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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 6618–6624
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The properties of gold nanospheres studied with dark field optical trapping

Lin Ling, Lu Huang, Jinxin Fu, Honglian Guo, Jiafang Li, H. Daniel Ou-Yang, and Zhi-Yuan Li  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 6618-6624 (2013)
http://dx.doi.org/10.1364/OE.21.006618


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Abstract

We demonstrate trapping and characterization of multiple gold nanospheres with a setup composed of dark field imaging and optical tweezers. The number of trapped nanospheres is quantified by the overall dark-field scattering intensity. The spectra of the scattering intensity show that there is no interparticle coupling among trapped nanospheres when the density of nanospheres in the trap is low enough (less than 10 particles), while the density of nanosphere increases the interparticle coupling of nanospheres becomes obvious. In addition, the trapping potential of a single gold nanosphere is obtained by trapping an ensemble of gold nanospheres.

© 2013 OSA

1. Introduction

Since Ashkin observed the acceleration and trapping of particles by optical trap in 1970 [1

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

], optical tweezers have been developed from two-dimension to three-dimension [2

2. A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19(8), 283–285 (1971). [CrossRef]

]. The number of optical traps is also extended from single trap to dual-optical traps [3

3. E. Fällman and O. Axner, “Design for fully steerable dual-trap optical tweezers,” Appl. Opt. 36(10), 2107–2113 (1997). [CrossRef] [PubMed]

], even multi-optical traps [4

4. J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185(1-3), 77–82 (2000). [CrossRef]

6

6. L. Ling, H. L. Guo, L. Huang, E. Qu, Z. L. Li, and Z. Y. Li, “The measurement of displacement and optical force in multi-optical tweezers,” Chin. Phys. Lett. 29(1), 014214 (2012). [CrossRef]

]. At the beginning, the optical trap is formed by TEM00 mode Gaussian laser beam, then various kinds of modes such as hollow beam [7

7. J. P. Yin, Y. F. Zhu, W. B. Wang, Y. Z. Wang, and W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15(1), 25–33 (1998). [CrossRef]

], Laguerre-Gaussian beam [8

8. A. T. O’Neil and M. J. Padgett, “Axial and lateral trapping efficiency of Laguerre–Gaussian modes in inverted optical tweezers,” Opt. Commun. 193(1-6), 45–50 (2001). [CrossRef]

] and vector beam are adopted [9

9. Q. W. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004). [CrossRef] [PubMed]

,10

10. L. Huang, H. L. Guo, J. F. Li, L. Ling, B. H. Feng, and Z. Y. Li, “Optical trapping of gold nanoparticles by cylindrical vector beam,” Opt. Lett. 37(10), 1694–1696 (2012). [CrossRef] [PubMed]

]. These special modes give the optical trap some new characters, like orbital angular momentum, larger trap stiffness and trap depth. A variety of objects can be trapped such as organelles in cells [11

11. T. Ketelaar, H. S. van der Honing, and A. M. Emons, “Probing cytoplasmic organization and the actin cytoskeleton of plant cells with optical tweezers,” Biochem. Soc. Trans. 38(3), 823–828 (2010). [CrossRef] [PubMed]

], gold nanoparticles [12

12. K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19(13), 930–932 (1994). [CrossRef] [PubMed]

] and carbon nanotubes [13

13. T. Rodgers, S. Shoji, Z. Sekkat, and S. Kawata, “Selective aggregation of single-walled carbon nanotubes using the large optical field gradient of a focused laser beam,” Phys. Rev. Lett. 101(12), 127402 (2008). [CrossRef] [PubMed]

]. Gold nanoparticles, which support local surface plasmon resonance (SPR) [14

14. M. Hu, J. Y. Chen, Z. Y. Li, L. Au, G. V. Hartland, X. D. Li, M. Marquez, and Y. N. Xia, “Gold nanostructures: engineering their plasmonic properties for biomedical applications,” Chem. Soc. Rev. 35(11), 1084–1094 (2006). [CrossRef] [PubMed]

