## Numerical investigation of passive optical sorting of plasmon nanoparticles |

Optics Express, Vol. 19, Issue 15, pp. 13922-13933 (2011)

http://dx.doi.org/10.1364/OE.19.013922

Acrobat PDF (1128 KB)

### Abstract

We explore the passive optical sorting of plasmon nanoparticles and investigate the optimal wavelength and optimal beam shape of incident field. The condition for optimal wavelength is found by maximising the nanoparticle separation whilst minimising the temperature increase in the system. We then use the force optical eigenmode (FOEi) method to find the beam shape of incident electromagnetic field, maximising the force difference between plasmon nanoparticles. The maximum force difference is found with respect to the whole sorting region. The combination of wavelength and beam shape study is demonstrated for a specific case of gold nanoparticles of radius 40nm and 50nm respectively. The optimum wavelength for this particular situation is found to be above 700nm. The optimum beam shape depends upon the size of sorting region and ranges from plane-wave illumination for infinite sorting region to a field maximising gradient force difference in a single point.

© 2011 OSA

## 1. Introduction

1. G. Raschke, S. Kowarik, T. Franzl, C. Sonnichsen, T. A. Klar, J. Feldmann, A. Nichtl, and K. Kurzinger, “Biomolecular recognition based on single gold nanoparticle light scattering,” Nano Lett. **3**, 935–938 (2003). [CrossRef]

2. J. Stehr, C. Hrelescu, R. A. Sperling, G. Raschke, M. Wunderlich, A. Nichtl, D. Heindl, K. Kurzinger, W. J. Parak, T. A. Klar, and J. Feldmann, “Gold nanostoves for microsecond dna melting analysis,” Nano Lett. **8**, 619–623 (2008). [CrossRef] [PubMed]

3. D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science **297**, 1160–1163 (2002). [CrossRef] [PubMed]

*active*and

*passive*. Active sorting techniques use fluorescent signals [4

4. D. W. Galbraith, M. T. Anderson, and L. A. Herzenberg, “Flow cytometric analysis and facs sorting of cells based on gfp accumulation,” Methods Cell Biol. **58**, 315–341 (1999). [CrossRef] [PubMed]

5. T. N. Buican, M. J. Smyth, H. A. Crissman, G. C. Salzman, C. C. Stewart, and J. C. Martin, “Automated single-cell manipulation and sorting by light trapping,” Appl. Opt. **26**, 5311–5316 (1987). [CrossRef] [PubMed]

6. K. Grujic, O. G. Helleso, J. P. Hole, and J. S. Wilkinson, “Sorting of polystyrene microspheres using a y-branched optical waveguide,” Opt. Express **13**, 1–7 (2005). [CrossRef] [PubMed]

7. S. C. Chapin, V. Germain, and E. R. Dufresne, “Automated trapping, assembly, and sorting with holographic optical tweezers,” Opt. Express **14**, 13095–13100 (2006). [CrossRef] [PubMed]

8. P. J. Rodrigo, R. L. Eriksen, V. R. Daria, and J. Gluckstad, “Interactive light-driven and parallel manipulation of inhomogeneous particles,” Opt. Express **10**, 1550–1556 (2002). [PubMed]

9. M. Pelton, K. Ladavac, and D. G. Grier, “Transport and fractionation in periodic potential-energy landscapes,” Phys. Rev. E **70**, 031108 (2004). [CrossRef]

10. K. Xiao and D. G. Grier, “Multidimensional optical fractionation of colloidal particles with holographic verification,” Phys. Rev. Lett. **104**, 028302 (2010). [CrossRef] [PubMed]

11. T. Cizmar, M. Siler, M. Sery, P. Zemanek, V. Garces-Chavez, and K. Dholakia, “Optical sorting and detection of submicrometer objects in a motional standing wave,” Phys. Rev. B **74**, 035105 (2006). [CrossRef]

12. I. Ricardez-Vargas, P. Rodriguez-Montero, R. Ramos-Garcia, and K. Volke-Sepulveda, “Modulated optical sieve for sorting of polydisperse microparticles,” Appl. Phys. Lett. **88**, 121116 (2006). [CrossRef]

13. L. Paterson, E. Papagiakoumou, G. Milne, V. Garces-Chavez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. **87**, 123901 (2005). [CrossRef]

14. R. F. Marchington, M. Mazilu, S. Kuriakose, V. Garces-Chavez, P. J. Reece, T. F. Krauss, M. Gu, and K. Dholakia, “Optical deflection and sorting of microparticles in a near-field optical geometry,” Opt. Express **16**, 3712–3726 (2008). [CrossRef] [PubMed]

