OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 6 — Mar. 24, 2014
  • pp: 6653–6660
« Show journal navigation

Application of flat-top focus to 2D trapping of large particles

Hao Chen and K. C. Toussaint, Jr.  »View Author Affiliations


Optics Express, Vol. 22, Issue 6, pp. 6653-6660 (2014)
http://dx.doi.org/10.1364/OE.22.006653


View Full Text Article

Acrobat PDF (1159 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The 2D optical trapping ability of larger-than average-particles is compared for three different beam types: a flat-top, a Gaussian beam, and a donut shaped beam. Optical force-displacement curves are calculated in four different size regimes of particle diameters (1.5-20 μm). We find that the trapping efficiency increases linearly with ratio of particle diameter to wavelength for all three beams. As the ratio reaches a specific threshold value, the flat-top focus exhibits the largest trapping efficiency compared to the other two beam types. We experimentally demonstrate that flat-top focusing provides the largest transverse trapping efficiency for particles as large as 20 μm in diameter for our given experimental conditions. The overall trend in our experimental results follows that observed in our simulation model. The results from this study could facilitate light manipulation of large particles.

© 2014 Optical Society of America

1. Introduction

Optical tweezers, which harness optical forces to trap and manipulate objects, was first reported several decades ago and has since found numerous applications [1

1. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992). [CrossRef] [PubMed]

5

5. W. H. Wright, G. J. Sonek, and M. W. Berns, “Radiation Trapping Forces on Microspheres with Optical Tweezers,” Appl. Phys. Lett. 63(6), 715–717 (1993). [CrossRef]

]. Indeed, this technology has been successfully implemented in various research applications such as atom cooling [6

6. S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70(3), 685–706 (1998). [CrossRef]

], single-molecule manipulation [7

7. J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single Myosin Molecule Mechanics: Piconewton Forces and Nanometre Steps,” Nature 368(6467), 113–119 (1994). [CrossRef] [PubMed]

, 8

8. K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008). [CrossRef] [PubMed]

], particle sorting and transportation in micrometer-scale channels [9

9. M. Werner, F. Merenda, J. Piguet, R. P. Salathé, and H. Vogel, “Microfluidic array cytometer based on refractive optical tweezers for parallel trapping, imaging and sorting of individual cells,” Lab Chip 11(14), 2432–2439 (2011). [CrossRef] [PubMed]

], and assembling of 3D artificial structures [10

10. J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. J. Padgett, J. Cooper, and Z. J. Laczik, “3D manipulation of particles into crystal structures using holographic optical tweezers,” Opt. Express 12(1), 220–226 (2004). [CrossRef] [PubMed]

, 11

11. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002). [CrossRef] [PubMed]

]. The facile manipulation of particles of various shapes, sizes, and types has been a result of exploiting the various degrees-of-freedom of the trapping laser, particularly its amplitude, phase, spatial mode, wavelength and polarization [3

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

, 12

12. O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013). [CrossRef] [PubMed]

15

15. 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]

]. Furthermore, since its inception, it has been well-understood that for the single-beam gradient force trap, the trapping strength is proportional to the intensity gradient of an optical field, and as such, the general route to obtaining the largest intensity gradient is to focus a standard Gaussian beam as tightly as possible. However, diffraction limits how tightly an optical field can be focused. In addition, trapping at the extremes of particles sizes, i.e., either very small or large particle diameters with respect to the optical wavelength, is challenging. Small particles undergo Brownian motion and large particles more greatly experience the effects of gravity. While various techniques have been developed over the years to improve the trapping efficiency of small particles much less has been done with respect to large particles. The ability to trap and manipulate objects that are tens of microns in diameter, with low input power, is useful in handling biological structures without damaging them. Thus, an interesting avenue to pursue with respect to trapping large particles is to use non-standard beam shapes such as a beam with a flat-top intensity distribution. Such a beam is characterized by a uniform intensity distribution with a sharp intensity roll-off along its edges and can be derived from the super-Gaussian (SG) function [16

16. M. Santarsiero and R. Borghi, “Correspondence between super-Gaussian and flattened Gaussian beams,” J. Opt. Soc. Am. A 16(1), 188–190 (1999). [CrossRef]

], which forms a continuous transition from a Gaussian to a flat-top. At the extreme case of SG, it tends to a rectangular function with an infinite gradient at both edges.