] modes, are considered to have great applications in nanophotonics, medicine and many other areas [15

15. J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic filminduced by aligned gold nanorods,” Appl. Phys. Lett. 96(26), 263103 (2010). [CrossRef]

, 16

16. F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative analysis of dipole and quadrupole excitation in the surface plasmon resonance of metal nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008). [CrossRef]

]. Gold spheres with diameters ranging from 18 to 254nm have been trapped steadily in three-dimensions in experiment [17

17. P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005). [CrossRef] [PubMed]

], and the spectroscopy of a single trapped gold particle has been measured [18

18. J. Prikulis, F. Svedberg, M. Käll, J. Enger, K. Ramser, M. Goksör, and D. Hanstorp, “Optical spectroscopy of single trapped metal nanoparticles in solution,” Nano Lett. 4(1), 115–118 (2004). [CrossRef]

]. Optical trapping of gold nanorods and nanowires were also reported [19

19. L. Tong, V. D. Miljković, and M. Käll, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano Lett. 10(1), 268–273 (2010). [CrossRef] [PubMed]

]. Two-photon absorption of gold was observed as the optical trap is formed by pulsed laser [20

20. B. Agate, C. Brown, W. Sibbett, and K. Dholakia, “Femtosecond optical tweezers for in-situ control of two-photon fluorescence,” Opt. Express 12(13), 3011–3017 (2004). [CrossRef] [PubMed]

], and the optical trap formed by pulsed laser can split due to the strong absorption of the trapped gold spheres [21

21. Y. Jiang, T. Narushima, and H. Okamoto, “Nonlinear optical effects in trapping nanoparticles with femtosecond pulses,” Nat. Phys. 6(12), 1005–1009 (2010). [CrossRef]

]. As a tool of micro manipulation, optical tweezers can array gold particles on certain substrate [22

22. M. J. Guffey and N. F. Scherer, “All-optical patterning of au nanoparticles on surfaces using optical traps,” Nano Lett. 10(11), 4302–4308 (2010). [CrossRef] [PubMed]

].

One important issue in optical tweezers is the quantification of trapping parameters for different objects. The trap stiffness, escape distance, maximum lateral optical force of a single particle can be determined by forced oscillation, escape velocity, and Brownian motion [23

23. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004). [CrossRef] [PubMed]

28

28. K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594 (2004). [CrossRef]

]. The potential of a particle in optical trap could be calibrated by thermal noise analysis [29

29. E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys A. 66(7), S75–S78 (1998). [CrossRef]

]. The trapping potential of multiple trapped dielectric spheres could be measured by the force balance between repulsive osmotic and confining gradient-force pressures [30

30. J. Junio, J. Ng, J. A. Cohen, Z. F. Lin, and H. D. Ou-Yang, “Ensemble method to measure the potential energy of nanoparticles in an optical trap,” Opt. Lett. 36(8), 1497–1499 (2011). [CrossRef] [PubMed]

].

In this paper, we studied the optical trapping and light scattering properties of multiple trapped gold spheres with a setup composed of DF imaging and optical tweezers system. We measured the trapping potential for a single gold nanosphere by trapping an ensemble of gold nanospheres with a focused laser beam. In section 2, we illustrated the setup in our experiment. In section 3, we used both DF imaging and scattering spectra to count the trapped gold spheres and measured the trapping potential. In section 4 we gave a summary.

2. Experimental setup

The optical tweezers setup in our experiments is based on a microscopy (Leica DMIRB), as is schematically shown in Fig. 1
Fig. 1 Schematic diagram of the experimental setup. The wide red line represents 1064nm laser, and the thin green line represents the visible light emitted from the tungsten Lamp. A beam of 1064nm laser was expanded by lens L1 and L2, and then focused by the objective to form the optical trap. DF imaging system was mainly formed by condenser and objective. The DF image of the trapped spheres can be observed by eyepiece and CCD camera.
. The wide red line represents 1064nm laser, and the thin green line represents visible light emitted from tungsten lamp. The laser beam was expanded by lens L1 and L2, and then focused by an objective (N.A 0.7-1.4 OIL) and formed the optical trap. There is a rotating module right behind the condenser (N.A. 1.4 OIL), which can change the status from bright field (BF) to DF. We usually set the objective’s N.A to be 0.9 in order to balance the DF imaging and optical trapping performance. When the microscopy works at the DF imaging mode, the trapped gold spheres can be observed by eyepiece and CCD camera (Cool snapfx). The scattering spectra of the trapped gold spheres can be measured by the spectrometer (Ocean Optics, QE 65000). As the CCD camera and spectrometer were placed at the same place, they could not work simultaneously.

3. Optical trapping of multiple gold spheres

The gold spheres used in this experiment are bought from STREM (79-6045), and the diameter of the spheres is 50nm and the standard deviation is 2nm. In this experiment, the laser power was 204mW at the input threshold of the objective, and the transmission of the objective is about 60%. Similar to micron dielectric spheres, optical trap can trap a single or multiple gold spheres steadily. Usually, the more the trapped spheres the larger the intensity of the scattering light from the trapped spheres. There should be some relationship between the scattering intensity and the number of the trapped gold spheres. We diluted the bought gold sphere solution, so that the spheres entered the trap one by one most of the time. We recorded the intensity change of the images captured by the CCD camera. Figure 2(a)
Fig. 2 (a)A typical pseudo color image of the trapped gold spheres captured by the CCD.(b)Measured scattering intensity change with the time. Numbers indicated in the figure represent the gold sphere quantity in the trap.
is one of the images captured by the CCD. We summed the gray scales of all the pixels included in the red rectangle and obtained its change with the time. The result is shown in Fig. 2(b). The numbers marked in the figure represent the particle quantity in the trap. It can be seen that the intensity change is stepwise and the step sizes are integer multiples of certain value, which implies that only one gold sphere enters or escapes from the trap in most cases. As the size of the gold spheres (50 ± 2nm) is not exactly the same, the scattering intensity of each trapped sphere is a little different from each other. That’s why the size of the steps in Fig. 2(b) is a little different from each other. In addition, the depth sometimes is nearly double of the others. We think there should be two gold spheres entering the trap at the same time. This technique of scattering intensity measurement provides a good method to monitor the number of gold spheres trapped in the trap in the real time.

We substituted the CCD with a spectrometer and measured the scattering spectra of the trapped gold spheres. Figure 3(a)
Fig. 3 (a)Several spectra of the trapped gold spheres captured at ten different time points. Inset is the normalized spectra of scattering intensity. (b) Peak intensities of the spectra in (a) versus the estimated number of the trapped gold spheres. The black dots are the experimental data, and the red curve is the linear fitting one.
shows the spectra measured at ten different time points. We found that the peak positions of all the spectra are the same as that for only one gold sphere in the trap, but the amplitudes of the spectra increase with the number of gold spheres in the trap. This means that there is no interparticle coupling among trapped gold spheres [31

31. K. H. Su, Q. H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]

]. Because the peak intensities of these spectra have nearly stepwise change, so it’s reasonable to guess that the peak intensity of the spectra is proportional to the number of the trapped gold spheres. Figure 3(b) is the scattering peak intensities obtained from Fig. 3(a) versus the estimated number of gold spheres. The black dots are the experimental data, and the red curve is the fitting result. It can be seen that the scattering amplitude of gold sphere is linearly proportional to the number of gold spheres in the trap. In order to compare these spectra in detail, we normalized them as seen in inset of Fig. 3(a). We can see that there is no interparticle coupling when the spheres in the trap are not dense enough.

