computing skeletons in three dimensions," Pattern Recognition 32, 1225-1236 (1999).
[CrossRef]

Onorato, R. M.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, and P. D. Yang, "Tunable nanowire nonlinear optical probe," Nature 447, 1098-1101 (2007).
[CrossRef] [PubMed]

Pauzauskie, P. J.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, and P. D. Yang, "Tunable nanowire nonlinear optical probe," Nature 447, 1098-1101 (2007).
[CrossRef] [PubMed]

Plewa, J.

Radenovic, A.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, and P. D. Yang, "Tunable nanowire nonlinear optical probe," Nature 447, 1098-1101 (2007).
[CrossRef] [PubMed]

Roichman, Y.

Sanniti Di Baja, G.

G. Borgefors, I. Nyström, and G. Sanniti Di Baja, "Computing skeletons in three dimensions," Pattern Recognition 32, 1225-1236 (1999).
[CrossRef]

Savin, T.

T. Savin and P. S. Doyle, "Static and dynamic errors in particle tracking microrheology," Biophys. J. 88, 623-638 (2005).
[CrossRef]

Saykally, R. J.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, and P. D. Yang, "Tunable nanowire nonlinear optical probe," Nature 447, 1098-1101 (2007).
[CrossRef] [PubMed]

Schnars, U.

U. Schnars and W. P. O. Jüptner, "Digital recording and reconstruction of holograms," Meas. Sci. Tech. 13, R85-R101 (2002).
[CrossRef]

Shen, Z. X.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, "Patterning and fusion of CuO nanorods with a focused laser beam," Nanotechnology 16, 1238-1244 (2005).
[CrossRef]

Sheng, J.

Sherman, G. C.

Solomon, M. J.

D. Mukhija and M. J. Solomon, "Translational and rotational dynamics of colloidal rods by direct visualization with confocal microscopy," J. Colloid Interface Sci. 314, 98-106 (2007).
[CrossRef] [PubMed]

Sow, C. H.

Y. W. Zhu, T. Yu, F. C. Cheong, X. J. Xui, C. T. Lim, V. B. C. Tan, J. T. L. Thong, and C. H. Sow, "Large-scale synthesis and field emission properties of vertically oriented CuO nanowire films," Nanotechnology 16, 88-92 (2007).
[CrossRef]

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, "Patterning and fusion of CuO nanorods with a focused laser beam," Nanotechnology 16, 1238-1244 (2005).
[CrossRef]

Sow, C.-H.

T. Yu, F.-C. Cheong, and C.-H. Sow, "The manipulation and assembly of CuO nanorods with line optical tweezers," Nanotechnology 15, 1732-1736 (2004).
[CrossRef]

Stolarski, A.

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, "Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability," Phys. Rev. Lett. 101, 128301 (2008).
[CrossRef] [PubMed]

Sun, B.

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

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, "Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability," Phys. Rev. Lett. 101, 128301 (2008).
[CrossRef] [PubMed]

Tan, V. B. C.

Y. W. Zhu, T. Yu, F. C. Cheong, X. J. Xui, C. T. Lim, V. B. C. Tan, J. T. L. Thong, and C. H. Sow, "Large-scale synthesis and field emission properties of vertically oriented CuO nanowire films," Nanotechnology 16, 88-92 (2007).
[CrossRef]

Tanner, E.

Thong, J. T. L.

Y. W. Zhu, T. Yu, F. C. Cheong, X. J. Xui, C. T. Lim, V. B. C. Tan, J. T. L. Thong, and C. H. Sow, "Large-scale synthesis and field emission properties of vertically oriented CuO nanowire films," Nanotechnology 16, 88-92 (2007).
[CrossRef]