In the present work, we explore the effect of flat-top focusing on the 2D trapping of larger-than-average-particles (LAPS) with diameters in the range of 1-20 μm. Specifically, using a lens of numerical aperture (NA) of ~0.745, we employ moderate focusing of a radially polarized beam to generate a flat-top focus, an approach that we recently demonstrated [17

17. H. Chen, S. Tripathi, and K. C. Toussaint, “Demonstration of flat-top focusing under radial polarization illumination,” Opt. Lett. 39(4), 834–837 (2014). [CrossRef]

]. We compare the results of using a flat-top focus for trapping of LAPS to that of using a beam with a donut intensity distribution, generated from azimuthally polarized light, and to that of using the standard linearly polarized Gaussian beam. Using a three-dimensional (3D) finite element method (FEM) approach, we calculate the Maxwell stress tensor in order to model the force-displacement curves for these beams for the aforementioned particle sizes. We find that as the ratio of particle diameter to wavelength α reaches a specific threshold value, the flat-top focus exhibits the largest trapping efficiency compared to the other two beam types. In the case of our specific experimental parameters, we determine that the flat-top focus demonstrates the best trapping efficiency when trapping particles larger than 13.5 μm. We find that the overall trend in our experimental results follows that observed in simulation.

2. Computational methods

To calculate the force that acts on arbitrarily shaped micro and nanoparticles the computational procedure consists of two steps. First, the electromagnetic field distribution along the surface of the object must be solved. Next, Maxwell stress tensor analysis is applied [18

18. C. Rockstuhl and H. P. Herzig, “Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders,” J. Opt. A, Pure Appl. Opt. 6(10), 921–931 (2004). [CrossRef]

, 19

19. J. D. Jackson, Classical Electrodynamics (Wiley, 1975).

].

In this study, we simulate the electromagnetic field in the vicinity of focus for a standard linearly polarized Gaussian beam, a radially polarized beam, and an azimuthally polarized beams using commercial 3D FEM software (COMSOL Multiphysics v4.3b) [20

20. B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. 2. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. A 253, 358–379 (1959).

, 21

21. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000). [CrossRef] [PubMed]

]. We have recently reported the intensity profile for these beams elsewhere [17

17. H. Chen, S. Tripathi, and K. C. Toussaint, “Demonstration of flat-top focusing under radial polarization illumination,” Opt. Lett. 39(4), 834–837 (2014). [CrossRef]

]. We analyze the optical trapping ability of these beams when used to manipulate spherical polystyrene particles of diameters 1.5, 5, 10, and 20 μm. The simulation region is a 3D cylinder and the dimensions dependent on the diameter of the particle. For the four particle sizes used, the aspect ratio (height to radius) of the cylinder is 1.2, 1.5, 1.6 and 1.8 for the 1.5, 5, 10, and 20-μm diameter particles, respectively. The grid size of the sampled incident field in the simulation volume is dependent on the predefined mesh size which is set as λ/20, where λ is the wavelength of light. For the FEM simulation, the biggest advantage is the option to apply a non-uniform mesh size in order to be computationally efficient. Thus, in our approach, we apply a finer mesh for the region of interest and a coarser mesh elsewhere. We set the global maximum element size as λ/5, and the minimum element size at the surface of a particle as λ/20. In addition, a perfect matched layer is set at all surrounding boundaries [22

22. K. Kitamura, K. Sakai, and S. Noda, “Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam,” Opt. Express 19(15), 13750–13756 (2011). [CrossRef] [PubMed]

]. Finally, Maxwell’s stress tensor is introduced to calculate the forces on the particles.

