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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 12 — Jun. 6, 2011
  • pp: 11422–11428
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Light-assisted templated self assembly using photonic crystal slabs

Camilo A. Mejia, Avik Dutt, and Michelle L. Povinelli  »View Author Affiliations


Optics Express, Vol. 19, Issue 12, pp. 11422-11428 (2011)
http://dx.doi.org/10.1364/OE.19.011422


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Abstract

We explore a technique which we term light-assisted templated self-assembly. We calculate the optical forces on colloidal particles over a photonic crystal slab. We show that exciting a guided resonance mode of the slab yields a resonantly-enhanced, attractive optical force. We calculate the lateral optical forces above the slab and predict that stably trapped periodic patterns of particles are dependent on wavelength and polarization. Tuning the wavelength or polarization of the light source may thus allow the formation and reconfiguration of patterns. We expect that this technique may be used to design all-optically reconfigurable photonic devices.

© 2011 OSA

1. Introduction

Self-assembly methods [1

1. G. M. Whitesides and B. Grzybowski, “Self-assembly at all scales,” Science 295(5564), 2418–2421 (2002). [CrossRef] [PubMed]

] have been used to construct complex materials including three dimensional photonic crystals [2

2. Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 13(6), 409–413 (2001). [CrossRef]

]. However, a fundamental constraint is that only energetically favorable structures are formed. To overcome this problem, templated self-assembly methods have been introduced [3

3. Y. Yin, Y. Lu, B. Gates, and Y. Xia, “Template-assisted self-assembly: a practical route to complex aggregates of monodispersed colloids with well-defined sizes, shapes, and structures,” J. Am. Chem. Soc. 123(36), 8718–8729 (2001). [CrossRef] [PubMed]

,4

4. A. van Blaaderen, R. Ruel, and P. Wiltzius, “Tempate-directed colloidal crystallization,” Nature 385(6614), 321–324 (1997). [CrossRef]

]. The template guides particle arrangement, allowing the formation of diverse — albeit static — crystal structures. Here we consider how optical forces can be used to direct assembly and reconfiguration of particles on a photonic crystal slab, which serves as an optically reconfigurable template. Our calculations predict the formation of stably trapped crystal patterns that depend on the wavelength and polarization of the light source. We envision that the process of light-assisted templated self-assembly may be used for fabrication of complex photonic materials and all-optically reconfigurable photonic devices.

Optical forces have been studied extensively since the discovery of optical tweezers [5

5. 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), 288–292 (1986). [CrossRef] [PubMed]

,6

6. A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987). [CrossRef] [PubMed]

]. While standard optical tweezers use a focused laser beam to trap and manipulate particles, structured light fields [7

7. K. Dholakia and W. M. Lee, “Optical trapping takes shape: the use of structured light fields,” Adv. At. Mol. Opt. Phys. 56, 261–337 (2008).

,8

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

] allow even greater control over particle deflection, transport, and sorting, with applications from the physical sciences to biology. Recently, researchers have used light fields near microphotonic devices to trap and manipulate particles. This work leverages the strong electromagnetic gradients near devices such as nanoapertures [9

9. K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999). [CrossRef]

], gratings [10

10. B. K. Wilson, T. Mentele, S. Bachar, E. Knouf, A. Bendoraite, M. Tewari, S. H. Pun, and L. Y. Lin, “Nanostructure-enhanced laser tweezers for efficient trapping and alignment of particles,” Opt. Express 18(15), 16005–16013 (2010). [CrossRef] [PubMed]

], photonic-crystal microcavities [11

11. M. Barth and O. Benson, “Manipulation of dielectric particles using photonic crystal cavities,” Appl. Phys. Lett. 89(25), 253114 (2006). [CrossRef]

,12

12. A. Rahmani and P. C. Chaumet, “Optical trapping near a photonic crystal,” Opt. Express 14(13), 6353–6358 (2006). [CrossRef] [PubMed]

], slot waveguides [13

13. A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009). [CrossRef] [PubMed]

] and plasmonic structures [14

14. K. Wang, E. Schonbrun, and K. B. Crozier, “Propulsion of gold nanoparticles with surface plasmon polaritons: evidence of enhanced optical force from near-field coupling between gold particle and gold film,” Nano Lett. 9(7), 2623–2629 (2009). [CrossRef] [PubMed]

17

17. M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett. 100(18), 186804 (2008). [CrossRef] [PubMed]

] to generate large optical forces. However, much of this work has considered single-particle traps.

