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Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 10 — May. 16, 2005
  • pp: 3673–3680
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Numerical modeling of optical levitation and trapping of the “stuck” particles with a pulsed optical tweezers

Jian-liao Deng, Qing Wei, Yu-zhu Wang, and Yong-qing Li  »View Author Affiliations


Optics Express, Vol. 13, Issue 10, pp. 3673-3680 (2005)
http://dx.doi.org/10.1364/OPEX.13.003673


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Abstract

We present the theoretical analysis and the numerical modeling of optical levitation and trapping of the stuck particles with a pulsed optical tweezers. In our model, a pulsed laser was used to generate a large gradient force within a short duration that overcame the adhesive interaction between the stuck particles and the surface; and then a low power continuous-wave (cw) laser was used to capture the levitated particle. We describe the gradient force generated by the pulsed optical tweezers and model the binding interaction between the stuck beads and glass surface by the dominative van der Waals force with a randomly distributed binding strength. We numerically calculate the single pulse levitation efficiency for polystyrene beads as the function of the pulse energy, the axial displacement from the surface to the pulsed laser focus and the pulse duration. The result of our numerical modeling is qualitatively consistent with the experimental result.

© 2005 Optical Society of America

1. Introduction

Optical tweezers is a single-beam gradient force optical trap, formed by tightly focusing a laser beam with an objective lens of high numerical aperture (NA). It has become a powerful tool for trapping and manipulation of dielectric and biological micron-sized particles typically using continuous wave (cw) laser[1

1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986). [CrossRef] [PubMed]

4

4. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994). [CrossRef] [PubMed]

]. It has been routinely applied to manipulate living cells, bacteria, viruses, chromosomes and other organelles [5

5. A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature , 330, 769–771 (1987) [CrossRef] [PubMed]

6

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

], and recently been applied to the study of molecular motors at the single-molecule level [4

4. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994). [CrossRef] [PubMed]

,7

7. A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-molecule biomechanics with optical methods”, Science , 283, 1689–1695 (1999). [CrossRef] [PubMed]

] the physics of colloid systems [8

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

, 9

9. P.T. Korda, M.B. Taylor, and D.G. Grier, “Kinetically Locked-In Colloidal Transport in an Array of Optical Tweezers”, Phys. Rev. Lett. 89, 128301-1 (2002). [CrossRef]

], the mechanical properties of polymers [10

10. C. Bustamante, Z. Bryant, and S.B. Smith, “Ten years of tension: single-molecule DNA mechanics”, Nature (London) , 421, 423–427 (2003). [CrossRef]

11

11. B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, “Identifying kinetic barriers to mechanical unfolding of the T-thermophila ribozyme”, Science , 292, 1892–1895 (2003). [CrossRef]

], and the control of optically trapped structures [12

12. L. Paterson, M.P. MacDonald, J. Arlt, P.E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science , 292, 912–914 (2001). [CrossRef] [PubMed]

13

13. M.P. MacDonald, L. Peterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science , 296, 1101–1103 (2002). [CrossRef] [PubMed]

]. The combination of near-infrared Raman spectroscopy with optical tweezers allows characterizing optically trapped living cells and other particles [14

14. C. A. Xie, M. A. Dinno, and Y. Q. Li, “Near-infrared Raman spectroscopy of single optically trapped biological cells,” Opt. Lett. 27, 249–251 (2002). [CrossRef]

17

17. J. L. Deng, Q. Wei, M. H. Zhang, Y. Z. Wang, and Y. Q. Li, “Study of the effect of alcohol on single human red blood cells using near-infrared laser tweezers Raman spectroscopy,” J. Raman Spectrosc. 36, 257–261 (2005). [CrossRef]

]. Agate and co-workers have demonstrated that femtosecond optical tweezers are just as effective as cw optical tweezers [18

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

]. The trapping force generated by the cw optical tweezers is typically in the order of 10-12 N [4

4. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994). [CrossRef] [PubMed]

