2330 J. Opt. Soc. Am. A/Vol 23, No 9/September 2006 only the good efficiency of the traps but also that the seat- 10. J. Stratton, Electromagnetic Theory (McGraw-Hill, ring is weak and does not perturb the incident waves 1941) significantly. For this type of dielectric contrast, a born 11. J. A. Kong, Electromagnetic Waue (EMW,2000 approximation can be used to compute the field in the sys- 12. A. R. Zakharian, M. Mansuript "Radiation pressure and the distri tem and confirm these cor inclusions force in dielectric media, "Opt. 321-2336 13. A. Ashkin, Trapping of by resonance radiation 6. CONCLUSIONS sure, Phys. Rev. Lett. 40, 729-732(1978) 14. J. P Gordon. "Radiation forces and momenta in dielectric We have demonstrated in this paper that both trapping media, "Phys. Rev. A 8, 14-21(1973 nd binding forces in a complex arrangement of particles 15. P C Chaumet and M. Nieto-Vesperinas,"Time-averaged an be predicted without approximations on particle size total force on a dipolar sphere in an electromagnetic field, permittivity, or separation. The theoretical model, based Opt.Lett.25,1065-1067(2001) on an extension of Mie theory to cylindrical particles com- 16. R. Arias-Gonzalez and M. Nieto- Vesperinas, " Optical forces on small particles: attractive and repulsive nature bined with the Foldy-Lax multiple-scattering equations d plasmon-resonance conditions, J. Opt. Soc. Am.A nd the Maxwell stress tensor, has been shown to predict 01-1209(2003 some recent experimental results reasonably well with 17. E. M. Purcell and C. R. Pennypacker, "Scattering imited requirements on computer memory. Such model- ing capability represents a step forward in the under- 18. P. C. Chaumet and M. Nieto-Vesperinas, "Coupled dipole standing of optical tweezers, optical matter, and other method determination of the electromagnetic force systems where large particles are manipulated by radia particle over a fat dielectric substrate, " Phys. Rev. B 61 tion pressure 14119-14127(2000) 19. C. Rockstuhl and H. P. Herzig, " Rigorous lied to the analysis of the optical ACKNOWLEDGMENTS J. Opt. A, P 921-931(2004 It is a pleasure to acknowledge many stimulating discus- 20. A. Madrazo and M. Nieto- Vesperinas, Scattering of ns with J -M. Fournier. This work is sponsored by the Department of the U. S. Air Force under Air Force con- tract FA8721-05-C-0002 and by the Chinese Nation 2t onducting plane,"J.Opt. Soc. Am. A 12, 1298-1309 A. Madrazo and M. Nieto-Vesperinas, " Surface structure Foundation under contracts 60371010 and 60531020 Opinions, interpretations, conclusions, and recommenda- lectromagnetic waves from a r in front of a tions are those of the author and are not necessarily en- onducting grating: theory for the reflection photon eling microscope, J. Opt. Soc. Am. A 13, Corresponding author T. M. Grzegorczyk can be 22. F. Depasse and J.-M. Vigoureux, Optical binding force reached by e-mail at tomasz@mit. edu. 23. P C Chaumet and M. Nieto- Vesperinas, "Optical binding of REFERENCES articles with or without the of a fat dielectr urface, Phys. Rev. B 64, 035422(2001) 1. A. Ashkin. "Acceleration and tra of particles by 24. L. Tsang, J. Kong, K. Ding, and C. Ao, Scattering of Electromagnetic Waves: Numerical Simulations 2. A. Ashkin and M. Dziedzic (1971 5. LL Foldy, " The multiple scattering of waves, "Phys. Rev. 3. A. Ashkin and J. M. Dziedzic, "Optical levitation in high 26. M. Lax, "Multiple scattering of waves. Il. The effective field acuum, " Appl. Phys. Lett. 28, 333-335(1976) 4. A. Ashkin, "Applications of laser radiation pressure, 27. M. Lester and M. Nieto-Vesperinas, "Optical forces on Science210,1081-1088(1980) 5. M. M. Burns. J.M. Fournier. and A. Go microparticles in an evanescent laser field, Opt Lett. 24 "Optical binding, "Phys. Rev. Lett. 63, 1233-123 urns. J 28. B A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Ab initio nd binding in intense study of the radiation media, "Opt tical fields. "Science 249, 749-754(1990) 92809291(2005 7. J-M. Fournier. G 29. B. A. Kemp, T M. Grzegorczyk, and J. A. Kong, Lorentz R. Proe.SPI5514,309-317 Waves Appl.20,827-839(2006) (2004) 30. P. Zemanek, V. Karasek, and A. Sasso, "Optical forces 8. A Casaburi, G. Pesce, P Zemanek, and A Sasso, Two- and 240,401-415(2004) Commun.251,393-404(2005 T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Stable 31. and, Rousaiat e. Assem b inga quet, sco ichanat ices ia optical trapping based on optical binding forces, "Phys. Rev various optical schemes, in Proc. SPIE 5930, 238-247 Let.6,113903(2006) 2005only the good efficiency of the traps but also that the scat￾tering is weak and does not perturb the incident waves significantly. For this type of dielectric contrast, a Born approximation can be used to compute the field in the sys￾tem and confirm these conclusions. 6. CONCLUSIONS We have demonstrated in this paper that both trapping and binding forces in a complex arrangement of particles can be predicted without approximations on particle size, permittivity, or separation. The theoretical model, based on an extension of Mie theory to cylindrical particles com￾bined with the Foldy–Lax multiple-scattering equations and the Maxwell stress tensor, has been shown to predict some recent experimental results reasonably well with limited requirements on computer memory. 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