The time-averaged force acting on a particle is given by the integral of the stress tensor over the surface enclosing the particle [18

18. C. Rockstuhl and H. P. Herzig, “Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders,” J. Opt. A, Pure Appl. Opt. 6(10), 921–931 (2004). [CrossRef]

, 19

19. J. D. Jackson, Classical Electrodynamics (Wiley, 1975).

],
F={ε2Re[(En)E*]ε4(EE*)n+μ2Re[(Hn)H*]μ4(HH*)n}dS
(1)
where S is the surface of the particle and n is the normal to the surface pointing outward. Eand H are the localized electric and magnetic fields on the surface of the particle, respectively, while ε and μ are the respective electric permittivity and magnetic permeability of the surrounding medium. Note that the optical force is entirely determined by the electric and magnetic field on the surface S. To estimate the transverse optical force exerted on the particle, a polystyrene sphere (ε = 2.6, μ = 1) is placed in the focal plane with a given transverse displacement from the optical axis, and the radial components of force are then calculated. Our simulation runs on a 16 core, 2.60GHz, Intel Xeon E5-2670(128GB memory), and takes up to 10 hours to obtain the force-displacement curves for the largest particle diameter. After the optical force distribution is obtained, it is straightforward to extract the maximum trapping force and stiffness of the trap.

3. Experimental methods

Figure 1
Fig. 1 Schematic diagram of experimental setup. M: Mirror, OBJ: objective. BS: beamsplitter. P: polarizer. See text for details.
shows a schematic diagram of the optical trapping setup. A spectrally tunable, 3W, Ti:Sapphire laser source (Spectra-Physics Mai-Tai HP DeepSee) that produces 100 femtosecond-duration pulses at 80-MHz repetition rate is operated in pseudo-CW mode [23

23. 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]

]. The output, linearly polarized, beam from the source is spectrally centered at 800 nm and spatially filtered before passing through a linear polarizer. Next, the beam is sent to a flip mirror which, when in the up position, directs the beam via gold mirrors and a 50:50 beamsplitter to the input of an upright microscope (Olympus IX81) with a 60 × [plan apochromatic, numerical aperture (NA) = 0.8] oil-immersion objective. When the flip mirror is in the down position, the linearly polarized Gaussian beam is first converted to a radially polarized vector beam using a radial polarization converter (Arcopix) before being directed into the microscope. We have recently demonstrated that the focusing a radially polarized beam by a lens of ~0.745 NA will produce a flat-top intensity distribution at the focus. To generate an azimuthal vector beam, a polarization rotator consisting of two half-wave plates with an angle of 45° with respect to each other, is placed between the beamsplitter and the radial polarizer [24

24. Q. W. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002). [CrossRef] [PubMed]

]. A halogen lamp, white light source (Dolan Jenner, 190) is used to image the particles (Duke Scientific) onto a CCD camera (Watec, 902H3-Ultimate), which is preceded by a laser-blocking band-pass filter (Brightline FF01-680/SP-25). For all beams, the power at the output objective is kept constant at 5 mW. The input beam waist diameter is fixed to be ~4 mm. Note that since the generated flat-top and donut beams at the focus are non-Gaussian, the standard definition of beam waist does not apply here. Trapping chambers are made with a 13-mm diameter gasket (Invitrogen CoverWell) sandwiched between two microscope coverslips (Corning). All particles used in the experiment are suspended in water and a typical concentration of 1:1000 is used. The sample is placed on a motorized stage driven by a picomotor linear actuator (Newport 8303) with 30-nm resolution.

The ability of an optical trap to convert incoming laser light (power) into a useful trapping force is measured using the dimensionless trapping efficiency parameter [1

1. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992). [CrossRef] [PubMed]

],
Q=FmaxcnP
(2)
ε=[1.7007337+1.0221606(δ/r)]/[1+1.0458291(δ/r)0.00148(δ/r)2], where Fmax is the maximum trapping force exerted on the particle, c is the speed of light, n is the refractive index of the surrounding medium, and P is the input laser power. The trapping efficiency is assessed via the Stokes drag-force method in which the sample stage is driven at velocity v, inducing a drag force on the particle according to F = 6πεηrv, where η is the dynamic viscosity of the medium, is the correction factor for the particle in contact with the substrate, δ is the separation distance, and r is the radius of the particle [25

25. M. E. O’Neill, “A sphere in contact with a plane wall in a slow linear shear flow,” Chem. Eng. Sci. 23(11), 1293–1298 (1968). [CrossRef]

, 26

26. A. J. Goldman, R. G. Cox, and H. Brenner, “Slow viscous motion of a sphere parallel to a plane wall—II Couette flow,” Chem. Eng. Sci. 22(4), 653–660 (1967). [CrossRef]

]. Experimentally, Q is determined by vibrating the trapped particle with progressively increasing speed in the transverse plane until it is ejected from the trap. These velocities are used to find the applied viscous drag force from which Q is calculated. This entire process is repeated 10 times for each input beam.

