## Numerical study of the properties of optical vortex array laser tweezers |

Optics Express, Vol. 21, Issue 22, pp. 26418-26431 (2013)

http://dx.doi.org/10.1364/OE.21.026418

Acrobat PDF (4816 KB)

### Abstract

Chu *et al*. constructed a kind of Ince-Gaussian modes (IGM)-based vortex array laser beams consisting of *p* x *p* embedded optical vortexes from Ince-Gaussian modes, *IG ^{e}_{p,p}* modes [Opt. Express

**16**, 19934 (2008)]. Such an IGM-based vortex array laser beams maintains its vortex array profile during both propagation and focusing, and is applicable to optical tweezers. This study uses the discrete dipole approximation (DDA) method to study the properties of the IGM-based vortex array laser tweezers while it traps dielectric particles. This study calculates the resultant force exerted on the spherical dielectric particles of different sizes situated at the IGM-based vortex array laser beam waist. Numerical results show that the number of trapping spots of a structure light (i.e. IGM-based vortex laser beam), is depended on the relation between the trapped particle size and the structure light beam size. While the trapped particle is small comparing to the beam size of the IGM-based vortex array laser beams, the IGM-based vortex array laser beams tweezers are suitable for multiple traps. Conversely, the tweezers is suitable for single traps. The results of this study is useful to the future development of the vortex array laser tweezers applications.

© 2013 Optical Society of America

## 1. Introduction

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

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

3. A. Ashkin and J. M. Dziedzic, “Observation of light scattering from nonspherical particles using optical levitation,” Appl. Opt. **19**(5), 660–668 (1980). [CrossRef] [PubMed]

4. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science **235**(4795), 1517–1520 (1987). [CrossRef] [PubMed]

5. K. Dholakia and P. Zemánek, “Colloquium: Gripped by light: Optical binding,” Rev. Mod. Phys. **82**(2), 1767–1791 (2010). [CrossRef]

6. Y. Liu and M. Yu, “Multiple traps created with an inclined dual-fiber system,” Opt. Express **17**(24), 21680–21690 (2009). [CrossRef] [PubMed]

7. K. T. Gahagan and G. A. Swartzlander Jr., “Optical vortex trapping of particles,” Opt. Lett. **21**(11), 827–829 (1996). [CrossRef] [PubMed]

8. D. W. Zhang and X.-C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett. **28**(9), 740–742 (2003). [CrossRef] [PubMed]

9. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science **292**(5518), 912–914 (2001). [CrossRef] [PubMed]

12. J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. **198**(1-3), 21–27 (2001). [CrossRef]

*et al*. construct a kind of IGM-based vortex array laser beams consisting

*p*x

*p*embedded optical vortexes from Ince-Gaussian modes,

*IG*modes [13

^{e}_{p,p}13. S.-C. Chu, C.-S. Yang, and K. Otsuka, “Vortex array laser beam generation from a Dove prism-embedded unbalanced Mach-Zehnder interferometer,” Opt. Express **16**(24), 19934–19949 (2008). [CrossRef] [PubMed]

13. S.-C. Chu, C.-S. Yang, and K. Otsuka, “Vortex array laser beam generation from a Dove prism-embedded unbalanced Mach-Zehnder interferometer,” Opt. Express **16**(24), 19934–19949 (2008). [CrossRef] [PubMed]

14. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A **11**(4), 1491–1499 (1994). [CrossRef]

21. B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. I. superthermal spin-up,” Astrophys. J. **470**, 551–565 (1996). [CrossRef]

## 2. IGM-based vortex array laser beams [1313. S.-C. Chu, C.-S. Yang, and K. Otsuka, “Vortex array laser beam generation from a Dove prism-embedded unbalanced Mach-Zehnder interferometer,” Opt. Express **16**(24), 19934–19949 (2008). [CrossRef] [PubMed]

]

**16**(24), 19934–19949 (2008). [CrossRef] [PubMed]

## 3. Approach to calculate optical force of IGM-based vortex array laser tweezers

### 3.1 Discrete-dipole approximation (DDA) method [1414. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A **11**(4), 1491–1499 (1994). [CrossRef]

–2121. B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. I. superthermal spin-up,” Astrophys. J. **470**, 551–565 (1996). [CrossRef]

]

14. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A **11**(4), 1491–1499 (1994). [CrossRef]

21. B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. I. superthermal spin-up,” Astrophys. J. **470**, 551–565 (1996). [CrossRef]

