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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 11 — Oct. 31, 2012
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Optical forces on submicron particles induced by full Poincaré beams

Li-Gang Wang  »View Author Affiliations


Optics Express, Vol. 20, Issue 19, pp. 20814-20826 (2012)
http://dx.doi.org/10.1364/OE.20.020814


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Abstract

In this paper, we have considered the optical forces acting on submicron particles induced by arbitrary-order full Poincaré (FP) beams. Different from the traditional scalar beams, the optical forces of the FP beams include three contributions: the scattering, gradient, and curl forces. The last contribution is due to both the vectorial properties of the FP beams’ polarization and the rotating phase structure of the FP beams. We analytically derive all components of the optical forces of the FP beams acting on Rayleigh particles. The numerical results show that the optical curl force is very significant to the absorbing Rayleigh particles, and it has the same order with the scattering force. The total vortex force fields and their trapping effects of different order FP beams on the absorbing dielectric and metallic Rayleigh particles are discussed in detail. Our results may stimulate further investigations on the trapping effect of various vector-vortex beams on submicron or nanometer sized objects.

© 2012 OSA

1. Introduction

Optical trapping and manipulation have been widely used in various fields of application in physics, chemistry, and biology for the non-contact advantage, since Ashkin first demonstrated the optical trapping of particles using the radiation force produced by focused Gaussian beams [1

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

], especially starting from the demonstration of single-beam optical trapping (also named as optical tweezers) in 1986 [2

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]

]. Traditionally, optical forces on small particles can be theoretically divided into two contributions: the gradient (or dipole) force and the scattering (or radiation pressure) force. The former is proportional to the gradient of the light intensity, while the latter is proportional to the Poynting vector. For many scalar (or linear-polarized) light fields without vortex phase structures, the usual gradient and scattering light forces provide the well-known descriptions. For the complex-vector or complex-vortex beams, such as radially polarized beams [3

3. 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]

5

5. 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]

], cylindrical vector beams [6

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

, 7

7. Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express 18(10), 10828–10833 (2010). [CrossRef] [PubMed]

], and vortex beams [8

8. J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010). [CrossRef] [PubMed]

], currently most theoretical investigations are based on the ray optics [3

3. 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 [4

4. 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]

, 5

5. 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

8. J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010). [CrossRef] [PubMed]

].

In this paper, we investigate the optical trapping effects of arbitrary-order full Poincaré (FP) beams acting on submicron or nanometer sized particles. The FP beams are very recently proposed by Beckley et. al. [20

20. A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18(10), 10777–10785 (2010). [CrossRef] [PubMed]

], and their main property is that the state of light polarization can span over the entire full Poincaré sphere with changing the azimuthal angle. Soon later, Han et. al. [21

21. W. Han, W. Cheng, and Q. Zhan, “Flattop focusing with full Poincaré beams under low numerical aperture illumination,” Opt. Lett. 36(9), 1605–1607 (2011). [CrossRef] [PubMed]

] further proposed and experimentally demonstrated the second-order FP beams with high-quality flattop profiles. To our best knowledge, the trapping effect of these FP beams has not yet been investigated. Here we focus on their light force effects on small particles, and derive all components of the optical forces of the FP beams acting on Rayleigh particles, and discuss the total vortex force fields and the corresponding trapping effects.

2. Formula of any order FP beams

3. Optical force of the m-th FP beams acting on Rayleigh particles

Usually the optical force, acting on a Rayleigh particle, is split into two parts: the gradient and scattering forces. However, since 2000 [9

9. P. C. Chaumet and M. Nieto-Vesperinas, “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett. 25(15), 1065–1067 (2000). [CrossRef] [PubMed]

], one has gradually realized that there is an additional term contributed from the non-uniform distribution of polarization of light [12

12. S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009). [CrossRef] [PubMed]

]. Now it is well known that for continuous-wave harmonic vector light fields, the timed-averaged optical force on a Rayleigh particle is given by [11

11. V. Wong and M. A. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B 73(7), 075416 (2006). [CrossRef]

, 12

12. S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009). [CrossRef] [PubMed]

]
F=14Re(α)|E|2+k2Im(α)Re(E*×B)+12Im(α)Im[(E*)E],
(6)
where α is the complex polarizability, which can be given by [22

22. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef]

]
α=α01iα0k3/(6πε0)
(7)
for a spherical particle with its radius amuch smaller than the light wavelength λ, and
α0=4πε0a3(εp/εm)1(εp/εm)+2
(8)
is the well known Clausius-Mossotti relation. In the above equations, k=ω/c, ε0 is the vacuum’s permittivity, c is the speed of light in vacuum, and εp and εm are the relative permittivities of the particle and the surrounding medium, respectively. In Eq. (6), the first term is known as the traditional gradient force, and the second term is the dissipative radiation-pressure force, and it can be simplified into the scattering force for non-absorption systems. The third term is recently explained as the optical curl force associated to the non-uniform distribution of the spin density of the light field [12

12. S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009). [CrossRef] [PubMed]

]. For our cases of the FP beams, the optical curl force is associated with the distributions of both the azimuthal phase and rotating polarization.