4. Results and discussion

Figure 2
Fig. 2 Simulation results showing the transverse component of optical force (along the x-coordinate) on polystyrene particles (shown as dashed overlaid circles) with diameters: (a) 1.5 μm, (b) 5 μm, (c) 10 μm, and (d) 20 μm. The particles are located at the focal plane and illuminated with 5 mW of 800-nm wavelength light for the flat-top, Gaussian, and donut shaped focus, shown in blue, red, and black, respectively. The insets are zoomed-in views of the peaks of the force curves, where the parameter β is the ratio of the maximum force for the flat-top compared to the Gaussian.
shows the simulated transverse optical forces exerted on polystyrene particles of diameters 1.5, 5, 10, and 20 μm when illuminated by Gaussian, flat-top, and donut beams. As shown in Fig. 2(a), the maximum trapping force exerted by a flat-top is smaller than both Gaussian and donut shaped focus when the particle size is 1.5 μm. Overall, we observe that the ratio β of maximum transverse trapping force for the flat-top compared to the Gaussian profile is ~0.63, 0.86, 0.99, and 1.03 for the 1.5, 5, 10 and 20-μm diameter particles, respectively, as shown in the insets of Figs. 2(a)-2(d). Note that the abrupt change observed in the transverse force curve for the 10-μm and 20-μm diameter particles is a result of the relatively coarse sampling (step sizes of 500 nm) in the simulation at this particle size scale; this can result in less resolution in determining the exact maximum value of the trapping force.

Experimental results (blue bars) of transverse trapping efficiency are plotted in Fig. 3(a-d)
Fig. 3 Comparison of trapping efficiency using beams with flat-top, Gaussian and donut shaped focus for particles with diameters: (a) 1.5 μm, (b) 5 μm, (c) 10 μm, and (d) 20 μm. The experimental results (in blue) are shown to be in agreement with simulation (in red). (e) Plot of the trapping efficiency as a function of α (ratio of particle diameter to wavelength) using beams with flat-top (blue), Gaussian (red), and donut shaped (black) focus. The dashed vertical line points to the critical value at which the trapping efficiency of the flat-top focus becomes the largest, which, for the experimental parameters used in this paper, corresponds to a particle diameter of ~13.5 μm.
, and overall trend in our experimental results follows the trend observed in the simulation results (red bars). Note that the error in all cases is ~2% except for the case of the 1.5-μm diameter particle illuminated by a flat-top focus (the error is ~6.4%). Figure 3(e) shows the trapping efficiency using flat-top, Gaussian and donut shaped focus as a function of α. We observe from the plot that the trapping efficiency scales linearly with α. This observed linear behavior in Q is consistent with what has been reported previously for the particular range of particle diameters used in this study [5

5. W. H. Wright, G. J. Sonek, and M. W. Berns, “Radiation Trapping Forces on Microspheres with Optical Tweezers,” Appl. Phys. Lett. 63(6), 715–717 (1993). [CrossRef]

]. In addition, the flat-top focus is seen to have the largest slope. As a result, below a critical value of α, the flat-top focus has the lowest trapping efficiency for the smallest diameter particles. In contrast, above the critical value, the trapping efficiency is largest for the flat-top focus. For the specific wavelength, numerical aperture, and spot size used in our experiments, we find that this critical value corresponds to a particle with diameter of 13.5 μm. It is worth noting that particles are trapped in 2D in the focal plane in our experiment. As the NA is 0.745 in our case, the axial gradient force is smaller than the scattering force, and thus cannot stably trap the particle axially. Thus, by pushing the particle against the coverslip, we restrict its motion to the transverse plane.