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

18. R. Schmehl, B. M. Nebeker, and E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two-dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A **14**(11), 3026–3036 (1997). [CrossRef]

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

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

18. R. Schmehl, B. M. Nebeker, and E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two-dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A **14**(11), 3026–3036 (1997). [CrossRef]

19. J. J. Goodman, B. T. Draine, and P. J. Flatau, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Opt. Lett. **16**(15), 1198–1200 (1991). [CrossRef] [PubMed]

16. A. G. Hoekstra, M. Frijlink, L. B. Waters, and P. M. Sloot, “Radiation forces in the discrete-dipole approximation,” J. Opt. Soc. Am. A **18**(8), 1944–1953 (2001). [CrossRef] [PubMed]

*> can be separated into two components, incident force <*

_{i}**F**

*> and scattering force <*

_{inc,i}**F**

*>:where <*

_{sca,i}**F**

*> due to the gradient of the incident field and <*

_{inc,i}**F**

*> due to the fields radiated by all other dipoles except dipole*

_{sca,i}**F**

*> and <*

_{inc,i}**F**

*> can be founded in Ref [17*

_{sca,i}17. L. Ling, F. Zhou, L. Huang, and Z.-Y. Li, “Optical forces on arbitrary shaped particles in optical tweezers,” J. Appl. Phys. **108**(7), 073110 (2010). [CrossRef]

### 3.2 Relations between cutting dipole number in the DDA method and simulation precision

24. The Language of Technical Computing, http://www.mathworks.com/.

*resultant force on a spherical dielectric particle due to an incident plane wave*.

*”*This study used the drafted DDA code to simulate the same situation, and then compared the DDA results with the exact solutions of the Lorentz-Mie scattering theory. It gave us the estimations of how many

*cutting dipole numbers*should be used in the coming simulations of section 4.

*resultant force on a spherical dielectric particle due to an incident plane wave*” using both the drafted DDA code and the Lorentz-Mie scattering theory. Comparing the results from two approaches gave us “the relation between the

*particle cutting rate*and the

*relative error*of the DDA calculations”. Figure 2(a) shows the extinction efficiency

*Q*

_{ext}at different

*size parameter x*( = 2

*πa*/

*λ*), where

*λ*is the incident plane wave wavelength. Figure 2(b) shows the relative error of DDA-calculations in

*Q*

_{ext}at different size parameter

*x*. Figure 2(c) shows the scattering efficiency times the asymmetry parameter,

*gQ*

_{sca}, at different

*x*. Figure 2(d) shows the relative error of DDA-calculations in

*gQ*

_{sca}at different

*x*. In Fig. 2, the black dotted line shows the results of the Lorentz-Mie scattering theory. The red, blue, purple and green dotted lines show the results of DDA calculations with cutting dipole number N = 512, 4096, 13824 and 32768, respectively. In Fig. 2, when N = 4096, the error in the extinction efficiency

*Q*

_{ext}and the error in the scattering efficiency times the asymmetry parameter,

*gQ*

_{sca}, are both smaller than 4%. When N = 32768, both errors are smaller than 2%. This study used

*particle-decomposing space of (lattice) number*N = 32768 in all of the following DDA calculations to ensure that the relative errors of all results are smaller than 2%. It is because the accuracy of the calculated values,

*Q*

_{ext}and

*gQ*

_{sca}, of three situations (i.e., with cutting dipole number N = 4096, N = 13824, and N = 32768) are both very high, three curves in both Figs. 2(a) and 2(c) are almost overlapped and are hard to be visually distinguished.

## 4. Numerical results and discussions

*λ*is 1.064μm, beam waist

*w*

_{0}is 1.0μm. In all of the simulations, the vortex array laser beams propagate along the

*z*-axis with linear polarization along

*x*-axis. The particles are silicon spheres with refractive index

*n*= 1.59, and the surrounding medium is water with refractive index

*n*= 1.33. Sections 4.1 and 4.2 show the simulation results of several different-size particles trapped by

*p*= 2 and

*p*= 4 IGM-based vortex array laser tweezers, respectively. This study uses the symbol

*a*to denote the trapped particle radius. The following numerical results of section 4 are all shown in a 6μm x 6μm window situated at the beam waist

*x*-

*y*plane.

### 4.1 p = 2 Vortex array laser beam

*p*= 2 IGM-based vortex array laser tweezers while the surrounding media is water. Figure 3(a) shows the intensity distribution of the

*p*= 2 vortex array laser beam. The trapped particle radius in results, in Figs. 3(b)–3(f), are 0.1µm, 0.3µm, 0.5µm, 0.7µm and 1.0µm, respectively. In Figs. 3(b)–3(f), the color background plots the distributions of the normalized absolute value of the resultant force on the trapped particle with particle transverse

*x*-

*y*position, where the force values are normalized by the resultant peak force value in the calculated region. The dark arrows in Figs. 3(b)–3(f) show the

*vector of resultant force*on the particle while the particle is situated at the position of the arrow tail.

*p*= 2 IGM-based vortex array laser beam while the trapped particle radius are smaller than 0.5µm. In Fig. 3(e), the most part of the resultant force vectors still point to five spots, but the resultant forces on the particle in the region between the center trapping spot and outer four trapping spots are relative weak. Besides, the center trapping spot is much larger than the four outer trapping spots. That is, the probability that the particle be trapped in the center trapping spot is much higher than the particle be trapped at four outer trapping spots as the particle radius is 0.7µm. However, in Fig. 3(f), the resultant forces on the particle only point to the center of the vortex array laser beam. The results shows that the

*p*= 2 IGM-based vortex array laser tweezers tend to trap particles at the beam center when the trapped particle has a large radius

*a.*In this situation (i.e.

*a*= 1.0µm), the IGM-based vortex array laser tweezers behave likes a conventional linear polarized lowest-order Gaussian beam tweezers, i.e. the tweezers tend to trap particles at the beam center.

*p*= 2 IGM-based vortex array laser tweezers changes from five into one. The “number of trapping spots” means the number of regions that particle could be trapped by the vortex array laser beams. Note that the number of trapping spots of a vortex array laser beam does not suddenly change at a specific particle radius. Figure 3 shows that, as the trapped particle size is increasing, the resultant force vectors gradually change their directions from “toward multiple trapping spots” to “toward single center trapping spot.” Firstly, the results shows that

*the number of trapping spots of a structure light (here, p = 2 IGM-based vortex laser beam), depends on the trapped particle size.*Fig. 3 also shows that

*the particle-trapped position of a same structure light is dependent on the trapped particle size*. It implies that once we put some different-size particles into the IGM-based vortex laser beam tweezers, only the smaller particles can be trapped at the positions apart from the beam center. Secondly, Fig. 3 also shows that “

*different-size particles suffer different resultant force distributions while being situated under a same IGM-based vortex laser beam field.*” Both interesting behaviors of the vortex array laser beam can be applied to the particle-separation microfluidics system. To integrate the vortex array laser beam with the microchip fluidics system [27

27. R.-J. Yang, C.-C. Chang, S.-B. Huang, and G.-B. Lee, “A new focusing model and switching approach for electrokinetic flow inside microchannels,” J. Micromech. Microeng. **15**(11), 2141–2148 (2005). [CrossRef]

29. M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, “Microfluidic sorting of mammalian cells by optical force switching,” Nat. Biotechnol. **23**(1), 83–87 (2005). [CrossRef] [PubMed]

### 4.2 p = 4 Vortex array laser beam

*p*= 4 vortex array laser beam. The trapped particle radius in results, in Figs. 4(b)–4(f), are 0.1µm, 0.3µm, 0.5µm, 1.0µm and 1.5µm, respectively.

*p*= 4 IGM-based vortex array laser beam, shown in Fig. 4(a). That is, the trapped particles tend to be trapped at the nine bright spots on the square structure and the four bright spots outside the square structure of the

*p*= 4 GM-based vortex array laser tweezers. It implies that the tweezers can trap at least thirteen particles when the trapped particle radii are smaller than 0.1µm. In Fig. 4(c), the resultant force vectors also point to the thirteen spots, but part of resultant force become weaker, i.e. the trapping forces of some particle-trapped spots become weaker when the trapped particle radius is 0.3µm. In Fig. 4(d), the resultant force vectors inside the beam square structure point to the center of the square structure. It shows that the number of trapping spots of the tweezers is now only five, while the trapped particle radii are 0.5µm. The situation of Fig. 4(e) is similar to Fig. 3(e). As the particle size growing larger (i.e.

*a*= 1.0µm), though the particle can still be trapped at five particle-trapped spots, the possibility for the particle to be trapped at the outer four particle-trapped spots become small. The particle of radius 1.0µm tends to be trapped at the beam center. In Fig. 4(f), the results shows that the

*p*= 4 IGM-based vortex array laser tweezers can only trap particles at the beam center when the trapped particle have a large radius:

*a*= 1.5µm. Similarly, in this situation (i.e.