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Y. W. Zhu, T. Yu, F. C. Cheong, X. J. Xui, C. T. Lim, V. B. C. Tan, J. T. L. Thong, and C. H. Sow, "Large-scale synthesis and field emission properties of vertically oriented CuO nanowire films," Nanotechnology 16, 88-92 (2007).
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Y. W. Zhu, T. Yu, F. C. Cheong, X. J. Xui, C. T. Lim, V. B. C. Tan, J. T. L. Thong, and C. H. Sow, "Large-scale synthesis and field emission properties of vertically oriented CuO nanowire films," Nanotechnology 16, 88-92 (2007).
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Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, "Brownian motion of an ellipsoid," Science 314, 626-630 (2009).
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Y. W. Zhu, T. Yu, F. C. Cheong, X. J. Xui, C. T. Lim, V. B. C. Tan, J. T. L. Thong, and C. H. Sow, "Large-scale synthesis and field emission properties of vertically oriented CuO nanowire films," Nanotechnology 16, 88-92 (2007).
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T. Yu, F.-C. Cheong, and C.-H. Sow, "The manipulation and assembly of CuO nanorods with line optical tweezers," Nanotechnology 15, 1732-1736 (2004).
[CrossRef]

Nature

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, and P. D. Yang, "Tunable nanowire nonlinear optical probe," Nature 447, 1098-1101 (2007).
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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic representation of holographic video microscopy. The sample scatters light from a collimated laser beam. Both the scattered and unscattered laser light are collected by an oil-immersion objective lens and relayed to a video camera, which records the intensity of their interference pattern. (b) Unprocessed holographic micrograph I(r) of an inclined CuO nanorod in water. (c) Normalized image b(r) of the nanorod.

Fig. 2.
Fig. 2.

(a) Numerically refocused version of Fig. 1(c). in the plane of best focus. (c) Intensity profile along the nanorod’s axis indicating a length of 4.9 μm. (d) Intensity profile transverse to the nanorod’s axis indicating a diameter slightly less than 200 nm.

Fig. 3.
Fig. 3.

Volumetric reconstruction of a diffusing nanorod (a) inclined at roughly 45° to the focal plane and (b) oriented nearly perpendicularly to the focal plane.

Fig. 4.
Fig. 4.

(a) Evolution of the nanorod’s mean-square orientational fluctuations together with a fit to Eq. (9). Shaded region indicates statistical uncertainty in Δs 2 (t). Inset: Location of ŝ(t) at 1/3 s intervals, colored by time. (b) Evolution of the mean-square displacement along and transverse to the nanorod’s axis. Shaded region indicates the statistical uncertainty in ΔR 2 (t). The similar error range for ΔR 2 (t) is omitted for clarity. Inset: Displacement of the nanorod’s center of mass R(t) during the first 20 s of the 5 min trajectory, plotted as a three-dimensional ribbon extended along the nanorod’s orientation ŝ(t). Scale bar indicates 2 μm.

Equations (13)

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E 0 ( r , z ) = u 0 ( r ) e ikz ε ̂ 0
E s ( r , z ) = E s ( r , z ) ε ̂ ( r , z )
I ( r ) = u 0 2 ( r ) + 2 { u 0 ( r ) E s ( r , 0 ) ε ̂ 0 · ε ̂ ( r , 0 ) } + E s ( r , 0 ) 2 .
b ( r ) = 1 + 2 { E s ( r , 0 ) u 0 ( r ) ε ̂ 0 · ε ̂ ( r , 0 ) } + E s ( r , 0 ) 2 u 0 2 ( r ) .
b ( r ) 1 + 2 { E ˜ s ( r , 0 ) } .
E ˜ s ( r , z ) e ikz 4 π 2 B ( q ) H ( q , z ) e i q · r d 2 q ,
H ( q , z ) = e iz ( k 2 q 2 ) 1 2
σ 2 σ 0 2 λ 2 2 n m 2
Δ s 2 ( t ) s ̂ ( t ) s ̂ ( 0 ) 2 = 2 [ 1 ( 1 ε s 2 ) exp ( 2 D r ( t τ 3 ) ) ] ,
D r = 3 k B T πη L 3 [ ln ( L σ ) γ ]
Δ R 2 ( t ) [ R ( t ) R ( 0 ) ] · s ̂ ( 0 ) 2 = 2 D ( t τ 3 ) + 2 ε 2 and
Δ R 2 ( t ) [ R ( t ) R ( 0 ) ] × s ̂ ( 0 ) 2 = 4 D ( t τ 3 ) + 4 ε 2 ,
D = k B T 2 πηL [ ln ( L σ ) γ ] and D = k B T 4 πηL [ ln ( L σ ) + γ ] .

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