]. This weak force is efficient to confine micro-particles suspended in liquids, but not sufficient to levitate the particles that are stuck on the glass surface, where they have to overcome the binding force. Recently Ambardekar and co-worker have demonstrated that both the stuck dielectric and biological micron-sized particles can be levitated and manipulated with a pulsed optical tweezers [19

19. A. A. Ambardekar and Y. Q. Li, Optical levitation and manipulation of stuck particles with pulsed optical tweezers, Opt. Lett. (in print)

]. In their experiment, an infrared pulse laser at 1.06 µm was used to generate a large gradient force (up to 10-9 N) within a short duration (~45 µs) that overcame the adhesive interaction between the stuck particle and the surface; and then a low-power cw diode laser at 785 nm was used for trapping and manipulating the levitated particle.

Here, we present a theoretical analysis and the numerical modeling of optical levitation and trapping of stuck particles with a pulsed optical tweezers. We describe the radiation force generated by the pulsed optical tweezers as a pulsed gradient force and describe the binding interaction between the stuck beads and glass surface as the dominative van der Waals force with a randomly distributed binding strength. The equation of motion for the bead will be used to describe the trajectory of the bead’s position as the stuck bead is detached from the surface and moves to the trap center. We will calculate the single pulse levitation efficiency for polystyrene beads as the functions of the pulse energy, the axial displacement from the surface to the pulsed laser focus and the pulse duration by solving the equation of motion for the polystyrene bead.

2. Theory

2.1 Pulsed optical tweezers

The pulsed optical tweezers is composed of two parts: the cw trapping system and the pulsed levitation system. The focus of the pulsed laser beam is at the same position as the focus of the cw trapping beam. The configuration is shown in Fig. 1. The polystyrene bead radius is a, and the distance from the bottom of bead to the surface is h, which is very small when the bead is “stuck” on the surface. In order to detach the stuck bead from the surface with the pulsed tweezers, the focus of the both pulsed and cw beam is initially adjusted to have an axial displacement z0 from the surface of the bottom glass plate. Then, a pulse is fired to generate large gradient force acting on the stuck bead within the pulse duration. This pulsed gradient force will break the binding interaction between the bead and the surface so that the stuck bead is levitated and moves into the focus of the cw beam.

Fig. 1. Schematics of the pulsed optical tweezers
Fig. 2. (a) The beads were stuck on the surface. (b) The marked bead was levitated with a pulse and moved to the focus.

Figure 2 shows the image of a 2-µm polystyrene bead that sticks on the glass surface before the application of a pulse (the image was defocused with an axial distance z) and the image of the levitated bead that was detached with the application of a pulse and moved to the focus of the cw beam [19

19. A. A. Ambardekar and Y. Q. Li, Optical levitation and manipulation of stuck particles with pulsed optical tweezers, Opt. Lett. (in print)

].

2.2 Gradient forces

In order to describe the equation of motion for the bead, we begin with modeling the radiation forces generated by the cw and the pulsed beams that were applied to the bead.

Assume that the beam intensity of the focused laser beams can be described with a Guassian expression.

I(x,y,z,t)=I0ω02ω(z)2exp(2(x2+y2)ω(z)2)
+2Uτπω02ω(z)2exp((tτ)2)exp(2(x2+y2)ω(z)2),
(1)

where the first term describes the cw beam with an intensity I0 and the second term describes the pulse beam with the single pulse energy U per unit cross-section area, the pulse duration τ. Here we assume that the pulse beam is completely overlapped with the cw beam and they have the same spatial intensity distribution. ω(z) is the radius of the beam waist at point z along the light propagation and it can be expressed as

ω(z)=ω0(1+(zzs)2)12,
(2)

where ω0 is the radius of the beam waist at the point z=0 and zsω020 is a distance parameter. The radiation force acting on the bead includes the scattering force Fscatt and gradient force Fgrad . In the levitation experiment with pulsed optical tweezers, the stuck bead is not at the focus of the pulsed beam but with an axial displacement. Thus, the scattering force can be neglected comparing to the gradient force. Ashkin has calculated the forces of a single-beam gradient laser trap on a dielectric sphere in the ray optical regime [3

3. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optical regime,” in Methods in Cell Biology, vol.55, M.P. Sheetz, ed. (Academic Press, San Diego, 1998), pp.1–27. [CrossRef]

]. Here, we use an approximate expression for the gradient force. It is known that the gradient force arises from intensity gradient of the inhomogeneous field, Fgrad ∝∇I(x,y,z) [4

4. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994). [CrossRef] [PubMed]

]. Here, we approximately express the gradient force acting on the bead that is located on the beam axis (with x=0 and y=0), produced by the cw beam as

Fcw=kzz(1+(zzs)2)2,
(3a)

where kz is the spring constant and z the position deviation of the bead center from the beam focus (z=h+a-z 0). The express in Eq. (3a) is consistent with the harmonic approximation of an optical trap, in which the restoring force acting on the bead is described as -kzz for z≪zs [4

4. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994). [CrossRef] [PubMed]

]. Eq. (3a) is a good approximation for z<0.5zs, but it can not correctly represent the actual gradient force for z>0.5zs where the force decreases sharply, so we must multiply a correction term

Fcw=kzz(1+(zzs)2)2exp((zzs)4)
(3b)

Similarly, we approximately represent the gradient force produced by the pulsed beam as

Fpulse=2Eτπz(1+(zzs)2)2exp((tτ)2)exp((zzs)4)
(4)

where E is a parameter in proportion to the single pulse energy U.

2.3 The equation of motion

As a pulse is fired to the stuck bead, the bead will be detached under the action of the pulse gradient force and then moves to the trap center under the action of the cw gradient force. The equation of motion describing this levitation process of the bead can be represented as

mz̈=Fcw+Fpulse+FS+FV,
(5)

where m is the mass of the bead (m=(4/3)πa 3 ρ and ρ the density of bead), FS the viscose force, FV the van der Waals force. Here, we have neglected the gravity force of the bead and the random force due to Brownian motion that are much smaller than the gradient forces. In addition, we have modeled the adhesive interaction between the stuck bead and the surface by the van der Waals force because it dominates at short distance comparing to the electrostatic force [20

20. T. G. M. van de Ven. Colloidal Hydrodynamics, (Academic Press, San Diego, 1989).

].

The van der Waals force, FV, can be approximately expressed as [20

20. T. G. M. van de Ven. Colloidal Hydrodynamics, (Academic Press, San Diego, 1989).

]

FV=Aa6h2f(p),
(6)

where f(p)=(1+3.54p)/(1+1.77 p) for p<1 and f(p)=0.98/p-0.434/p 2+0.067/p 3 for p>1 with p=2πh/λL , λL is the London retardation wavelength, usually of the order of 100nm, A is the Hamaker constant, typically in the order of 10-19~10-21J [20

20. T. G. M. van de Ven. Colloidal Hydrodynamics, (Academic Press, San Diego, 1989).

].

The viscose force, FS, exerted on the bead due to the viscosity of the suspending medium is given by

FS=6πaηλz˙=Dz˙
(7)

where D is the damping coefficient (D=6πaηλ), η the viscosity of the surrounding medium, and λa correction term that depends on the proximity of the bead to a planar boundary surface such as the cover slip or microscope slide. For the motion near a planar boundary, this position-dependent term is represented by [21

21. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1965).

]

λ=1198(ah+a)+12(ah+a)3.
(8)

The equation of motion Eq. 5 can be solved numerically on the initial value condition when t=0, h=10-9m, and =0 for the bead’s position at different time after a laser pulse is introduced to a target stuck bead.