*a*= 1.5µm), the

*p*= 4 IGM-based vortex array laser tweezers behave like a conventional linear polarized lowest-order Gaussian beam tweezers, i.e. the tweezers tend to trap particles at the beam center.

## 5. Discussion

### 5.1 The change in the ratio between the scattering force and the incident force

_{sca,max}/F

_{inc,max}, with the trapped particle radius

*a*. As the particle radius increases, the ratio F

_{sca,max}/F

_{inc,max}increases, and the change in the ratio F

_{sca,max}/F

_{inc,max}is at a great scale. It means that when the ratio of the particle radius to the beam waist

*a/w*

_{0}increases, the portion of incident field that interacts with the particle will increase, i.e. the incident field will be strongly scattered by the trapped particle. Equation (7) shows that total resultant force on a trapped particle is the sum of the incident force and the scattering force. At the same time, Fig. 5 shows that when the trapped particle radius is 10% of the beam waist, the ratio F

_{sca,max}/F

_{inc,max}is smaller than 0.01., i.e. in this situation, most of the resultant force on the trapped particle is from the incident force. In means that the force acting on the particle is very close to the gradient of the incident light field in this situation. Thus, while trapping small particles (the value

*a/w*

_{0}is small) by IGM-based vortex array laser tweezers, the particle-trapping position will be the bright spots of the IGM-based vortex array laser beams. Since there are multiple bright spots in the IGM-based vortex array laser beam distribution, the vortex array laser tweezers are suitable as multiple traps for small particles. On the contrary, when the trapped particle radius becomes larger, the ratio F

_{sca,max}/F

_{inc,max}grows larger, i.e. the resultant force on the trapped particle will gradually depart from the gradient of the incident light field. Simulation results of section 4 show that as the trapped particle radius increases, the number of trapping spots of the vortex array laser tweezers will decrease. Finally, the vortex array laser tweezers can only trap particles at the beam center, which is similar to the conventional linear polarized lowest-order Gaussian beam tweezers.

### 5.2 The influence on the resultant force of a particle while an additional particle exists

*the existence of a large particle at the beam center will not frustrate the trapping of the smaller particle at the outer trapping spots.*The green arrows in Fig. 6 indicate the original trapped location of the smaller particle while there is only the small particle under the vortex array laser beam. Comparing Figs. 6(a) and 6(b) shows that the existence of an additional large trapped particle may only shift the trapped location of other small particle to a little degree. And a lager additional particle leads to more influence on the small particle than a smaller additional particle. The results are not surprised, since the scattering field of large particle is larger than a small particle. Besides, as what we already knew, the scattering force/field from a large particle is much larger than a small particle. Thus, Figs. 6(a) and 6(b) have shown enough proof that,

*no matter the additional trapped particle at the beam center is large or small, the vortex array laser beam still can trap smaller particle at the outer trapping spots at the same time.*Fig. 6(c) is just an auxiliary proof, which shows that above statements will not be violated as increasing the size of trapping particle at the outer trapping spots. The results of this section also implies that the resultant force distributions this study find (i.e., Figs. 4 and 5) are of great value for the reference in situation that trapping multiple particles by vortex array laser beams at the same time.

### 5.3 The similarity of as the dimension scaling

*a*and beam waist

*w*

_{0}. It is interesting to learn that while keeping the ratio

*a/w*

_{0}, the resultant force distribution on the trapped particle is almost the same for all IGM-based vortex array laser tweezers. For example, Fig. 7 shows two resultant force distributions of

*p*= 4 IGM-based vortex array laser tweezers. In two groups of simulations, “Figs. 7(a) and 7(b)” and “Figs. 7(c) and 7(d)”, we keep the laser beam waist and trapped particle radius different, but keep the ratio

*a/w*

_{0}= 0.1 and the ratio

*a/w*

_{0}= 0.3, respectively. In Figs. 7(a)–7(d), the particle radius and beam waist are: (

*w*

_{0}= 1.0µm,

*a*= 0.1µm), (

*w*

_{0}= 10µm,

*a*= 1µm), (

*w*

_{0}= 1.0µm,

*a*= 0.3µm) and (

*w*

_{0}= 3.0µm,

*a*= 0.9µm), respectively. The resultant force vector (dark arrows) in Figs. 7(a) and 7(b) are almost same. Also, the resultant force vectors (dark arrows) in Figs. 7(c) and 7(d) are almost same. In other words, as in discussing the property of the IGM-based vortex array laser tweezers, the ratio

*a/w*

_{0}is the key parameter, i.e. the number of trapping spots of IGM-based vortex laser tweezers is closely dependent on the relation between the trapped particle size and the trapping beam size.