2. Approach and results

The system we consider is shown schematically in Fig. 1
Fig. 1 Light-assisted templated self-assembly using a photonic crystal slab.
. In an experiment, light would illuminate the photonic crystal slab from below. The structured light fields above the slab give rise to optical forces on particles in solution, which can potentially result in trapping. Due to the variation of the electromagnetic field over spatial length scales comparable to the particle diameter, the dipole approximation cannot be assumed. However, the optical force can be found by using full-vectorial calculations of Maxwell’s equations to calculate the Maxwell Stress Tensor [21

21. M. I. Antonoyiannakis and J. B. Pendry, “Electromagnetic forces in photonic crystals,” Phys. Rev. B 60(4), 2363–2374 (1999). [CrossRef]

].

For concreteness, we consider a silicon photonic crystal (ε = 11.9) with a square lattice of holes of radius 0.2a and thickness 0.6a resting on a silica substrate (ε = 2.1), where a is the lattice constant of the photonic crystal. The holes in the photonic crystal and the region above the crystal are filled with water (ε = 1.77). The incident light is an x-polarized plane wave propagating in the z direction.

We calculate the force on polystyrene spheres (ε = 2.28) of radius 0.1a. The center of the sphere is placed at a height of 0.25a above the slab surface. We calculate the Maxwell stress tensor on the surface of an integration box of size 0.3a centered on the particle [21

21. M. I. Antonoyiannakis and J. B. Pendry, “Electromagnetic forces in photonic crystals,” Phys. Rev. B 60(4), 2363–2374 (1999). [CrossRef]

,24

24. J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley & Sons, 1999).

]. The calculation is done in a computational cell that includes one period of the photonic crystal slab. Periodic boundary conditions are used in the lateral directions (x and y), and perfectly matched layer boundaries are used in the z direction. The forces calculated in this manner represent the optical forces on a periodic array of polystyrene spheres above the photonic crystal slab.

We plot the dimensionless quantity Fzc/ϕ, where Fz is the z-component of the optical force, ϕ is the incident power per unit cell and c is the speed of light [see Fig. 2(b)] for a sphere positioned equidistant from the four closest holes. For each of the three resonance frequencies shown in Fig. 2(a), we observe a peak in the optical force. The sign of the force is negative, indicating that the particles are attracted toward the slab. For comparison, we calculate the radiation pressure of a plane wave on a spherical particle in the absence of the photonic crystal. We obtain a repulsive force of Fzc/ϕ ~1x10−5, three orders of magnitude smaller than the attractive optical force above the photonic crystal. We expect that even larger optical forces can be achieved by using a photonic-crystal slab with higher-Q resonances. Higher Q has been correlated with decreasing hole size [18

18. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

].

The intensity for these resonances is shown in Figs. 3(a)
Fig. 3 Normalized intensity for normally incident x-polarized light for R1, R2, and R3, respectively at a height of (a)–(c) 0.25a above the surface of the slab and (d)–(f) 0.1a above the surface of the slab. White circles indicate hole positions.
3(c) at a height of 0.25a above the surface of the slab. Figures 3(d)3(f) shows the intensity at a height of 0.1a (equal to the particle radius). The intensity |E|2 is normalized to the source intensity |E0|2. We observe that each resonance has a different field profile. There is a slight change in field profile with height, and the intensity is higher closer to the slab.

Different light polarizations correspond to different self-assembled patterns, as shown in Fig. 5
Fig. 5 (a) Pattern for x-polarization, (b) Pattern for y-polarization.
. Due to the symmetry of the photonic crystal, the patterns for y-polarized light are the same as those for x-polarized light, but rotated 90° [Figs. 5(a) and 5(b)].