4. Conclusion

Optical force-displacement curves of flat-top, Gaussian, and donut shaped focus for different particle sizes (1.5-20 μm) are obtained by calculating the Maxwell stress tensor over the surface enclosing the particle. The transverse optical trapping efficiency was observed both experimentally and theoretically for comparison. We found that the trapping efficiency increased linearly with ratio of particle diameter to wavelength for all beams, with the efficiency for the flat-top focus becoming comparable to the Gaussian by a certain threshold value. In the case of our specific experimental parameters, we determined that this threshold corresponded to a particle with a diameter of 13.5 μm. In addition, we experimentally verified that the transverse trapping efficiency for the flat-top focus becomes larger than that of the Gaussian beam when the particle size approaches 20 μm. The overall trend in our experimental results follows the trend observed in our simulations. In addition, we note that although the trapping by flat-top focus that we presented is based on 2D optical trapping, we anticipate that the associated larger transverse gradient force and axial scattering force makes it useful for optical levitation studies.

Acknowledgments

This work was supported by the University of Illinois at Urbana-Champaign (UIUC) research start-up funds.

References and links

1.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992). [CrossRef] [PubMed]

2.

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(5), 288–290 (1986). [CrossRef] [PubMed]

3.

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

4.

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

5.

W. H. Wright, G. J. Sonek, and M. W. Berns, “Radiation Trapping Forces on Microspheres with Optical Tweezers,” Appl. Phys. Lett. 63(6), 715–717 (1993). [CrossRef]

6.

S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70(3), 685–706 (1998). [CrossRef]

7.

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single Myosin Molecule Mechanics: Piconewton Forces and Nanometre Steps,” Nature 368(6467), 113–119 (1994). [CrossRef] [PubMed]

8.

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008). [CrossRef] [PubMed]

9.

M. Werner, F. Merenda, J. Piguet, R. P. Salathé, and H. Vogel, “Microfluidic array cytometer based on refractive optical tweezers for parallel trapping, imaging and sorting of individual cells,” Lab Chip 11(14), 2432–2439 (2011). [CrossRef] [PubMed]

10.

J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. J. Padgett, J. Cooper, and Z. J. Laczik, “3D manipulation of particles into crystal structures using holographic optical tweezers,” Opt. Express 12(1), 220–226 (2004). [CrossRef] [PubMed]

11.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002). [CrossRef] [PubMed]

12.

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013). [CrossRef] [PubMed]

13.

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]

14.

M. G. Donato, S. Vasi, R. Sayed, P. H. Jones, F. Bonaccorso, A. C. Ferrari, P. G. Gucciardi, and O. M. Maragò, “Optical trapping of nanotubes with cylindrical vector beams,” Opt. Lett. 37(16), 3381–3383 (2012). [CrossRef] [PubMed]

15.

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]

16.

M. Santarsiero and R. Borghi, “Correspondence between super-Gaussian and flattened Gaussian beams,” J. Opt. Soc. Am. A 16(1), 188–190 (1999). [CrossRef]

17.

H. Chen, S. Tripathi, and K. C. Toussaint, “Demonstration of flat-top focusing under radial polarization illumination,” Opt. Lett. 39(4), 834–837 (2014). [CrossRef]

18.

C. Rockstuhl and H. P. Herzig, “Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders,” J. Opt. A, Pure Appl. Opt. 6(10), 921–931 (2004). [CrossRef]

19.

J. D. Jackson, Classical Electrodynamics (Wiley, 1975).

20.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. 2. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. A 253, 358–379 (1959).

21.

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000). [CrossRef] [PubMed]

22.

K. Kitamura, K. Sakai, and S. Noda, “Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam,” Opt. Express 19(15), 13750–13756 (2011). [CrossRef] [PubMed]

23.

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]

24.

Q. W. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002). [CrossRef] [PubMed]

25.

M. E. O’Neill, “A sphere in contact with a plane wall in a slow linear shear flow,” Chem. Eng. Sci. 23(11), 1293–1298 (1968). [CrossRef]

26.