10. K. Xiao and D. G. Grier, “Multidimensional optical fractionation of colloidal particles with holographic verification,” Phys. Rev. Lett. **104**, 028302 (2010). [CrossRef] [PubMed]

15. M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature **426**, 421–424 (2003). [CrossRef] [PubMed]

19. Y. Y. Sun, L. S. Ong, and X. C. Yuan, “Composite-microlens-array-enabled microfluidic sorting,” Appl. Phys. Lett. **89**, 141108 (2006). [CrossRef]

20. M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia, “Optical eigenmodes; exploiting the quadratic nature of the energy flux and of scattering interactions,” Opt. Express **19**, 933–945 (2011). [CrossRef] [PubMed]

21. A. S. Zelenina, R. Quidant, G. Badenes, and M. Nieto-Vesperinas, “Tunable optical sorting and manipulation of nanoparticles via plasmon excitation,” Opt. Lett. **31**, 2054–2056 (2006). [CrossRef] [PubMed]

22. R. Quidant, S. Zelenina, and M. Nieto-Vesperinas, “Optical manipulation of plasmonic nanoparticles,” Appl. Phys. A: Mater. Sci. Process. **89**, 233–239 (2007). [CrossRef]

## 2. Description of FOEi method

**E**

*in a way that maximises the exerted force*

_{inc}*F*

**=**

^{u}**F**·

**u**in a specified direction

**u**(Fig. 1). Since our incident field of angular frequency

*ω*can be decomposed into a sum of

*μ*monochromatic plane waves (

*e*), we can write (using summation over repeating indices) where

^{iωt}*a*are the complex expansion coefficients and

^{μ}*a*coefficients modulate both phase and amplitude of each and single plane wave independently. The scattered field generated upon interaction with the particle has the same expansion coefficients, so that we can write

^{μ}**E**, which is a sum of incident and scattered field, can then be written as where

**E**

*is a solution of the scattering problem for an incident field given by plane wave*

^{μ}**u**is given by where

*n*is outward unit normal to an element d

_{j}*s*of the curve

*C*enclosing the particle for which we optimise the force and 〈·〉 is optical-cycle average. The Maxwell stress tensor,

*σ*, can be written for the final field

_{ij}**E**as [23] Using Eq. (2), we can rewrite Eq. (4) as

*a*we obtain

^{μ}*M*are given by the line integrals in Eq. (7) and

^{μν}**a**is the vector form of

*a*. We remark that the matrix is Hermitian (

^{μ}**M**=

**M**

^{†}) and thus its eigenvalues are real. This means that the force

*F*

**is in a symmetric sesquilinear form, which is just an extension of quadratic form to complex numbers. Any symmetric sesquilinear form can be visualised as an ellipsoid with the length of principal axes equal to the eigenvalues**

^{u}*λ*of the matrix

_{n}**M**. This has far reaching implications for our optimisation process since the surface of the ellipsoid generated by the symmetric sesquilinear form is extremized at the end points of principal axes. This means that finding the eigenvalues

*λ*of the matrix

_{n}**M**and selecting the largest one from the set extremizes our problem. The eigenvector (force optical eigenmode)

20. M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia, “Optical eigenmodes; exploiting the quadratic nature of the energy flux and of scattering interactions,” Opt. Express **19**, 933–945 (2011). [CrossRef] [PubMed]

*Numerical considerations:*We use COMSOL Multiphysics v4.1 RF module in scattering formulation to calculate the total field solutions

**E**

*for corresponding incident plane waves*

^{μ}**E**

*for particle*

^{μ}*p*

_{1}. We subsequently use the solutions

**E**

*to find the elements*

^{μ}**M**

_{1}and determine the eigenvalues and corresponding eigenvectors. The principal eigenvector gives the optimum force for particle

*p*

_{1}in a single position. The same procedure is repeated for a second type of particle,

*p*

_{2}, delivering matrix

**M**

_{2}. The matrices

**M**

_{1}and

**M**

_{2}then encode all the information about interactions of the incident fields with the particles. Finding the matrix elements

*M*of matrix

^{μν}**M**is computationally very intensive as combinations of

*N*(

*N*+ 1)/2 solutions need to be constructed and integrated over a sphere boundary. Here

*N*denotes number of plane waves in the angular spectrum representation and thus the number of pixels on spatial light modulator. As the azimuthal discretization of angular spectrum representation increases the number of combinations in 3D significantly, we have restricted the simulations to 2D to illustrate the method.

*r*by

*d*such that it creates a cylinder with a volume equal to the volume of the sphere with the same radius. The extrusion factor

*d*is given by The validity of the COMSOL model was tested in 3D by comparing the optical forces and scattering and absorption efficiencies with Mie theory. The difference between the COMSOL model and the Mie model was less than 2 percent. In 2D, optical forces and scattering and absorption efficiencies were calculated using several independent methods to ensure the model validity.

## 3. Plasmon resonances in the system

24. P. B. Johnson and R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B **6**, 4370–4379 (1972). [CrossRef]

*r*

_{1}= 50nm and

*r*

_{2}= 40nm. We consider a substrate of glass with refractive index

*n*= 1.5. The particles are assumed to be dispersed in water with

_{g}*n*= 1.33 (Fig. 1).

_{w}*Q*and absorption

_{sca}*Q*efficiencies for

_{abs}*r*

_{1}= 50nm gold nanoparticle. Note that the 3D efficiencies calculated from Mie theory and the corresponding 2D efficiencies (transformed to 3D) for p-polarisation follow very similar pattern, which differs only in amplitude and a slight blue shift of 2D resonance peaks with respect to 3D resonances. Figure 2(b) shows the 3D forces along the substrate acting on the gold nanoparticles calculated for plane-wave incident at near critical angle of

*θ*= 64°. The slight shift in resonances due to the different sizes of nanoparticles creates a force difference improvement with a peak around 550nm (black curve in Fig. 2(b)).

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

*F*

_{2D}was calculated in 2D using Eq. (8) and the dynamic viscosity of water at

*T*= 20°

*C*is

*η*= 1.002 × 10

^{−3}Pa · s. Figure 2(c) shows the speed difference generated by force differences in Fig. 2(b) and the average temperature increase as the particle enters the sorting field. The estimate of average temperature increase was calculated using [26

26. G. Baffou, R. Quidant, and C. Girard, “Heat generation in plasmonic nanostructures: influence of morphology,” Appl. Phys. Lett. **94**, 153109 (2009). [CrossRef]

*Q*

_{1}and

*Q*

_{2}are 3D powers of heat generation in nanoparticles and

*κ*

_{0}= 0.6W · m

^{−1}· K

^{−1}is the thermal conductivity of water. This temperature increase is reached very quickly as the particle enters the sorting field. Results in Fig. 2(c) and Fig. 2(d) suggest, that heating at wavelengths above 700nm is quite low and the sorting speed remains high. For this reason we set the vacuum wavelength for our method to

*λ*

_{0}= 700nm. Please note that a slight (30nm) blue shift in the resonances of 2D case does not have significant impact on the choice of this wavelength for the 3D scenario.

## 4. Optimising the force difference in region of interest (ROI)

*N*incident plane waves defined by

**k**

*vectors (*

_{θ}*θ*= 〈−70°,...,70°〉 with a step of 2°) is used for discretization (see Fig. 1). The limits of

*θ*correspond to experimental limitation for

*NA*= 1.4 oil immersion objective. The goal is to optimise the force difference along

**u**= (1, 0).

**M**

_{1}and

**M**

_{2}, the equation for force difference in a single point for our choice of particles is Due to the symmetry of the system two optimum solutions exists - one optimising the force difference in +

*x*direction and the second for −

*x*direction. In subsequent discussions we always choose the solution optimising the force in +

*x*direction. The field locally optimising the force difference for gold nanoparticles of our choice is on Fig. 3. Notice that the field creates a very strong field gradient in the +

*x*direction around point

*x*= 0, where we want to maximise the force difference for our testing particles. Also notice that the back focal plane pattern corresponding to this field has significant contributions from plane waves propagating in the opposite −

*x*direction. Although this might seem surprising, we need to realise that the final goal of our method is to interfere the plane waves in such a way to create the strongest gradient in +

*x*direction. Apparently the counter-propagating waves increase the number of degrees of freedom for efficient interference leading to strong gradient and are thus utilised automatically by the FOEi method. It also make sense that the increased intensity at the back focal plane appears for near critical angle plane waves as those plane waves contribute the most to the intensity near the glass/water interface. Note that the phase at the back focal plane is also significantly altered to maximise the force difference.