In our case, we consider a paraxial FP beam radiating on a Rayleigh spherical particle, as shown in Fig. 1(a). For a FP beam, its polarization changes as the azimuthal angle φ varies and gradually rotates as the beam propagates along the zaxis. Substituting Eq. (4) into Eq. (6), after tedious calculations, we can analytically obtain the components of optical force due to different contributions as follows:
Fg,x=Re[α]I02Pε0cxw2(z){1+Ω2[1mw2(z)2(x2+y2)]},
(9a)
Fg,y=Re[α]I02Pε0cyw2(z){1+Ω2[1mw2(z)2(x2+y2)]},
(9b)
Fg,z=Re[α]I02P2ε0cz(z2+ZR2)[2(x2+y2)w2(z)(Ω2+1)Ω2(m+1)1],
(9c)
Fs,x=Im[α]P2ε0cεmI0Ω{krz2+ZR2[zΩcosφzsinφcos(m(ϕφ))+ZRsinφsin(m(ϕφ))]mrΩsinφ},
(9d)
Fs,y=Im[α]P2ε0cεmI0{krz2+ZR2[zsinφ+zΩcosφcos(m(ϕφ))ZRΩcosφsin(m(ϕφ))]+mrΩsin[m(ϕφ)+φ]},
(9e)
Fs,z=Im[α]P2ε0cεmI0{k(1+Ω2)[1r2(z2ZR2)2(z2+ZR2)2]ZRz2+ZR2(mΩ2+Ω2+1)},
(9f)
Fc,x=Im[α]PI0kr2ε0c(z2+ZR2){zcosφ+Ωsinφ(zcos[m(ϕφ)]ZRsin[m(ϕφ)])},
(9g)
Fc,y=Im[α]PI0Ω2ε0c{krz(z2+ZR2)(Ωsinφ+cosφcos[m(ϕφ)])+krZR(z2+ZR2)cosφsin[m(ϕφ)]mrsin[m(ϕφ)+φ]+mrΩcosφ},
(9h)
where I0=|E0|2, φ=tan1(y/x), and P denotes the input laser power. In the above, the subscripts “g” and “s” denote the components of the gradient and scattering forces, respectively; the subscript “c” denotes the contribution of the optical curl force due to the third term in Eq. (6), i.e., due to the non-uniform distribution of light polarization, which only affects the transverse optical force for the paraxial vector beams; and the subscripts “x”, “y” and “z” on the forces denote the directions of the force’s components. Therefore, using Eqs. (9a)-(9h), we can easily obtain the components of the resultant optical force along the x, y and z directions, as follows:
Fx=Fg,x+Fs,x+Fc,x,
(10a)
Fy=Fg,y+Fs,y+Fc,y,
(10b)
Fz=Fg,z+Fs,z.
(10c)
Thus we can analyze the trapping effects of any order FP beams acting on the Rayleigh particles. It should be pointed out that, in our Eqs. (2)-(4) we have used the paraxial condition which will be violated for a tight-focusing condition when the beam spot size is smaller than the wavelength (i.e., 2w0<λ). In Ref [23

23. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996). [CrossRef]

], one use an important dimensional parameter, s=1/(kw0)=λ/(2πw0), to describe the accuracy of the paraxial approximation. When γ=π/3, the paraxial condition is very well. In our case, we will takew0=2λ, so s=0.08. Therefore the parameters used in our calculations still give out the sufficient accuracy with small uncertainty (close to the weak-focusing condition).

In the following section, we will show how the order number m affects on the trapping efficiency and how important the optical curl forces (Fc,x and Fc,y) are when the Rayleigh particles are the absorbing media.

4. Numerical results and discussions

Without loss of generality, in all our simulations we choose the following parameters: λ=500nm, m=2µm, P=1W, εm=1 (for air). Other parameters will be given out in the text.