3. Discussion

The photonic-crystal slabs studied here can be fabricated in a silicon-on-insulator wafer using standard techniques [25

25. J. Pan, Y. Huo, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103114 (2008). [CrossRef]

]. The lattice constant of the photonic crystal can be scaled to place a given guided resonance at a particular wavelength of interest [26

26. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

]. For a = 760nm, for example, R1 occurs at λ = c/n = 1609nm, while R2 occurs at 1532nm. For a = 375nm, R1 is at 794nm and R2 is at 748nm. An upper bound on the power required for trapping was obtained by setting the height of the potential depth |ΔU| > 10 KBT [5

5. 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), 288–292 (1986). [CrossRef] [PubMed]

]. The power density for a = 760nm was 1 mW/unit cell for R1, which has a modest Q of ~260. The required power decreases with increasing Q. Moreover, the power calculated in this manner is likely to be an overestimate. Our results indicate that the particles will be attracted to the surface of the slab. As seen in Fig. 3, the intensity increases closer to the slab surface, producing a higher force than the values shown in Fig. 4, which were calculated for a height of 0.25a (for a particle touching the slab surface, the height is 0.1a).

In an experiment, particles may be trapped one by one, or a few at a time, in order to build up ordered patterns. We believe that the red dots shown in Figs. 4 and 5 are good predictors of the patterns that will be formed in this manner. In our computations, due to the boundary conditions on the unit cell, we are in fact calculating the optical force on periodic arrays of particles above the photonic crystal slab. However, since interparticle interactions [27

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

] are negligible in this system, the force on an individual particle above the slab will be nearly identical.

To show that interparticle interactions are weak compared to the force on a particle from the photonic crystal, we considered the geometry shown in Fig. 6(a)
Fig. 6 (a) Schematic of the system (b) Transmission spectrum of photonic-crystal slab with and without particles above (c) Fx c/ϕ on particle 1 for 3 different positions of particle 2 (d) Fy c/ϕ on particle 1 for 3 different positions of particle 2. The legend indicates the position of particle 2 in (b), (c), and (d).
. A first particle (labeled “1”, blue circle) was placed over the slab at a position of [0.3a, 0.3a, 0.25a]. A second particle was placed in one of three alternate positions (labeled “2”, green circles). Figure 6(b) shows that the presence of the particles does not visibly affect the transmission spectrum. In Figs. 6(c) and 6(d), we plot the lateral forces on particle 1 for different positions of particle 2. It can be seen that particle 2 has minimal effect on the force.

As an additional check, we recalculated the force maps of Figs. 4(d)4(f) using a larger computational cell of size 2a x 2a, with one particle per computational cell. No changes were observed in the force maps.

Lastly, we checked that when particles were placed at each of the red dots in Fig. 4(d)4(f), the configuration was stable to perturbation. One particle per unit cell was displaced, and it was verified that the restoring force was in the appropriate direction to restore the initial pattern.

4. Conclusions

We predict that optical forces above photonic crystal slabs will lead to a variety of complex, stably trapped crystal patterns. Changing the wavelength or polarization of the incident light may be used to reconfigure the patterns.

In the system studied here, the particles do not significantly affect the transmission spectrum [Fig. 6(b)]. We have checked that even if the particles are placed inside the holes in the slab or on the slab surface, the shift in the resonance is a small fraction of the resonance width (~15% or less). For larger particles, particles of higher index, and/or higher Q slab resonances, particle trapping may begin to shift the resonance position. This opens up the possibility for intriguing phenomena such as self-induced or bistable trapping, effects which have previously been studied for particle trapping near photonic cavities [28

28. M. Barth and O. Benson, “Manipulation of dielectric particles using photonic crystal cavities,” Appl. Phys. Lett. 89(25), 253114 (2006). [CrossRef]

]. This is an interesting direction for further research.

We expect the approach of light-assisted self-assembly, described here, to be of broad utility for fabrication of complex photonic materials, sensors, and filters. It is intriguing to consider whether metamaterials based on metal nanoclusters [29

29. J. H. Lee, Q. Wu, and W. Park, “Metal nanocluster metamaterial fabricated by the colloidal self-assembly,” Opt. Lett. 34(4), 443–445 (2009). [CrossRef] [PubMed]

], for example, could be assembled in the manner we describe, using the optical response of the nanoclusters to tune or adjust assembly.