The above experiments were done with diluted concentration of gold spheres. We also measured the scattering intensity of the undiluted solution (with a concentration of2.36×102/μm3). To comparison, we normalized the spectra of single and multiple trapped gold spheres and displayed in one figure as shown in Fig. 4
Fig. 4 The normalized scattering spectra of the trapped single and multiple gold nanoparticles.
. From Fig. 4, we can see that the peak frequency is a little red shift and broadened. This is because while the concentration of solution becomes high, lots of gold spheres run into the optical trap simultaneously, there exists interparticle coupling when distance among the particles is short. It has been well proven that the interparticle coupling can bring about red-shifting and broadening of the spectrum [32

32. C. A. Mirkin, R. L. Letsinger, R. C. Mucic, and J. J. Storhoff, “A DNA-based method for rationally assembling nanoparticles into macroscopic materials,” Nature 382(6592), 607–609 (1996). [CrossRef] [PubMed]

]

4. Summary

In summary, we have discussed the trapping of gold spheres by optical tweezers experimentally. As gold particle has large scattering and absorption cross section, only gold spheres with smaller size can be trapped. We developed two methods based on the setup of DF imaging and optical trap system to analyze the number of the trapped gold spheres in the situation when the concentration of the trapped spheres is low. One is counting the scattering intensity of the DF image of the trapped spheres, and the other is measuring the peak value of the scattering spectra of the trapped spheres. When there are lots of spheres in the optical trap, the scattering spectra broadens because of the interparticle coupling among the spheres. The potential energy of single trapped nanosphere is obtained by trapping an ensemble of nanaspheres. From the potential energy we obtained (0.023 kBT at 1mW laser power), it looks that trapping efficiency is a little low, this is due to the fact that the N.A. is low in order to get good dark field image. The successful optical trapping of single and multiple gold spheres by optical tweezers is expected to open up a new way to study the plasmonic properties of metal nanoparticle ensembles in situ and in real time.

Acknowledgment

This work was supported by the National Basic Research Foundation of China under Grant No.2011CB922002 and the National Natural Science Foundation of China under Grant No.11104342.

References and links

1.

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

2.

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19(8), 283–285 (1971). [CrossRef]

3.

E. Fällman and O. Axner, “Design for fully steerable dual-trap optical tweezers,” Appl. Opt. 36(10), 2107–2113 (1997). [CrossRef] [PubMed]

4.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185(1-3), 77–82 (2000). [CrossRef]

5.

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

6.

L. Ling, H. L. Guo, L. Huang, E. Qu, Z. L. Li, and Z. Y. Li, “The measurement of displacement and optical force in multi-optical tweezers,” Chin. Phys. Lett. 29(1), 014214 (2012). [CrossRef]

7.

J. P. Yin, Y. F. Zhu, W. B. Wang, Y. Z. Wang, and W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B 15(1), 25–33 (1998). [CrossRef]

8.

A. T. O’Neil and M. J. Padgett, “Axial and lateral trapping efficiency of Laguerre–Gaussian modes in inverted optical tweezers,” Opt. Commun. 193(1-6), 45–50 (2001). [CrossRef]

9.

Q. W. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004). [CrossRef] [PubMed]

10.

L. Huang, H. L. Guo, J. F. Li, L. Ling, B. H. Feng, and Z. Y. Li, “Optical trapping of gold nanoparticles by cylindrical vector beam,” Opt. Lett. 37(10), 1694–1696 (2012). [CrossRef] [PubMed]

11.

T. Ketelaar, H. S. van der Honing, and A. M. Emons, “Probing cytoplasmic organization and the actin cytoskeleton of plant cells with optical tweezers,” Biochem. Soc. Trans. 38(3), 823–828 (2010). [CrossRef] [PubMed]

12.

K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19(13), 930–932 (1994). [CrossRef] [PubMed]

13.

T. Rodgers, S. Shoji, Z. Sekkat, and S. Kawata, “Selective aggregation of single-walled carbon nanotubes using the large optical field gradient of a focused laser beam,” Phys. Rev. Lett. 101(12), 127402 (2008). [CrossRef] [PubMed]

14.

M. Hu, J. Y. Chen, Z. Y. Li, L. Au, G. V. Hartland, X. D. Li, M. Marquez, and Y. N. Xia, “Gold nanostructures: engineering their plasmonic properties for biomedical applications,” Chem. Soc. Rev. 35(11), 1084–1094 (2006). [CrossRef] [PubMed]

15.