First, let us discuss the magnitude and direction distributions of different force components due to the different physical contributions under two cases: non-absorbing and absorbing dielectric particles in Fig. 2
Fig. 2 The magnitude and direction distributions of (a) the gradient force, (b) the curl force, (c) the scattering force, and (d) total force in the plane of z=0 for the FP beam with m=1 and γ=π/4. Other parameters are a=50nm and εp=2.56 (no absorption).
and Fig. 3
Fig. 3 The magnitude and direction distributions of (a) the gradient force, (b) the curl force, (c) the scattering force, and (d) total force in the plane of z=0 for the FP beam with m=1 and γ=π/4. Other parameters are a=50nm and εm=2.56+i2.56 (with absorption).
, respectively. For a non-absorbing particle, it is clear that the magnitude of the transverse gradient force in Fig. 2(a) is greatly larger than those of the curl and scattering forces, therefore the total transverse force is mainly manifesting the transverse restoring force, see Fig. 2(d). It is also shown that the magnitude of the curl force is the same order with that of the scattering force, see Figs. 2(b)-2(c) and Figs. 3(b)-3(c). Actually, in our case the optical curl force is also a kind of scattering force originated from the curl of the light angular momentum including the orbital and spin angular momentums, as pointed out in Ref [12

12. S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009). [CrossRef] [PubMed]

]. For a strong-absorbing particle, the magnitudes of both the curl and scattering forces can be comparable to or larger than that of the gradient force by comparing Figs. 3(b)-3(c) with Fig. 3(a). Therefore the total transverse optical force may demonstrate the swirling force field. Comparing Fig. 2 with Fig. 3, it is shown that, the imaginary part of the particle’s permittivity has more impact on the magnitudes of the curl and scattering forces than that of the gradient force, which results in the vortex force field in Fig. 3(d) although the relative vector distributions of the curl and scattering forces are the same in both Figs. 2(b-c) and Figs. 3(b-c) except for their magnitudes.

For better to understand the distinct property of the FP beams, Fig. 4
Fig. 4 The magnitude and direction distributions of (a) the gradient force, (b) the curl force, (c) the scattering force, and (d) total force in the plane of z=0 for a linear-polarized Gaussian beam. Other parameters are the same as in Fig. 3.
and Fig. 5
Fig. 5 The magnitude and direction distributions of (a) the gradient force, (b) the curl force, (c) the scattering force, and (d) total force in the plane of z=0 for a linear-polarized LG01 beam. Other parameters are the same as in Fig. 3.
, respectively, plot the forces of a linear-polarized Gaussian beam and a linear-polarized LG01 beam for z=0 and γ=π/2 in Eq. (1). The other parameters are the same as in Fig. 3. From Fig. 4, we can see that both the transverse curl and scattering forces are zeros and the total transverse force is only contributed from the gradient force for a linear-polarized paraxial Gaussian beam, and these are very different from that of the FP beam (Fig. 2 and Fig. 3). The result obtained in Fig. 4 is actually the same as that in Ref [14

14. I. Iglesias and J. J. Sáenz, “Scattering forces in the focal volume of high numerical aperture microscope objectives,” Opt. Commun. 284(10-11), 2430–2436 (2011). [CrossRef]

] under the paraxial approximation. For a linear-polarized LG01 beam, see Fig. 5, the gradient force in the center region is pointing to outside due to the doughnut shape, and the curl and scattering forces are, respectively, non-zeros in the yand x directions with the same magnitudes. In Fig. 5, we still can see that the transverse curl and scattering forces provide the rotation effect. However, by comparing the results of the first-order FP beam with a linear polarized LG01 beam, see Figs. 3(a)-3(d) with Figs. 5(a)-5(d), it is found that, the curl and scattering forces of the FP beam are more complex than those of the linear-polarized beam, and the resultant force distribution of the FP beam at the plane of z=0 has a more stable rotation structure than that of the LG01 beam.

In order to show how the light polarization affects on the resultant optical force, we plot Figs. 6
Fig. 6 Distributions of (a-c) the beam intensities and the states of polarization (different ellipses), and the magnitude and direction distributions of (d-f) the sum of the curl and scattering forces, and (g-i) the total transverse force at different planes: (a), (d), and (g) for z=0.5ZR, (b), (e), and (h) for z=0, and (c), (f), and (i) for z=0.5ZR. Other parameters are the same as in Fig. 3.
and 7
Fig. 7 Distributions of (a-c) the beam intensities and the states of polarization (different ellipses), and the magnitude and direction distributions of (d-f) the sum of the curl and scattering forces, and (g-i) the total transverse force at the different planes: (a), (d), and (g) for z=0.5ZR, (b), (e), and (h) for z=0, and (c), (f), and (i) for z=0.5ZR, with m=3 and γ0.356π. Other parameters are the same as in Fig. 3.
, as examples, to demonstrate the rotation of the optical force resulted from the rotation of the non-uniform polarization states as the beam propagates. In Fig. 6, for the first-order FP beam (m=1), as the beam propagates from z=0.5ZR to z=0.5ZR, the force field of the sum of the curl and scattering force gradually rotates and changes as the state of non-uniform polarization gradually rotates on the entire Poincaré sphere with changing the position z, see Figs. 6(d)-6(f). Combining with the centripetal distribution of the gradient force, the total transverse force demonstrates a bound rotating vortex field, see Figs. 6(g)-6(i), which provides a transverse stable but rotating trapping effect on the Rayleigh particle. There are similar result in the case of m=3, see Fig. 7, however the region of the vortex force field becomes larger and more complex in this case.

Now let us turn to discuss the effect of the particle’s absorption on the transverse optical force in detail. Since the transverse gradient force is always a centripetal force as a restoring force and it is also weakly affected by the particle’s absorption, also see Figs. 2 and 3, we use the maximal value of the transverse gradient force as a reference to compare the maximal curl and scattering forces with the corresponding gradient force. Figure 9
Fig. 9 Dependence of (a) Fcmax/Fgmax, (b) Fsmax/Fgmax, and (c) |Fc+Fs|max/Fgmax on the absorption factor Im[εp] for the cases of the different particle’s sizes, under the radiation of the FP beam with m=1 and γ=0.25π.
plots the dependences of the ratios of Fcmax/Fgmax, Fsmax/Fgmax, and |Fc+Fs|max/Fgmax on the imaginary part of the particle’s permittivity. Here all these forces are in the xy plane at z=0. It is found that with the increasing of Im[εp], the maximal optical curl and scattering forces increase and trend to be nearly the same order with the maximal gradient force. For the larger-sized particles, the ratios of the optical curl and scattering forces to the gradient force are much larger than the cases for the smaller-sized particles. This indicates that it is more efficiency to rotate the larger-sized particles with the large value of Im[εp].

Figure 10
Fig. 10 Dependence of (a) Fcmax/Fgmax, (b) Fsmax/Fgmax, and (c) (Fc+Fs)max/Fgmax on the order value m with a=50nm and εp=2.56+2.56i. Other parameters are γ=0.25π for m=1, γ=π/3 for m=2, γ=0.356π for Re[εp], λ= for m=4, and γ=0.373π for m=5.
shows the effect of the order number m on the ratios of Fcmax/Fgmax, Fsmax/Fgmax, and |Fc+Fs|max/Fgmax, under the fixed parameters of Im[εp] and the particle’s size. It is clear seen that these ratios are increasing with the increase of m, which indicate that the higher-order FP beam may have powerful ability to rotate the particle in the transverse plane under the same input power. Here we would like to point out that the model we used [see Eqs. (1)-(3)] can be optimized by replacing a single w0with two independent adjustable parametersw0x and w0y in Eqs. (2) and (3). Then the result of the trapping effect can be further improved.

In the above calculations, we have used the large value of Im[εp]. Actually, for the nano-scaled metallic particles, such large values of Im[εp] are possible. As examples, we have considered the distributions of total transverse optical forces of the second-order FP beam acting on the Al and Au nano-scaled particles with the size of a=50nm, see Fig. 11
Fig. 11 Distributions of the total transverse optical forces (in the unit of pN) of the second-order FP beam acting on (a-c) the Al nano-particle and (d-f) the Au nano-particle at different positions: (a) and (d) for z=0.5ZR, (b) and (e) for z=0, and (c) and (f) for z=0.5ZR. Other parameters are m=2 and γ=π/3.
. For an Al particle, its permittivity is εp=36.373+i9.412 at the wavelength λ=500nm [25

25. A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93(1), 139–143 (2008). [CrossRef]

]; while for an Au particle, its permittivity is εp=2.81+i3.18 at the same wavelength [10

10. J. R. Arias-González and M. Nieto-Vesperinas, “Optical forces on small particles: attractive and repulsive nature and plasmon-resonance conditions,” J. Opt. Soc. Am. A 20(7), 1201–1209 (2003). [CrossRef] [PubMed]

]. From Fig. 11, we can see that, for the metallic nano particles with the larger negative value of Re[εp] and the larger absorption, the vortex optical force field is very stable and it can rotate the particle along the dashed circle, see Figs. 11(a)-11(c). Of course, for the different order FP beam, the detailed distribution of the vortex force field may be different but the qualitative conclusion is similar. However, for the Au nano particle, at the operating wavelength, with the smaller value of Re[εp], the transverse stable rotating region [see the dashed circle in Figs. 11(d)-11(f)] will become larger and larger as the beam propagates along the z direction. From Fig. 11(d) to Fig. 11(f), we can see that, at z=0.5ZR, the resultant optical force field will drive the particle rotating into the center; while at z=0.5ZR, the particle may be spirally pushed out from the center to the outside region. The numerical results tell us that under certain parameters, the particle may be rotated out from the center. The condition for obtain the stable vortex force field should be further investigated.

5. Conclusion

We have investigated the optical radiation force of the arbitrary order FP beam acting on the non-absorbing or absorbing dielectric Rayleigh particles and metallic Rayleigh particles. Due to the vector and rotation properties of the FP beams’ polarizations, it is found that the optical curl force due to the present of the non-uniform polarization becomes significant to the absorbing Rayleigh particles, and it has the same order with the scattering force. The result shows that for the strong-absorbing particles, both the transverse curl and scattering force of the FP beams can be comparable to or larger than the transverse gradient force, and the total transverse optical force will present the rotating-vortex force field. For the very-weak or non-absorbing Rayleigh particles, the longitudinal force may provide the stable trapping effect, mainly due to the longitudinal gradient force. As the order number m of the FP beams increases, the rotating effect becomes more and more powerful in the transverse plane under the same input laser power. For the metallic Rayleigh particles with large negative Re[εp] and positive Im[εp], the actual trapping effect is stably trapped and rotated in the transverse plane. Our results are useful for analyzing the trapping and rotating effects of different order FP beams acting on the absorbing Rayleigh particles.

Acknowledgments

This work was supported by National Natural Science Foundation of China (No. 61078021), and the National Basic Research Program of China (Grant No. 2012CB921602).

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, 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.

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]

4.

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]

5.

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]

6.

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

7.

Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express 18(10), 10828–10833 (2010). [CrossRef] [PubMed]

8.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010). [CrossRef] [PubMed]

9.

P. C. Chaumet and M. Nieto-Vesperinas, “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett. 25(15), 1065–1067 (2000). [CrossRef] [PubMed]

10.

J. R. Arias-González and M. Nieto-Vesperinas, “Optical forces on small particles: attractive and repulsive nature and plasmon-resonance conditions,” J. Opt. Soc. Am. A 20(7), 1201–1209 (2003). [CrossRef] [PubMed]

11.

V. Wong and M. A. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B 73(7), 075416 (2006). [CrossRef]

12.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009). [CrossRef] [PubMed]

13.

X.-L. Wang, J. Chen, Y. Li, J. Ding, C.-S. Guo, and H.-T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010). [CrossRef] [PubMed]

14.

I. Iglesias and J. J. Sáenz, “Scattering forces in the focal volume of high numerical aperture microscope objectives,” Opt. Commun. 284(10-11), 2430–2436 (2011). [CrossRef]

15.

I. Iglesias and J. J. Sáenz, “Light spin forces in optical traps: comment on “Trapping metallic Rayleigh particles with radial polarization”,” Opt. Express 20(3), 2832–2834 (2012). [CrossRef] [PubMed]

16.

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization: reply to comment,” Opt. Express 20(6), 6058–6059 (2012). [CrossRef] [PubMed]

17.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011). [CrossRef]

18.

J. J. Sáenz, “Optical forces: Laser tractor beams,” Nat. Photonics 5(9), 514–515 (2011). [CrossRef]

19.

A. V. Novitsky and D. V. Novitsky, “Negative propagation of vector Bessel beams,” J. Opt. Soc. Am. A 24(9), 2844–2849 (2007). [CrossRef] [PubMed]

20.

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18(10), 10777–10785 (2010). [CrossRef] [PubMed]

21.

W. Han, W. Cheng, and Q. Zhan, “Flattop focusing with full Poincaré beams under low numerical aperture illumination,” Opt. Lett. 36(9), 1605–1607 (2011). [CrossRef] [PubMed]

22.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef]

23.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996). [CrossRef]

24.

L.-G. Wang and H.-S. Chai, “Revisit on dynamic radiation forces induced by pulsed Gaussian beams,” Opt. Express 19(15), 14389–14402 (2011). [CrossRef] [PubMed]

25.

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93(1), 139–143 (2008). [CrossRef]

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation
(260.5430) Physical optics : Polarization

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: June 29, 2012
Revised Manuscript: August 10, 2012
Manuscript Accepted: August 20, 2012
Published: August 27, 2012

Virtual Issues
Vol. 7, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Li-Gang Wang, "Optical forces on submicron particles induced by full Poincaré beams," Opt. Express 20, 20814-20826 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-19-20814


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References

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