## 6. Conclusions

## Acknowledgments

## References and links

1. | A. Ashkin, “Acceleration and trapping of particles by radia-tion pressure,” Phys. Rev. Lett. |

2. | A. Ashkin and J. M. Dziedzic, “Optical levitation by radia-tion pressure,” Appl. Phys. Lett. |

3. | A. Ashkin and J. M. Dziedzic, “Observation of light scattering from nonspherical particles using optical levitation,” Appl. Opt. |

4. | A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science |

5. | K. Dholakia and P. Zemánek, “Colloquium: Gripped by light: Optical binding,” Rev. Mod. Phys. |

6. | Y. Liu and M. Yu, “Multiple traps created with an inclined dual-fiber system,” Opt. Express |

7. | K. T. Gahagan and G. A. Swartzlander Jr., “Optical vortex trapping of particles,” Opt. Lett. |

8. | D. W. Zhang and X.-C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett. |

9. | L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science |

10. | Y. Song, D. Milam, and W. T. Hill Iii, “Long, narrow all-light atom guide,” Opt. Lett. |

11. | X. Xu, K. Kim, W. Jhe, and N. Kwon, “Efficient optical guiding of trapped cold atoms by a hollow laser beam,” Phys. Rev. A |

12. | J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. |

13. | S.-C. Chu, C.-S. Yang, and K. Otsuka, “Vortex array laser beam generation from a Dove prism-embedded unbalanced Mach-Zehnder interferometer,” Opt. Express |

14. | B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A |

15. | B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. |

16. | A. G. Hoekstra, M. Frijlink, L. B. Waters, and P. M. Sloot, “Radiation forces in the discrete-dipole approximation,” J. Opt. Soc. Am. A |

17. | L. Ling, F. Zhou, L. Huang, and Z.-Y. Li, “Optical forces on arbitrary shaped particles in optical tweezers,” J. Appl. Phys. |

18. | R. Schmehl, B. M. Nebeker, and E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two-dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A |

19. | J. J. Goodman, B. T. Draine, and P. J. Flatau, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Opt. Lett. |

20. | B. T. Draine and J. Goodman, “Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. |

21. | B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. I. superthermal spin-up,” Astrophys. J. |

22. | M. A. Bandres, “Elegant Ince-Gaussian beams,” Opt. Lett. |

23. | M. A. Bandres and J. C. Gutiérrez-Vega, “Ince-Gaussian modes of the paraxial wave equation and stable resonators,” J. Opt. Soc. Am. A |

24. | The Language of Technical Computing, http://www.mathworks.com/. |

25. | G. Gouesbet and G. Gréhan, |

26. | M. Born and E. Wolf, |

27. | R.-J. Yang, C.-C. Chang, S.-B. Huang, and G.-B. Lee, “A new focusing model and switching approach for electrokinetic flow inside microchannels,” J. Micromech. Microeng. |

28. | B. Ma, B. Yao, F. Peng, S. Yan, M. Lei, and R. Rupp, “Optical sorting of particles by dual-channel line optical tweezers,” J. Opt. |

29. | M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, “Microfluidic sorting of mammalian cells by optical force switching,” Nat. Biotechnol. |

**OCIS Codes**

(140.7010) Lasers and laser optics : Laser trapping

(350.4855) Other areas of optics : Optical tweezers or optical manipulation

**ToC Category:**

Optical Trapping and Manipulation

**History**

Original Manuscript: July 17, 2013

Revised Manuscript: October 21, 2013

Manuscript Accepted: October 21, 2013

Published: October 28, 2013

**Virtual Issues**

Vol. 9, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Chun-Fu Kuo and Shu-Chun Chu, "Numerical study of the properties of optical vortex array laser tweezers," Opt. Express **21**, 26418-26431 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26418

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### References

- A. Ashkin, “Acceleration and trapping of particles by radia-tion pressure,” Phys. Rev. Lett.24(4), 156–159 (1970). [CrossRef]
- A. Ashkin and J. M. Dziedzic, “Optical levitation by radia-tion pressure,” Appl. Phys. Lett.19(8), 283–285 (1971). [CrossRef]
- A. Ashkin and J. M. Dziedzic, “Observation of light scattering from nonspherical particles using optical levitation,” Appl. Opt.19(5), 660–668 (1980). [CrossRef] [PubMed]
- A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science235(4795), 1517–1520 (1987). [CrossRef] [PubMed]
- K. Dholakia and P. Zemánek, “Colloquium: Gripped by light: Optical binding,” Rev. Mod. Phys.82(2), 1767–1791 (2010). [CrossRef]
- Y. Liu and M. Yu, “Multiple traps created with an inclined dual-fiber system,” Opt. Express17(24), 21680–21690 (2009). [CrossRef] [PubMed]
- K. T. Gahagan and G. A. Swartzlander., “Optical vortex trapping of particles,” Opt. Lett.21(11), 827–829 (1996). [CrossRef] [PubMed]
- D. W. Zhang and X.-C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett.28(9), 740–742 (2003). [CrossRef] [PubMed]
- L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001). [CrossRef] [PubMed]
- Y. Song, D. Milam, and W. T. Hill Iii, “Long, narrow all-light atom guide,” Opt. Lett.24(24), 1805–1807 (1999). [CrossRef] [PubMed]
- X. Xu, K. Kim, W. Jhe, and N. Kwon, “Efficient optical guiding of trapped cold atoms by a hollow laser beam,” Phys. Rev. A63(6), 063401 (2001). [CrossRef]
- J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun.198(1-3), 21–27 (2001). [CrossRef]
- S.-C. Chu, C.-S. Yang, and K. Otsuka, “Vortex array laser beam generation from a Dove prism-embedded unbalanced Mach-Zehnder interferometer,” Opt. Express16(24), 19934–19949 (2008). [CrossRef] [PubMed]
- B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A11(4), 1491–1499 (1994). [CrossRef]
- B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J.333, 848–872 (1988). [CrossRef]
- A. G. Hoekstra, M. Frijlink, L. B. Waters, and P. M. Sloot, “Radiation forces in the discrete-dipole approximation,” J. Opt. Soc. Am. A18(8), 1944–1953 (2001). [CrossRef] [PubMed]
- L. Ling, F. Zhou, L. Huang, and Z.-Y. Li, “Optical forces on arbitrary shaped particles in optical tweezers,” J. Appl. Phys.108(7), 073110 (2010). [CrossRef]
- R. Schmehl, B. M. Nebeker, and E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two-dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A14(11), 3026–3036 (1997). [CrossRef]
- J. J. Goodman, B. T. Draine, and P. J. Flatau, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Opt. Lett.16(15), 1198–1200 (1991). [CrossRef] [PubMed]
- B. T. Draine and J. Goodman, “Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J.405, 685–697 (1993). [CrossRef]
- B. T. Draine and J. C. Weingartner, “Radiative torques on interstellar grains. I. superthermal spin-up,” Astrophys. J.470, 551–565 (1996). [CrossRef]
- M. A. Bandres, “Elegant Ince-Gaussian beams,” Opt. Lett.29(15), 1724–1726 (2004). [CrossRef] [PubMed]
- M. A. Bandres and J. C. Gutiérrez-Vega, “Ince-Gaussian modes of the paraxial wave equation and stable resonators,” J. Opt. Soc. Am. A21(5), 873–880 (2004). [CrossRef] [PubMed]
- The Language of Technical Computing, http://www.mathworks.com/ .
- G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie Theories (Springer, 2011).
- M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge, 1999).
- R.-J. Yang, C.-C. Chang, S.-B. Huang, and G.-B. Lee, “A new focusing model and switching approach for electrokinetic flow inside microchannels,” J. Micromech. Microeng.15(11), 2141–2148 (2005). [CrossRef]
- B. Ma, B. Yao, F. Peng, S. Yan, M. Lei, and R. Rupp, “Optical sorting of particles by dual-channel line optical tweezers,” J. Opt.14(10), 105702 (2012). [CrossRef]
- M. M. Wang, E. Tu, D. E. Raymond, J. M. Yang, H. C. Zhang, N. Hagen, B. Dees, E. M. Mercer, A. H. Forster, I. Kariv, P. J. Marchand, and W. F. Butler, “Microfluidic sorting of mammalian cells by optical force switching,” Nat. Biotechnol.23(1), 83–87 (2005). [CrossRef] [PubMed]

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