*F*over a certain range, in our case line segment defined by

*x*= 〈

*−l,l*〉. Displacing the particle in

*x*-direction causes the particle to experience different relative phases between the fields

**E**

*. Since we use combination of solutions to calculate matrix*

^{μ}**M**this relative phase can be taken into account using where

*k*= (2

_{w}*π*/

*λ*

_{0})

*n*and

_{w}*M*is the matrix calculated for particle at position

^{μν}*x*= 0. Using the translation relations for matrix

*M*we obtain

^{μν}*l*. Finding the optimum illumination for a ROI of any size is thus very efficient.

*l*= 500nm (Fig. 4) and

*l*= 5

*μ*m (Fig. 5) differs significantly from the single point optimised problem (Fig. 3). The optimised field corresponds in its bulk to the focusing of light into ROI. The solution is quite close to the Gaussian beam send to the edge of the back focal plane of the objective. However, the phase for plane waves above critical angle is significantly modulated and the intensity profile is not entirely Gaussian. The width of the beam at the back-focal plane optimising the

*l*= 5

*μ*m situation is also noticeble smaller than for the case of

*l*= 500nm. This is a direct consequence of Eq. (14). As we increase

*l*, the off-diagonal terms in matrix

*l*increases. In the limit

*l*→ ∞ only the diagonal terms remain. This means that the eigenmodes (eigenvectors of

*l*= 100mm (Fig. 6) is the plane wave near the critical angle. As the phase of

*a*for zero amplitude |

^{μ}*a*| is not well defined, it is not displayed in the graph. The result validates that the FOEi method is working correctly, as the near critical angle plane wave provides the highest intensity and force difference at the interface for infinite system.

^{μ}*F*on the size of ROI. To show the improvement compared to infinite system, we normalise Δ

*F*by Δ

*F*, where Δ

_{pw}*F*is the force difference for optimised infinite system (pw stands for plane wave). The result (Fig. 7(b)) indicates that the gain is significant for a wide range of experimentally interesting ROI sizes. The dip around

_{pw}*l*= 14

*μ*m is present due to discretization of

**k**-space described above. The increase in ratio Δ

*F*/Δ

*F*for

_{pw}*l*> 14

*μ*m is then equivalent to the formation of second beam focus in ROI due to onset of periodicity.

*Discussion of results:*The FOEi method is capable of finding the optimal beam shape for illumination such that the force difference is maximised over the whole sorting region. The computationally intensive calculation of matrices

**M**

_{1}and

**M**

_{2}is compensated by the fact that the same matrices can be used for finding optimal illumination for any size of sorting region. We note that even though the solution does not optimise the vertical force pointing towards the substrate, we found that this is the case for all our solutions. However, the sign of this force is wavelength and particle size dependent and as such the attractive vertical force is not a general feature of the method. Further, the vertical force is not constant in the sorting region, which might introduce some modulation of force difference due to the Faxen correction. To resolve this one may minimise the vertical force and use an auxiliary beam with constant vertical force over the whole sorting region. This would restrict the diffusion of particles in vertical direction in more controlled way. It is possible to modify the method to simultaneously optimise for several parameters of the system. In our case, the full optimised solution for sorting applications of plasmon nanoparticles would involve simultaneous maximalisation of force difference in ROI, minimisation of vertical force, and minimisation of heating. Such a problem reduces to finding matrices (operators) for all parameters of interest and choosing the eigenmodes optimising for such a set of parameters. It is very interesting, for plasmonic sorting in general, to find the beam shape of the field maximising the force difference and minimising the heating. This would also clearly identify the contribution of focusing to the overall improvement of force difference. This is a focus of our ongoing research.

## 5. Conclusion

## Acknowledgments

## References and links

1. | G. Raschke, S. Kowarik, T. Franzl, C. Sonnichsen, T. A. Klar, J. Feldmann, A. Nichtl, and K. Kurzinger, “Biomolecular recognition based on single gold nanoparticle light scattering,” Nano Lett. |

2. | J. Stehr, C. Hrelescu, R. A. Sperling, G. Raschke, M. Wunderlich, A. Nichtl, D. Heindl, K. Kurzinger, W. J. Parak, T. A. Klar, and J. Feldmann, “Gold nanostoves for microsecond dna melting analysis,” Nano Lett. |

3. | D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science |

4. | D. W. Galbraith, M. T. Anderson, and L. A. Herzenberg, “Flow cytometric analysis and facs sorting of cells based on gfp accumulation,” Methods Cell Biol. |

5. | T. N. Buican, M. J. Smyth, H. A. Crissman, G. C. Salzman, C. C. Stewart, and J. C. Martin, “Automated single-cell manipulation and sorting by light trapping,” Appl. Opt. |

6. | K. Grujic, O. G. Helleso, J. P. Hole, and J. S. Wilkinson, “Sorting of polystyrene microspheres using a y-branched optical waveguide,” Opt. Express |

7. | S. C. Chapin, V. Germain, and E. R. Dufresne, “Automated trapping, assembly, and sorting with holographic optical tweezers,” Opt. Express |

8. | P. J. Rodrigo, R. L. Eriksen, V. R. Daria, and J. Gluckstad, “Interactive light-driven and parallel manipulation of inhomogeneous particles,” Opt. Express |

9. | M. Pelton, K. Ladavac, and D. G. Grier, “Transport and fractionation in periodic potential-energy landscapes,” Phys. Rev. E |

10. | K. Xiao and D. G. Grier, “Multidimensional optical fractionation of colloidal particles with holographic verification,” Phys. Rev. Lett. |

11. | T. Cizmar, M. Siler, M. Sery, P. Zemanek, V. Garces-Chavez, and K. Dholakia, “Optical sorting and detection of submicrometer objects in a motional standing wave,” Phys. Rev. B |

12. | I. Ricardez-Vargas, P. Rodriguez-Montero, R. Ramos-Garcia, and K. Volke-Sepulveda, “Modulated optical sieve for sorting of polydisperse microparticles,” Appl. Phys. Lett. |

13. | L. Paterson, E. Papagiakoumou, G. Milne, V. Garces-Chavez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. |

14. | R. F. Marchington, M. Mazilu, S. Kuriakose, V. Garces-Chavez, P. J. Reece, T. F. Krauss, M. Gu, and K. Dholakia, “Optical deflection and sorting of microparticles in a near-field optical geometry,” Opt. Express |

15. | M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature |

16. | P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezers,” Phys. Rev. Lett. |

17. | K. Ladavac, K. Kasza, and D. G. Grier, “Sorting mesoscopic objects with periodic potential landscapes: optical fractionation,” Phys. Rev. E |

18. | G. Milne, D. Rhodes, M. MacDonald, and K. Dholakia, “Fractionation of polydisperse colloid with acousto-optically generated potential energy landscapes,” Opt. Lett. |

19. | Y. Y. Sun, L. S. Ong, and X. C. Yuan, “Composite-microlens-array-enabled microfluidic sorting,” Appl. Phys. Lett. |

20. | M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia, “Optical eigenmodes; exploiting the quadratic nature of the energy flux and of scattering interactions,” Opt. Express |

21. | A. S. Zelenina, R. Quidant, G. Badenes, and M. Nieto-Vesperinas, “Tunable optical sorting and manipulation of nanoparticles via plasmon excitation,” Opt. Lett. |

22. | R. Quidant, S. Zelenina, and M. Nieto-Vesperinas, “Optical manipulation of plasmonic nanoparticles,” Appl. Phys. A: Mater. Sci. Process. |

23. | J. D. Jackson, |

24. | P. B. Johnson and R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B |

25. | K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. |

26. | G. Baffou, R. Quidant, and C. Girard, “Heat generation in plasmonic nanostructures: influence of morphology,” Appl. Phys. Lett. |

**OCIS Codes**

(200.4880) Optics in computing : Optomechanics

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

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Optical Trapping and Manipulation

**History**

Original Manuscript: May 11, 2011

Revised Manuscript: June 17, 2011

Manuscript Accepted: June 19, 2011

Published: July 6, 2011

**Virtual Issues**

Vol. 6, Iss. 8 *Virtual Journal for Biomedical Optics*

**Citation**

M. Ploschner, M. Mazilu, T. Čižmár, and K. Dholakia, "Numerical investigation of passive optical sorting of plasmon nanoparticles," Opt. Express **19**, 13922-13933 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-13922

Sort: Year | Journal | Reset

### References

- G. Raschke, S. Kowarik, T. Franzl, C. Sonnichsen, T. A. Klar, J. Feldmann, A. Nichtl, and K. Kurzinger, “Biomolecular recognition based on single gold nanoparticle light scattering,” Nano Lett. 3, 935–938 (2003). [CrossRef]
- J. Stehr, C. Hrelescu, R. A. Sperling, G. Raschke, M. Wunderlich, A. Nichtl, D. Heindl, K. Kurzinger, W. J. Parak, T. A. Klar, and J. Feldmann, “Gold nanostoves for microsecond dna melting analysis,” Nano Lett. 8, 619–623 (2008). [CrossRef] [PubMed]
- D. Boyer, P. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163 (2002). [CrossRef] [PubMed]
- D. W. Galbraith, M. T. Anderson, and L. A. Herzenberg, “Flow cytometric analysis and facs sorting of cells based on gfp accumulation,” Methods Cell Biol. 58, 315–341 (1999). [CrossRef] [PubMed]
- T. N. Buican, M. J. Smyth, H. A. Crissman, G. C. Salzman, C. C. Stewart, and J. C. Martin, “Automated single-cell manipulation and sorting by light trapping,” Appl. Opt. 26, 5311–5316 (1987). [CrossRef] [PubMed]
- K. Grujic, O. G. Helleso, J. P. Hole, and J. S. Wilkinson, “Sorting of polystyrene microspheres using a y-branched optical waveguide,” Opt. Express 13, 1–7 (2005). [CrossRef] [PubMed]
- S. C. Chapin, V. Germain, and E. R. Dufresne, “Automated trapping, assembly, and sorting with holographic optical tweezers,” Opt. Express 14, 13095–13100 (2006). [CrossRef] [PubMed]
- P. J. Rodrigo, R. L. Eriksen, V. R. Daria, and J. Gluckstad, “Interactive light-driven and parallel manipulation of inhomogeneous particles,” Opt. Express 10, 1550–1556 (2002). [PubMed]
- M. Pelton, K. Ladavac, and D. G. Grier, “Transport and fractionation in periodic potential-energy landscapes,” Phys. Rev. E 70, 031108 (2004). [CrossRef]
- K. Xiao and D. G. Grier, “Multidimensional optical fractionation of colloidal particles with holographic verification,” Phys. Rev. Lett. 104, 028302 (2010). [CrossRef] [PubMed]
- T. Cizmar, M. Siler, M. Sery, P. Zemanek, V. Garces-Chavez, and K. Dholakia, “Optical sorting and detection of submicrometer objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006). [CrossRef]
- I. Ricardez-Vargas, P. Rodriguez-Montero, R. Ramos-Garcia, and K. Volke-Sepulveda, “Modulated optical sieve for sorting of polydisperse microparticles,” Appl. Phys. Lett. 88, 121116 (2006). [CrossRef]
- L. Paterson, E. Papagiakoumou, G. Milne, V. Garces-Chavez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005). [CrossRef]
- R. F. Marchington, M. Mazilu, S. Kuriakose, V. Garces-Chavez, P. J. Reece, T. F. Krauss, M. Gu, and K. Dholakia, “Optical deflection and sorting of microparticles in a near-field optical geometry,” Opt. Express 16, 3712–3726 (2008). [CrossRef] [PubMed]
- M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421–424 (2003). [CrossRef] [PubMed]
- P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezers,” Phys. Rev. Lett. 89, 128301 (2002). [CrossRef] [PubMed]
- K. Ladavac, K. Kasza, and D. G. Grier, “Sorting mesoscopic objects with periodic potential landscapes: optical fractionation,” Phys. Rev. E 70, 010901 (2004). [CrossRef]
- G. Milne, D. Rhodes, M. MacDonald, and K. Dholakia, “Fractionation of polydisperse colloid with acousto-optically generated potential energy landscapes,” Opt. Lett. 32, 1144–1146 (2007). [CrossRef] [PubMed]
- Y. Y. Sun, L. S. Ong, and X. C. Yuan, “Composite-microlens-array-enabled microfluidic sorting,” Appl. Phys. Lett. 89, 141108 (2006). [CrossRef]
- M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia, “Optical eigenmodes; exploiting the quadratic nature of the energy flux and of scattering interactions,” Opt. Express 19, 933–945 (2011). [CrossRef] [PubMed]
- A. S. Zelenina, R. Quidant, G. Badenes, and M. Nieto-Vesperinas, “Tunable optical sorting and manipulation of nanoparticles via plasmon excitation,” Opt. Lett. 31, 2054–2056 (2006). [CrossRef] [PubMed]
- R. Quidant, S. Zelenina, and M. Nieto-Vesperinas, “Optical manipulation of plasmonic nanoparticles,” Appl. Phys. A: Mater. Sci. Process. 89, 233–239 (2007). [CrossRef]
- J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Inc., 1999).
- P. B. Johnson and R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
- K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994). [CrossRef] [PubMed]
- G. Baffou, R. Quidant, and C. Girard, “Heat generation in plasmonic nanostructures: influence of morphology,” Appl. Phys. Lett. 94, 153109 (2009). [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.

« Previous Article | Next Article »

OSA is a member of CrossRef.