A. J. Goldman, R. G. Cox, and H. Brenner, “Slow viscous motion of a sphere parallel to a plane wall—II Couette flow,” Chem. Eng. Sci. 22(4), 653–660 (1967). [CrossRef]

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(260.5430) Physical optics : Polarization
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: December 11, 2013
Revised Manuscript: February 18, 2014
Manuscript Accepted: February 20, 2014
Published: March 14, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Hao Chen and K. C. Toussaint, "Application of flat-top focus to 2D trapping of large particles," Opt. Express 22, 6653-6660 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-6653


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992). [CrossRef] [PubMed]
  2. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986). [CrossRef] [PubMed]
  3. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]
  4. K. C. Neuman, S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004). [CrossRef] [PubMed]
  5. W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation Trapping Forces on Microspheres with Optical Tweezers,” Appl. Phys. Lett. 63(6), 715–717 (1993). [CrossRef]
  6. S. Chu, “The manipulation of neutral particles,” Rev. Mod. Phys. 70(3), 685–706 (1998). [CrossRef]
  7. J. T. Finer, R. M. Simmons, J. A. Spudich, “Single Myosin Molecule Mechanics: Piconewton Forces and Nanometre Steps,” Nature 368(6467), 113–119 (1994). [CrossRef] [PubMed]
  8. K. C. Neuman, A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008). [CrossRef] [PubMed]
  9. M. Werner, F. Merenda, J. Piguet, R. P. Salathé, H. Vogel, “Microfluidic array cytometer based on refractive optical tweezers for parallel trapping, imaging and sorting of individual cells,” Lab Chip 11(14), 2432–2439 (2011). [CrossRef] [PubMed]
  10. J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. J. Padgett, J. Cooper, Z. J. Laczik, “3D manipulation of particles into crystal structures using holographic optical tweezers,” Opt. Express 12(1), 220–226 (2004). [CrossRef] [PubMed]
  11. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002). [CrossRef] [PubMed]
  12. O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013). [CrossRef] [PubMed]
  13. L. Huang, H. L. Guo, J. F. Li, L. Ling, B. H. Feng, Z. Y. Li, “Optical trapping of gold nanoparticles by cylindrical vector beam,” Opt. Lett. 37(10), 1694–1696 (2012). [CrossRef] [PubMed]
  14. M. G. Donato, S. Vasi, R. Sayed, P. H. Jones, F. Bonaccorso, A. C. Ferrari, P. G. Gucciardi, O. M. Maragò, “Optical trapping of nanotubes with cylindrical vector beams,” Opt. Lett. 37(16), 3381–3383 (2012). [CrossRef] [PubMed]
  15. L. Huang, H. L. Guo, J. F. Li, L. Ling, B. H. Feng, Z. Y. Li, “Optical trapping of gold nanoparticles by cylindrical vector beam,” Opt. Lett. 37(10), 1694–1696 (2012). [CrossRef] [PubMed]
  16. M. Santarsiero, R. Borghi, “Correspondence between super-Gaussian and flattened Gaussian beams,” J. Opt. Soc. Am. A 16(1), 188–190 (1999). [CrossRef]
  17. H. Chen, S. Tripathi, K. C. Toussaint, “Demonstration of flat-top focusing under radial polarization illumination,” Opt. Lett. 39(4), 834–837 (2014). [CrossRef]
  18. C. Rockstuhl, H. P. Herzig, “Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders,” J. Opt. A, Pure Appl. Opt. 6(10), 921–931 (2004). [CrossRef]
  19. J. D. Jackson, Classical Electrodynamics (Wiley, 1975).
  20. B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. 2. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. A 253, 358–379 (1959).
  21. K. S. Youngworth, T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000). [CrossRef] [PubMed]
  22. K. Kitamura, K. Sakai, S. Noda, “Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam,” Opt. Express 19(15), 13750–13756 (2011). [CrossRef] [PubMed]
  23. B. Agate, C. Brown, W. Sibbett, K. Dholakia, “Femtosecond optical tweezers for in-situ control of two-photon fluorescence,” Opt. Express 12(13), 3011–3017 (2004). [CrossRef] [PubMed]
  24. Q. W. Zhan, J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002). [CrossRef] [PubMed]
  25. M. E. O’Neill, “A sphere in contact with a plane wall in a slow linear shear flow,” Chem. Eng. Sci. 23(11), 1293–1298 (1968). [CrossRef]
  26. A. J. Goldman, R. G. Cox, H. Brenner, “Slow viscous motion of a sphere parallel to a plane wall—II Couette flow,” Chem. Eng. Sci. 22(4), 653–660 (1967). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited