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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 9 — Jul. 6, 2010
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Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams

Yuichi Kozawa and Shunichi Sato  »View Author Affiliations


Optics Express, Vol. 18, Issue 10, pp. 10828-10833 (2010)
http://dx.doi.org/10.1364/OE.18.010828


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Abstract

Single-beam optical trapping of micrometer-sized dielectric particles is experimentally demonstrated using radially and azimuthally polarized beams. The axial and transverse optical trapping efficiencies of glass and polystyrene beads suspended in water are measured. The radially polarized beam exhibited the highest trapping efficiency in the axial direction due to the p polarization of the radial polarization on the particle surface. On the other hand, the azimuthally polarized beam had a higher transverse trapping efficiency than the radially polarized beam. These results are consistent with numerical predictions.

© 2010 OSA

1. Introduction

Single-beam optical trapping, which was first demonstrated by Ashkin in 1986 [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(5), 288–290 (1986). [CrossRef] [PubMed]

], is currently used for non-contact particle manipulation in a wide variety of scientific fields, including physics, chemistry, and biology. Most theoretical and experimental studies on the trapping efficiencies of micrometer- and nanometer-sized particles have considered only the intensity profile of focused laser beams [2

2. 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]

4

4. D. Ganic, X. Gan, and M. Gu, “Optical trapping force with annular and doughnut laser beams based on vectorial diffraction,” Opt. Express 13(4), 1260–1265 (2005). [CrossRef] [PubMed]

]. Recently, however, numerical calculations have predicted that the polarization of a focused beam affects the trapping force on a microscopic particle [5

5. H. Kawauchi, K. Yonezawa, Y. Kozawa, and S. Sato, “Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam,” Opt. Lett. 32(13), 1839–1841 (2007). [CrossRef] [PubMed]

8

8. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009). [CrossRef]

]. A radially polarized beam, which is a typical cylindrical vector beam [9

9. R. Peng, B. Yao, S. Yan, W. Zhao, and M. Lei, “Trapping of low-refractive-index particles with azimuthally polarized beam,” J. Opt. Soc. Am. B 26(12), 2242–2247 (2009). [CrossRef]

], is predicted to have a higher axial trapping efficiency than a linearly polarized beam. This enhanced trapping efficiency is due to all the rays of a radially polarized beam being p polarized if the center of the small particle is on the beam axis. By contrast, an azimuthally polarized beam, which is orthogonal to the radial polarization, will have a lower axial trapping efficiency than a linearly polarized beam because the beam is s polarized. The difference between these polarizations is due to Fresnel reflection on the particle surface, particularly when the particle is larger than the laser light wavelength (i.e., the ray optics regime). In fact, numerical calculations based on ray optics [5

5. H. Kawauchi, K. Yonezawa, Y. Kozawa, and S. Sato, “Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam,” Opt. Lett. 32(13), 1839–1841 (2007). [CrossRef] [PubMed]

] and the T-matrix method [6

6. S. Yan and B. Yao, “Radiation forces of a highly focused radially polarized beam on spherical particles,” Phys. Rev. A 76(5), 053836 (2007). [CrossRef]

,7

7. T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Forces in optical tweezers with radially and azimuthally polarized trapping beams,” Opt. Lett. 33(2), 122–124 (2008). [CrossRef] [PubMed]

] predict that a radially polarized beam will provide more efficient axial trapping of transparent dielectric particles than a linearly polarized beam. Most recently, Michihata et al. have reported a larger axial trapping efficiency of radial polarization than that of linear one for the optical trapping of a glass bead with a diameter of 8 μm in air [10

10. M. Michihata, T. Hayashi, and Y. Takaya, “Measurement of axial and transverse trapping stiffness of optical tweezers in air using a radially polarized beam,” Appl. Opt. 48(32), 6143–6151 (2009). [CrossRef] [PubMed]

]. In this regard, however, since the radially polarized beam used in the measurement was converted from a linearly polarized Gaussian beam by using a segmented half-wave plate, the beam was not a complete doughnut-shape with radial polarization. It has been demonstrated that the difference between Gaussian and doughnut-shaped profiles of the incident beams should be considered for the estimation of the trapping force [11

11. S. Sato and H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28(1), 1–16 (1996). [CrossRef]

]. In addition, the effect of polarization on trapping efficiency has not been experimentally verified in water, which is the most widely employed condition in the optical trapping applications.

In this paper, we demonstrate single-beam optical trapping of micrometer-sized dielectric particles by radially and azimuthally polarized beams. The effect of polarization on the axial and transverse trapping efficiencies was experimentally measured in water.

2. Experimental setup

Figure 1
Fig. 1 Schematic diagram of the optical trapping setup
shows a schematic diagram of the optical trapping setup. A radially polarized beam was generated directly from a Nd:YAG laser cavity by inserting a c-cut YVO4 crystal in the cavity [12

12. Y. Kozawa, K. Yonezawa, and S. Sato, “Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal,” Appl. Phys. B 88(1), 43–46 (2007). [CrossRef]

]. An azimuthally polarized beam was obtained by converting a radially polarized beam using a pair of half-wave plates [Fig. 2(a)
Fig. 2 Polarization conversion of (a) radial into azimuthal polarization using two half-wave plates and (b) azimuthal into linear polarization using a quarter-wave plate and a linear polarizer. (c)−(e) show the measured intensity distributions of radially, azimuthally, and linearly polarized beams, respectively.
]. In addition, a doughnut-shaped linearly polarized beam, namely a Laguerre-Gaussian LG01 mode, was obtained by passing an azimuthally polarized beam through a quarter-wave plate and a linear polarizer [Fig. 2(b)]. Figures 2(c)-(e) show the measured intensity distributions before the focusing lens for the radially, azimuthally, and linearly polarized beams, respectively. These figures reveal that quite similar doughnut-shaped incident beams with different polarization states were obtained by polarization conversion. Therefore, only the polarization state of the focused laser beam can produce a different trapping force in the measurements. These beams were coupled to an upright microscope with a water-immersion objective (Carl Zeiss, Plan-Neofluar 63x, NA = 1.2). Particles were suspended in water. To measure the transverse force, the motorized stage of the microscope was controlled by a PC, as described below.

The axial trapping force along the propagation direction of a focused beam was estimated from the minimum laser power required to hold a particle three-dimensionally against gravity when the buoyant force was taken into account [13

13. H. Felgner, O. Müller, and M. Schliwa, “Calibration of light forces in optical tweezers,” Appl. Opt. 34(6), 977–982 (1995). [CrossRef] [PubMed]

]. The axial trapping force Fax can then be expressed as Fax = π (ρbρm)D3g / 6, where ρb and ρm are the densities of the particle and the medium respectively, D is the particle diameter, and g is the gravitational acceleration. To clearly detect a particle escaping from a trap, the particles should be large and dense enough to fall quickly in the water when the laser power is insufficient to hold the particle. Accordingly, glass beads (Duke Scientific Corp.) with nominal diameters of 5 and 10 μm were used in this experiment. Five measurements were performed for each bead and with each of the three beams (i.e., the radially, azimuthally, and linearly polarized beams). Particles with different diameters were then trapped and measured in the same manner.

The transverse (i.e., perpendicular to the axial direction) trapping force was estimated from the Stokes’ drag force exerted on a particle in the medium, which was set on the motorized stage that moved perpendicular to the beam axis. The transverse trapping force Ftr is expressed as Ftr = 3πηDvc, where η is the medium viscosity and vc is the stage velocity when the sphere completely escapes from the optical trap. Polystyrene beads (Duke Scientific Corp.) with nominal diameters of 3, 6, and 9 μm were used for the transverse force measurements, because these particles had narrow diameter distributions. The transverse trapping forces of radially and azimuthally polarized beams were measured. Linearly polarized beams were excluded from this measurement because the trapping force varies depending on the direction of the moving stage relative to the polarization direction, and the linearly polarized beams shown in Fig. 2(e) had insufficient polarization and intensity distributions for reliable force measurement.