J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic filminduced by aligned gold nanorods,” Appl. Phys. Lett. 96(26), 263103 (2010). [CrossRef]

16.

F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative analysis of dipole and quadrupole excitation in the surface plasmon resonance of metal nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008). [CrossRef]

17.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005). [CrossRef] [PubMed]

18.

J. Prikulis, F. Svedberg, M. Käll, J. Enger, K. Ramser, M. Goksör, and D. Hanstorp, “Optical spectroscopy of single trapped metal nanoparticles in solution,” Nano Lett. 4(1), 115–118 (2004). [CrossRef]

19.

L. Tong, V. D. Miljković, and M. Käll, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano Lett. 10(1), 268–273 (2010). [CrossRef] [PubMed]

20.

B. Agate, C. Brown, W. Sibbett, and K. Dholakia, “Femtosecond optical tweezers for in-situ control of two-photon fluorescence,” Opt. Express 12(13), 3011–3017 (2004). [CrossRef] [PubMed]

21.

Y. Jiang, T. Narushima, and H. Okamoto, “Nonlinear optical effects in trapping nanoparticles with femtosecond pulses,” Nat. Phys. 6(12), 1005–1009 (2010). [CrossRef]

22.

M. J. Guffey and N. F. Scherer, “All-optical patterning of au nanoparticles on surfaces using optical traps,” Nano Lett. 10(11), 4302–4308 (2010). [CrossRef] [PubMed]

23.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004). [CrossRef] [PubMed]

24.

P. Wu, R. Huang, C. Tischer, A. Jonas, and E. L. Florin, “Direct measurement of the nonconservative force field generated by optical tweezers,” Phys. Rev. Lett. 103(10), 108101 (2009). [CrossRef] [PubMed]

25.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70(4), 1813–1822 (1996). [CrossRef] [PubMed]

26.

L. A. Hough and H. D. Ou-Yang, “A new probe for mechanical testing of nanostructures in soft materials,” J. Nanopart. Res. 1(4), 495–499 (1999). [CrossRef]

27.

M. J. Lang, P. M. Fordyce, and S. M. Block, “Combined optical trapping and single-molecule fluorescence,” J. Biol. 2(1), 6 (2003). [CrossRef] [PubMed]

28.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594 (2004). [CrossRef]

29.

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys A. 66(7), S75–S78 (1998). [CrossRef]

30.

J. Junio, J. Ng, J. A. Cohen, Z. F. Lin, and H. D. Ou-Yang, “Ensemble method to measure the potential energy of nanoparticles in an optical trap,” Opt. Lett. 36(8), 1497–1499 (2011). [CrossRef] [PubMed]

31.

K. H. Su, Q. H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]

32.

C. A. Mirkin, R. L. Letsinger, R. C. Mucic, and J. J. Storhoff, “A DNA-based method for rationally assembling nanoparticles into macroscopic materials,” Nature 382(6592), 607–609 (1996). [CrossRef] [PubMed]

33.

L. Ling, F. Zhou, L. Huang, and Z. Y. Li, “Optical forces on arbitrary shaped particles in optical tweezers,” J. Appl. Phys. 108(7), 073110 (2010). [CrossRef]

OCIS Codes
(020.7010) Atomic and molecular physics : Laser trapping
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: January 7, 2013
Revised Manuscript: February 26, 2013
Manuscript Accepted: March 3, 2013
Published: March 8, 2013

Virtual Issues
Vol. 8, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Lin Ling, Lu Huang, Jinxin Fu, Honglian Guo, Jiafang Li, H. Daniel Ou-Yang, and Zhi-Yuan Li, "The properties of gold nanospheres studied with dark field optical trapping," Opt. Express 21, 6618-6624 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-6618