3. Results and discussion

3.1 Levitation trajectory

As a pulse is fired at t=0, we can obtain the position h (or z) of the bead as the function of time (the levitation trajectory) by solving the equation of motion Eq. (5) numerically. As an example, we selected the parameters for the polystyrene bead as a=2µm, ρ=1.0495×103 kg/m 3, λL =100nm, the viscosity of water as η=10-3Ns/m2, the parameters for the cw laser as kz=10-5 N/m, zs=8µm, the parameters for the pulsed laser as τ=45µs, z0=6µm, A=1×10-19 J. We found that for given values of A=1×10-19 J, cw trap force constant kz, sphere size a, and initial displacement z0, if the value of E exceeds a threshold value ES (such as 7×10-7Ns/m), the bead’s position can jump from the sticking position (h=10-9m) to the trap position (h=4µm in Fig. 3). However, if the value of E is less than the threshold value ES, the stuck bead cannot be levitated. The threshold value ES can be calculated numerically. This behavior is consistent with the experimental observation [19

19. A. A. Ambardekar and Y. Q. Li, Optical levitation and manipulation of stuck particles with pulsed optical tweezers, Opt. Lett. (in print)

] Figure 3 shows the distance h of the bead from the glass surface versus the time as a single pulse is illuminated on the bead with the different pulse energy: (a) E=1.1×10-5 Ns/m; (b) E=7×10-7 Ns/m; and (c) E=0.

Fig. 3. The position h of the bead versus time at the different pulse energy. Curve a is for E=1.1×10-5Ns/m; b for E=7×10-7Ns/m; c for E=0.

3.2 The levitation efficiency versus the pulse energy

The success in levitation relies on the magnitude of the pulsed gradient force and the binding condition between the stuck bead and the surface. For the given bead and aqueous solution, the pulsed gradient force depends on the pulse energy, the pulse duration and the axial displacement z0 . Experimentally, we found that even with the same pulsed gradient force (so as the same pulse energy, duration, and axial displacement), some beads can be successfully levitated, but some beads in the same liquid sample cannot be levitated. We attributed this phenomenon to the effect of the variation in binding condition between the individual stuck bead and the surface. This leads to the levitation efficiency at a given pulse energy, the pulse duration, or the axial displacement z0 .

We modeled the change in the adhesive interaction between the stuck beads and glass surface among individual beads by considering the Hamaker constant A as a randomly distributed parameter, satisfying a normal distribution, with a probability density function of

p{A}=12πσe(Aζ)22σ2,
(9)

where ζ and σ 2 are the mean value and the variance of A, respectively. The cumulative distribution function of the normal distribution is

P{A}=12πσAe(tζ)22σ2dt=Φ(Aζσ),
(10)

where Φ(u)=u12πet22dt..

In the numerical calculation (such as in Fig. 3), we found that for given values of pulse energy E, cw trap force constant kz, sphere size a, and initial displacement z0, if the value of A is less than a critical value AM, the bead’s position can jump from the sticking position (h=10-9m) to the trap position (h=4µm in Fig. 3). However, if the value of A exceeds the critical value AM, the stuck bead cannot be levitated. The critical value AM can be calculated numerically. Therefore, the probability that a stuck bead can be levitated with the given conditions in E, kz, a, and z0, can be calculated by P{AM}, where AM is the maximum value in which the bead can be levitated. Hence, the levitation efficiency is equal to P{AM}.

Figure 4 shows the theoretical levitation efficiency versus the E (that is proportion to single pulse energy) for a fixed z0=6µm and τ=45µs. In this calculation, the Hamaker constant A was selected with a normal distribution with ξ=1×10-19 J, σ=0.5×10-19 J. The line curve is the Boltzmann fit of the computational data. One can see that the levitation efficiency increases with the increase in E and can reach up to 94.5% at E=1.1×10-6 Ns/m. As a comparison, shown in the right of Fig. 4, the experimental measurement in the levitation efficiency is found to be qualitatively consistent with the numerical calculation.

Fig. 4. The levitation efficiency versus the E with a fixed z0=6µm andτ=45µs.

3.3 The levitation efficiency versus the axial displacement z0 and pulse duration

We also calculate the levitation efficiency versus the axial displacement z0 and pulse duration τ. Figure 5 shows the dependence of the levitation efficiency on the displacement z0 with the fixed E=1.1×10-6 Ns/m and τ=45µs. The optimum efficiency was obtained at z0~6µm.