Figure 3
Fig. 3 Calculated trapping efficiencies along (a) axial and (b) transverse directions. The circle in (a) and the quarter sector in (b) indicate the particle circumference.
shows the trapping efficiencies calculated using parameters determined from the experimental conditions using the ray optics model [2

2. 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. H. Kawauchi, K. Yonezawa, Y. Kozawa, and S. Sato, “Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam,” Opt. Lett. 32(13), 1839–1841 (2007). [CrossRef] [PubMed]

]. Quantitative evaluation by the ray optics model is generally inadequate for particles whose sizes are comparable to the wavelength of the focused laser beam. However, ray optics calculations can reveal the qualitative behavior of the trapping efficiency for radial and azimuthal polarizations. Figure 3(a) shows the magnitude of the axial trapping efficiencies Qax for radially, azimuthally, and linearly polarized beams. The vertical axis indicates the position of the focus along the beam axis at a distance Sz from the center of the trapped particle with a radius of 1. The refractive indices of the particle and the medium are assumed to be 1.56 (glass bead) and 1.33 (water), respectively. The maximum angle of incidence is 64.5°, corresponding to the objective, which has an NA of 1.2, in water. As Fig. 3(a) clearly shows, the trapping efficiency for radial polarization is larger than those of linear and azimuthal polarizations when the focus is located near the upper surface (Sz = 1) of the particle. The maximum trapping efficiency for a radially polarized beam is approximately 1.2 times larger than that for a linearly polarized one. On the other hand, the maximum efficiency for an azimuthally polarized beam is 0.83 times smaller than that for a linearly polarized one. The transverse trapping efficiencies Qtr for radially and azimuthally polarized beams were calculated [Fig. 3(b)]. Note that the trapping efficiency for a radially polarized beam is smaller than that for an azimuthally polarized one. The maximum trapping efficiencies for radially and azimuthally polarized beams along the transverse direction are 0.31 and 0.34, respectively.

3. Results and discussion

To estimate the trapping efficiency in the axial direction, the minimum laser powers required to hold glass beads with diameters of 5 to 12 μm for radially, azimuthally, and linearly polarized beams are plotted in Fig. 4(a)
Fig. 4 (a) Minimum power to hold a particle as a function of a diameter of glass beads for the incident beams with radial (circles), azimuthal (squares), and linear (triangles) polarization. (b) Corresponding maximum axial trapping efficiency.
. The glass bead diameters were estimated directly from microscope images [14

14. N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 021914 (2007). [CrossRef] [PubMed]

]. Figure 4(a) shows that a radially polarized beam requires the lowest laser power for all the glass bead sizes. On the other hand, the minimum laser power required to hold a bead is the largest for an azimuthally polarized beam. A linearly polarized beam takes intermediate values between those of radial and azimuthal polarizations. The axial trapping efficiency can be derived [Fig. 4(b)] using the relation Fax = Qax n P / c, where Qax is the trapping efficiency, n is the refractive index of the medium, P is the laser power at the focus, and c is the speed of light. For beads with diameters between 5 and 12 μm, the radial polarization has the highest axial trapping efficiency among the three polarization states. Even for radial polarization, the experimentally measured trapping efficiency was approximately 0.1 for all bead sizes, which is less than half of the calculated value. However, the experimental results are qualitatively in agreement with the calculation results shown in Fig. 3(a), because measurements of the axial trapping efficiency often tend to be smaller than those of the transverse trapping efficiency [13

13. H. Felgner, O. Müller, and M. Schliwa, “Calibration of light forces in optical tweezers,” Appl. Opt. 34(6), 977–982 (1995). [CrossRef] [PubMed]

].

Figure 5
Fig. 5 Measured transverse trapping force as a function of laser power for trapping polystyrene beads with nominal diameters of (a) 3 μm, (b) 6 μm, and (c) 9 μm.
shows the measured transverse trapping forces exerted on polystyrene beads with diameters of 3, 6, and 9 μm trapped by radially and azimuthally polarized beams. In all cases, the transverse trapping force of an azimuthally polarized beam was slightly larger than that of a radially polarized beam. The trapping efficiency in the transverse direction, which is given by the relation Ftr = Qtr n P / c, can be obtained from the slope of each line in Fig. 5. The straight lines in Fig. 5 were obtained by the least squares method. For a radially polarized beam, the estimated trapping efficiencies for polystyrene beads with diameters of 3, 6, and 9 μm were 0.34, 0.40, and 0.41, respectively. On the other hand, for an azimuthally polarized beam, the trapping efficiencies for beads with diameters of 3, 6, and 9 μm were 0.36, 0.45, and 0.47, respectively.

In the above experiments, we experimentally observed different trapping efficiencies for different polarization states of the beam. These results are consistent with numerical predictions [5

5. H. Kawauchi, K. Yonezawa, Y. Kozawa, and S. Sato, “Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam,” Opt. Lett. 32(13), 1839–1841 (2007). [CrossRef] [PubMed]

7

7. T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Forces in optical tweezers with radially and azimuthally polarized trapping beams,” Opt. Lett. 33(2), 122–124 (2008). [CrossRef] [PubMed]

]. In the ray optics regime, the higher axial trapping efficiency of radial polarization is explained by the lower reflectivity of the p polarization of a radially polarized beam. Thus, these experimental results demonstrate the advantage of using a radially polarized beam for optical trapping of micrometer-sized particles. They imply that a lower laser power can be employed to manipulate a particle or a living cell when using a radially polarized beam with than when using a linearly or circularly polarized laser beam. In addition, numerical calculations predict that a radially polarized beam is capable of trapping particles with much higher refractive indices such as semiconductors, which are difficult to trap using a conventional laser beam [5

5. H. Kawauchi, K. Yonezawa, Y. Kozawa, and S. Sato, “Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam,” Opt. Lett. 32(13), 1839–1841 (2007). [CrossRef] [PubMed]

,7

7. T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Forces in optical tweezers with radially and azimuthally polarized trapping beams,” Opt. Lett. 33(2), 122–124 (2008). [CrossRef] [PubMed]

].

4. Conclusion

We experimentally demonstrated single-beam optical trapping of micrometer-sized dielectric particles using radially and azimuthally polarized beams. The axial trapping efficiency was measured by trapping a glass bead suspended in water. A radially polarized beam gave the highest trapping efficiency in the axial direction. On the other hand, the transverse trapping efficiency for an azimuthally polarized beam was larger than that for a radially polarized one. These results are qualitatively in agreement with calculations in the ray optics regime.

Acknowledgements

This work was supported in part by Japan Society for the Promotion of Science, and Japan Science and Technology Agency, CREST.

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

2.

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]

3.

S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher-order mode Nd:YAG laser beams,” Electron. Lett. 27(20), 1831–1832 (1991). [CrossRef]

4.

D. Ganic, X. Gan, and M. Gu, “Optical trapping force with annular and doughnut laser beams based on vectorial diffraction,” Opt. Express 13(4), 1260–1265 (2005). [CrossRef] [PubMed]

5.

H. Kawauchi, K. Yonezawa, Y. Kozawa, and S. Sato, “Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam,” Opt. Lett. 32(13), 1839–1841 (2007). [CrossRef] [PubMed]

6.

S. Yan and B. Yao, “Radiation forces of a highly focused radially polarized beam on spherical particles,” Phys. Rev. A 76(5), 053836 (2007). [CrossRef]

7.

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Forces in optical tweezers with radially and azimuthally polarized trapping beams,” Opt. Lett. 33(2), 122–124 (2008). [CrossRef] [PubMed]

8.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009). [CrossRef]

9.

R. Peng, B. Yao, S. Yan, W. Zhao, and M. Lei, “Trapping of low-refractive-index particles with azimuthally polarized beam,” J. Opt. Soc. Am. B 26(12), 2242–2247 (2009). [CrossRef]

10.

M. Michihata, T. Hayashi, and Y. Takaya, “Measurement of axial and transverse trapping stiffness of optical tweezers in air using a radially polarized beam,” Appl. Opt. 48(32), 6143–6151 (2009). [CrossRef] [PubMed]

11.

S. Sato and H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28(1), 1–16 (1996). [CrossRef]

12.

Y. Kozawa, K. Yonezawa, and S. Sato, “Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal,” Appl. Phys. B 88(1), 43–46 (2007). [CrossRef]

13.

H. Felgner, O. Müller, and M. Schliwa, “Calibration of light forces in optical tweezers,” Appl. Opt. 34(6), 977–982 (1995). [CrossRef] [PubMed]

14.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 021914 (2007). [CrossRef] [PubMed]

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

History
Original Manuscript: February 1, 2010
Revised Manuscript: April 5, 2010
Manuscript Accepted: April 14, 2010
Published: May 10, 2010

Virtual Issues
Vol. 5, Iss. 9 Virtual Journal for Biomedical Optics
Unconventional Polarization States of Light (2010) Optics Express

Citation
Yuichi Kozawa and Shunichi Sato, "Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams," Opt. Express 18, 10828-10833 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-10-10828


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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(5), 288–290 (1986). [CrossRef] [PubMed]
  2. 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]
  3. S. Sato, M. Ishigure, and H. Inaba, “Optical trapping and rotational manipulation of microscopic particles and biological cells using higher-order mode Nd:YAG laser beams,” Electron. Lett. 27(20), 1831–1832 (1991). [CrossRef]
  4. D. Ganic, X. Gan, and M. Gu, “Optical trapping force with annular and doughnut laser beams based on vectorial diffraction,” Opt. Express 13(4), 1260–1265 (2005). [CrossRef] [PubMed]
  5. H. Kawauchi, K. Yonezawa, Y. Kozawa, and S. Sato, “Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam,” Opt. Lett. 32(13), 1839–1841 (2007). [CrossRef] [PubMed]
  6. S. Yan and B. Yao, “Radiation forces of a highly focused radially polarized beam on spherical particles,” Phys. Rev. A 76(5), 053836 (2007). [CrossRef]
  7. T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Forces in optical tweezers with radially and azimuthally polarized trapping beams,” Opt. Lett. 33(2), 122–124 (2008). [CrossRef] [PubMed]
  8. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009). [CrossRef]
  9. R. Peng, B. Yao, S. Yan, W. Zhao, and M. Lei, “Trapping of low-refractive-index particles with azimuthally polarized beam,” J. Opt. Soc. Am. B 26(12), 2242–2247 (2009). [CrossRef]
  10. M. Michihata, T. Hayashi, and Y. Takaya, “Measurement of axial and transverse trapping stiffness of optical tweezers in air using a radially polarized beam,” Appl. Opt. 48(32), 6143–6151 (2009). [CrossRef] [PubMed]
  11. S. Sato and H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28(1), 1–16 (1996). [CrossRef]
  12. Y. Kozawa, K. Yonezawa, and S. Sato, “Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal,” Appl. Phys. B 88(1), 43–46 (2007). [CrossRef]
  13. H. Felgner, O. Müller, and M. Schliwa, “Calibration of light forces in optical tweezers,” Appl. Opt. 34(6), 977–982 (1995). [CrossRef] [PubMed]
  14. N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Towards absolute calibration of optical tweezers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 021914 (2007). [CrossRef] [PubMed]

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