Acknowledgments

We thank Steven G. Johnson for discussions of the stress-tensor feature in MEEP. Chenxi Lin, Jing Ma, and Eric Jaquay performed calculations relevant to this study. We thank the anonymous reviewers for helpful comments regarding interparticle interactions and self-trapping. This work is funded by an Army Research Office Young Investigator Award under award No. 56801-MS-YIP. Computation for the work described in this paper was supported by the University of Southern California Center for High-Performance Computing and Communications (www.usc.edu/hpcc).

References and links

1.

G. M. Whitesides and B. Grzybowski, “Self-assembly at all scales,” Science 295(5564), 2418–2421 (2002). [CrossRef] [PubMed]

2.

Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 13(6), 409–413 (2001). [CrossRef]

3.

Y. Yin, Y. Lu, B. Gates, and Y. Xia, “Template-assisted self-assembly: a practical route to complex aggregates of monodispersed colloids with well-defined sizes, shapes, and structures,” J. Am. Chem. Soc. 123(36), 8718–8729 (2001). [CrossRef] [PubMed]

4.

A. van Blaaderen, R. Ruel, and P. Wiltzius, “Tempate-directed colloidal crystallization,” Nature 385(6614), 321–324 (1997). [CrossRef]

5.

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), 288–292 (1986). [CrossRef] [PubMed]

6.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987). [CrossRef] [PubMed]

7.

K. Dholakia and W. M. Lee, “Optical trapping takes shape: the use of structured light fields,” Adv. At. Mol. Opt. Phys. 56, 261–337 (2008).

8.

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

9.

K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999). [CrossRef]

10.

B. K. Wilson, T. Mentele, S. Bachar, E. Knouf, A. Bendoraite, M. Tewari, S. H. Pun, and L. Y. Lin, “Nanostructure-enhanced laser tweezers for efficient trapping and alignment of particles,” Opt. Express 18(15), 16005–16013 (2010). [CrossRef] [PubMed]

11.

M. Barth and O. Benson, “Manipulation of dielectric particles using photonic crystal cavities,” Appl. Phys. Lett. 89(25), 253114 (2006). [CrossRef]

12.

A. Rahmani and P. C. Chaumet, “Optical trapping near a photonic crystal,” Opt. Express 14(13), 6353–6358 (2006). [CrossRef] [PubMed]

13.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009). [CrossRef] [PubMed]

14.

K. Wang, E. Schonbrun, and K. B. Crozier, “Propulsion of gold nanoparticles with surface plasmon polaritons: evidence of enhanced optical force from near-field coupling between gold particle and gold film,” Nano Lett. 9(7), 2623–2629 (2009). [CrossRef] [PubMed]

15.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008). [CrossRef]

16.

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009). [CrossRef]

17.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett. 100(18), 186804 (2008). [CrossRef] [PubMed]

18.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

19.

P. J. Reece, V. Garces-Chavez, and K. Dholakia, “Near-field optical micromanipulation with cavity enhanced evanescent waves,” Appl. Phys. Lett. 88(22), 221116 (2006). [CrossRef]

20.

E. Lidorikis, Q. Li, and C. M. Soukoulis, “Optical bistability in colloidal crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3613–3618 (1997). [CrossRef]

21.

M. I. Antonoyiannakis and J. B. Pendry, “Electromagnetic forces in photonic crystals,” Phys. Rev. B 60(4), 2363–2374 (1999). [CrossRef]

22.

K. S. Kunz and R. J. Luebbers, The Finite-Difference Time-Domain Method for Electromagnetics (CRC Press, 1993).

23.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010). [CrossRef]

24.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley & Sons, 1999).

25.

J. Pan, Y. Huo, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103114 (2008). [CrossRef]

26.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

27.

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

28.

M. Barth and O. Benson, “Manipulation of dielectric particles using photonic crystal cavities,” Appl. Phys. Lett. 89(25), 253114 (2006). [CrossRef]

29.