Figure 6 shows the dependence of the levitation efficiency on the pulse duration τ with the fixed E=1.1×10-6 Ns/m and z0=6µm. The levitation efficiency decreases with the increase in the pulse duration τ. The result of our numerical modeling in Figs. 45 is qualitatively consistent with the experimental result [19

19. A. A. Ambardekar and Y. Q. Li, Optical levitation and manipulation of stuck particles with pulsed optical tweezers, Opt. Lett. (in print)

].

Fig. 5. The dependence of the levitation efficiency on the displacement z0 with the fixed E=1.1×10-6Ns/m and τ=45µs.
Fig. 6. The dependence of the levitation efficiency on the pulse duration τ with the fixed E=1.1×10-6Ns/m and z0=6µm.

4. Conclusion

In summary, we have numerically modeled the optical levitation and trapping of the stuck particles with a pulsed optical tweezers. We described both the pulsed gradient force and the binding interaction force between the stuck bead and the glass surface. We numerically calculated the single pulse levitation efficiency for polystyrene bead as the functions of the pulse energy, the axial displacement from the surface to the pulsed laser focus and the pulse duration. The result of our numerical modeling is qualitatively consistent with the experimental result.

Acknowledgments

This work is supported by grant No. 022261006 and 036105016 from Shanghai Optical-Tech Special Project.

References and links

1.

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986). [CrossRef] [PubMed]

2.

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science , 235, 1517–1520 (1987) [CrossRef] [PubMed]

3.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optical regime,” in Methods in Cell Biology, vol.55, M.P. Sheetz, ed. (Academic Press, San Diego, 1998), pp.1–27. [CrossRef]

4.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994). [CrossRef] [PubMed]

5.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature , 330, 769–771 (1987) [CrossRef] [PubMed]

6.

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

7.

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, “Single-molecule biomechanics with optical methods”, Science , 283, 1689–1695 (1999). [CrossRef] [PubMed]

8.

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

9.

P.T. Korda, M.B. Taylor, and D.G. Grier, “Kinetically Locked-In Colloidal Transport in an Array of Optical Tweezers”, Phys. Rev. Lett. 89, 128301-1 (2002). [CrossRef]

10.

C. Bustamante, Z. Bryant, and S.B. Smith, “Ten years of tension: single-molecule DNA mechanics”, Nature (London) , 421, 423–427 (2003). [CrossRef]

11.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, “Identifying kinetic barriers to mechanical unfolding of the T-thermophila ribozyme”, Science , 292, 1892–1895 (2003). [CrossRef]

12.

L. Paterson, M.P. MacDonald, J. Arlt, P.E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science , 292, 912–914 (2001). [CrossRef] [PubMed]

13.

M.P. MacDonald, L. Peterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science , 296, 1101–1103 (2002). [CrossRef] [PubMed]

14.

C. A. Xie, M. A. Dinno, and Y. Q. Li, “Near-infrared Raman spectroscopy of single optically trapped biological cells,” Opt. Lett. 27, 249–251 (2002). [CrossRef]

15.

C. A. Xie and Y. Q. Li, “Raman spectra and optical trapping of highly refractive and nontransparent particles,” Appl. Phys. Lett. 81, 951–953 (2002). [CrossRef]

16.

C. A. Xie and Y. Q. Li, “Confocal micro-Raman spectroscopy of single biological cells using optical trapping and shifted excitation difference techniques,” J. Appl. Phys. 93, 2982–2986 (2003) [CrossRef]

17.

J. L. Deng, Q. Wei, M. H. Zhang, Y. Z. Wang, and Y. Q. Li, “Study of the effect of alcohol on single human red blood cells using near-infrared laser tweezers Raman spectroscopy,” J. Raman Spectrosc. 36, 257–261 (2005). [CrossRef]

18.

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

19.

A. A. Ambardekar and Y. Q. Li, Optical levitation and manipulation of stuck particles with pulsed optical tweezers, Opt. Lett. (in print)

20.

T. G. M. van de Ven. Colloidal Hydrodynamics, (Academic Press, San Diego, 1989).

21.

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1965).