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References

  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970). [CrossRef]
  2. A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett.19(8), 283–285 (1971). [CrossRef]
  3. E. Fällman and O. Axner, “Design for fully steerable dual-trap optical tweezers,” Appl. Opt.36(10), 2107–2113 (1997). [CrossRef] [PubMed]
  4. J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun.185(1-3), 77–82 (2000). [CrossRef]
  5. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002). [CrossRef]
  6. L. Ling, H. L. Guo, L. Huang, E. Qu, Z. L. Li, and Z. Y. Li, “The measurement of displacement and optical force in multi-optical tweezers,” Chin. Phys. Lett.29(1), 014214 (2012). [CrossRef]
  7. J. P. Yin, Y. F. Zhu, W. B. Wang, Y. Z. Wang, and W. Jhe, “Optical potential for atom guidance in a dark hollow laser beam,” J. Opt. Soc. Am. B15(1), 25–33 (1998). [CrossRef]
  8. A. T. O’Neil and M. J. Padgett, “Axial and lateral trapping efficiency of Laguerre–Gaussian modes in inverted optical tweezers,” Opt. Commun.193(1-6), 45–50 (2001). [CrossRef]
  9. Q. W. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express12(15), 3377–3382 (2004). [CrossRef] [PubMed]
  10. L. Huang, H. L. Guo, J. F. Li, L. Ling, B. H. Feng, and Z. Y. Li, “Optical trapping of gold nanoparticles by cylindrical vector beam,” Opt. Lett.37(10), 1694–1696 (2012). [CrossRef] [PubMed]
  11. T. Ketelaar, H. S. van der Honing, and A. M. Emons, “Probing cytoplasmic organization and the actin cytoskeleton of plant cells with optical tweezers,” Biochem. Soc. Trans.38(3), 823–828 (2010). [CrossRef] [PubMed]
  12. K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett.19(13), 930–932 (1994). [CrossRef] [PubMed]
  13. T. Rodgers, S. Shoji, Z. Sekkat, and S. Kawata, “Selective aggregation of single-walled carbon nanotubes using the large optical field gradient of a focused laser beam,” Phys. Rev. Lett.101(12), 127402 (2008). [CrossRef] [PubMed]
  14. M. Hu, J. Y. Chen, Z. Y. Li, L. Au, G. V. Hartland, X. D. Li, M. Marquez, and Y. N. Xia, “Gold nanostructures: engineering their plasmonic properties for biomedical applications,” Chem. Soc. Rev.35(11), 1084–1094 (2006). [CrossRef] [PubMed]
  15. J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic filminduced by aligned gold nanorods,” Appl. Phys. Lett.96(26), 263103 (2010). [CrossRef]
  16. F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative analysis of dipole and quadrupole excitation in the surface plasmon resonance of metal nanoparticles,” J. Phys. Chem. C112(51), 20233–20240 (2008). [CrossRef]
  17. P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett.5(10), 1937–1942 (2005). [CrossRef] [PubMed]
  18. J. Prikulis, F. Svedberg, M. Käll, J. Enger, K. Ramser, M. Goksör, and D. Hanstorp, “Optical spectroscopy of single trapped metal nanoparticles in solution,” Nano Lett.4(1), 115–118 (2004). [CrossRef]
  19. L. Tong, V. D. Miljković, and M. Käll, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano Lett.10(1), 268–273 (2010). [CrossRef] [PubMed]
  20. B. Agate, C. Brown, W. Sibbett, and K. Dholakia, “Femtosecond optical tweezers for in-situ control of two-photon fluorescence,” Opt. Express12(13), 3011–3017 (2004). [CrossRef] [PubMed]
  21. Y. Jiang, T. Narushima, and H. Okamoto, “Nonlinear optical effects in trapping nanoparticles with femtosecond pulses,” Nat. Phys.6(12), 1005–1009 (2010). [CrossRef]
  22. M. J. Guffey and N. F. Scherer, “All-optical patterning of au nanoparticles on surfaces using optical traps,” Nano Lett.10(11), 4302–4308 (2010). [CrossRef] [PubMed]
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  24. P. Wu, R. Huang, C. Tischer, A. Jonas, and E. L. Florin, “Direct measurement of the nonconservative force field generated by optical tweezers,” Phys. Rev. Lett.103(10), 108101 (2009). [CrossRef] [PubMed]
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