J. H. Lee, Q. Wu, and W. Park, “Metal nanocluster metamaterial fabricated by the colloidal self-assembly,” Opt. Lett. 34(4), 443–445 (2009). [CrossRef] [PubMed]

OCIS Codes
(220.4880) Optical design and fabrication : Optomechanics
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: May 17, 2011
Revised Manuscript: May 23, 2011
Manuscript Accepted: May 23, 2011
Published: May 26, 2011

Citation
Camilo A. Mejia, Avik Dutt, and Michelle L. Povinelli, "Light-assisted templated self assembly using photonic crystal slabs," Opt. Express 19, 11422-11428 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11422


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References

  1. G. M. Whitesides and B. Grzybowski, “Self-assembly at all scales,” Science 295(5564), 2418–2421 (2002). [CrossRef] [PubMed]
  2. Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. (Deerfield Beach Fla.) 13(6), 409–413 (2001). [CrossRef]
  3. Y. Yin, Y. Lu, B. Gates, and Y. Xia, “Template-assisted self-assembly: a practical route to complex aggregates of monodispersed colloids with well-defined sizes, shapes, and structures,” J. Am. Chem. Soc. 123(36), 8718–8729 (2001). [CrossRef] [PubMed]
  4. A. van Blaaderen, R. Ruel, and P. Wiltzius, “Tempate-directed colloidal crystallization,” Nature 385(6614), 321–324 (1997). [CrossRef]
  5. 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), 288–292 (1986). [CrossRef] [PubMed]
  6. A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330(6150), 769–771 (1987). [CrossRef] [PubMed]
  7. K. Dholakia and W. M. Lee, “Optical trapping takes shape: the use of structured light fields,” Adv. At. Mol. Opt. Phys. 56, 261–337 (2008).
  8. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]
  9. K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999). [CrossRef]
  10. B. K. Wilson, T. Mentele, S. Bachar, E. Knouf, A. Bendoraite, M. Tewari, S. H. Pun, and L. Y. Lin, “Nanostructure-enhanced laser tweezers for efficient trapping and alignment of particles,” Opt. Express 18(15), 16005–16013 (2010). [CrossRef] [PubMed]
  11. M. Barth and O. Benson, “Manipulation of dielectric particles using photonic crystal cavities,” Appl. Phys. Lett. 89(25), 253114 (2006). [CrossRef]
  12. A. Rahmani and P. C. Chaumet, “Optical trapping near a photonic crystal,” Opt. Express 14(13), 6353–6358 (2006). [CrossRef] [PubMed]
  13. A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009). [CrossRef] [PubMed]
  14. K. Wang, E. Schonbrun, and K. B. Crozier, “Propulsion of gold nanoparticles with surface plasmon polaritons: evidence of enhanced optical force from near-field coupling between gold particle and gold film,” Nano Lett. 9(7), 2623–2629 (2009). [CrossRef] [PubMed]
  15. A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008). [CrossRef]
  16. M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009). [CrossRef]
  17. M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable optical manipulation in the femtonewton range,” Phys. Rev. Lett. 100(18), 186804 (2008). [CrossRef] [PubMed]
  18. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]
  19. P. J. Reece, V. Garces-Chavez, and K. Dholakia, “Near-field optical micromanipulation with cavity enhanced evanescent waves,” Appl. Phys. Lett. 88(22), 221116 (2006). [CrossRef]
  20. E. Lidorikis, Q. Li, and C. M. Soukoulis, “Optical bistability in colloidal crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3613–3618 (1997). [CrossRef]
  21. M. I. Antonoyiannakis and J. B. Pendry, “Electromagnetic forces in photonic crystals,” Phys. Rev. B 60(4), 2363–2374 (1999). [CrossRef]
  22. K. S. Kunz and R. J. Luebbers, The Finite-Difference Time-Domain Method for Electromagnetics (CRC Press, 1993).
  23. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010). [CrossRef]
  24. J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley & Sons, 1999).
  25. J. Pan, Y. Huo, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103114 (2008). [CrossRef]
  26. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).
  27. K. Dholakia and P. Zemánek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82(2), 1767–1791 (2010). [CrossRef]
  28. M. Barth and O. Benson, “Manipulation of dielectric particles using photonic crystal cavities,” Appl. Phys. Lett. 89(25), 253114 (2006). [CrossRef]
  29. J. H. Lee, Q. Wu, and W. Park, “Metal nanocluster metamaterial fabricated by the colloidal self-assembly,” Opt. Lett. 34(4), 443–445 (2009). [CrossRef] [PubMed]

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