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation

ToC Category:
Research Papers

History
Original Manuscript: March 24, 2005
Revised Manuscript: April 25, 2005
Published: May 16, 2005

Citation
Jian-liao Deng, Qing Wei, Yu-zhu Wang, and Yong-qing Li, "Numerical modeling of optical levitation and trapping of the �??stuck�?? particles with a pulsed optical tweezers," Opt. Express 13, 3673-3680 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-10-3673


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References

  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, �??Observation of a single-beam gradient force optical trap for dielectric particles,�?? Opt. Lett. 11, 288-290 (1986). [CrossRef] [PubMed]
  2. A. Ashkin, and J. M. Dziedzic, �??Optical trapping and manipulation of viruses and bacteria,�?? Science, 235, 1517-1520 (1987) [CrossRef] [PubMed]
  3. A. Ashkin, �??Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optical regime,�?? in Methods in Cell Biology, vol.55, M.P. Sheetz, ed. (Academic Press, San Diego, 1998), pp.1-27. [CrossRef]
  4. K. Svoboda and S. M. Block, �??Biological applications of optical forces,�?? Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994). [CrossRef] [PubMed]
  5. A. Ashkin, J. M. Dziedzic and T. Yamane, �??Optical trapping and manipulation of single cells using infrared laser beams,�?? Nature, 330, 769-771 (1987) [CrossRef] [PubMed]
  6. K.C. Neuman and S.M. Block, �??Optical trapping�??, Rev. Sci. Instrum. 75, 2787-2809 (2004). [CrossRef]
  7. A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, R. M. Simmons, �??Single-molecule biomechanics with optical methods�??, Science, 283, 1689-1695 (1999). [CrossRef] [PubMed]
  8. D. G. Grier, �??A revolution in optical manipulation�??, Nature (London), 424, 810-816 (2003). [CrossRef]
  9. P.T. Korda, M.B. Taylor, D.G. Grier, �??Kinetically Locked-In Colloidal Transport in an Array of Optical Tweezers�??, Phys. Rev. Lett. 89, 128301-1 (2002). [CrossRef]
  10. C. Bustamante, Z. Bryant, and S.B. Smith, �??Ten years of tension: single-molecule DNA mechanics�??, Nature (London), 421, 423-427 (2003). [CrossRef]
  11. B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, C. Bustamante, �??Identifying kinetic barriers to mechanical unfolding of the T-thermophila ribozyme�??, Science, 292, 1892-1895 (2003). [CrossRef]
  12. L. Paterson, M.P. MacDonald, J. Arlt, P.E. Bryant and K. Dholakia, �??Controlled rotation of optically trapped microscopic particles,�?? Science, 292, 912-914 (2001). [CrossRef] [PubMed]
  13. M.P. MacDonald, L. Peterson, K.Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, �??Creation and manipulation of three-dimensional optically trapped structures,�?? Science, 296, 1101-1103 (2002). [CrossRef] [PubMed]
  14. C. A. Xie, M. A. Dinno, and Y. Q. Li, �??Near-infrared Raman spectroscopy of single optically trapped biological cells,�?? Opt. Lett. 27, 249-251 (2002). [CrossRef]
  15. C. A. Xie, and Y. Q. Li, �??Raman spectra and optical trapping of highly refractive and nontransparent particles,�?? Appl. Phys. Lett. 81, 951-953 (2002). [CrossRef]
  16. C. A. Xie, and Y. Q. Li, �??Confocal micro-Raman spectroscopy of single biological cells using optical trapping and shifted excitation difference techniques,�?? J. Appl. Phys. 93, 2982-2986 (2003) [CrossRef]
  17. J. L. Deng, Q. Wei, M. H. Zhang, Y. Z. Wang, and Y. Q. Li, �??Study of the effect of alcohol on single human red blood cells using near-infrared laser tweezers Raman spectroscopy,�?? J. Raman Spectrosc. 36, 257-261 (2005). [CrossRef]
  18. B. Agate, C. T. A. Brown, W. Sibbett, and K. Dholakia, �??Femtosecond optical tweezers for in-situ control of two-photon fluorescence,�?? Opt. Express, 12, 3011-3017 (2004). [CrossRef] [PubMed]
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