A closed-form analytical expression of the force on an infinite lossless dielectric cylinder due to multiple plane wave incidences is proposed. The formula for a TE polarization is derived and completes our previous work which was limited to TM polarizations. A unified form of the analytical expression of the force is proposed and used to study the curvature of the one dimensional potential of an optical lattice created by the interference of three plane waves. It is shown that the points of zero curvature yield optical vortices which can be used to stably trap particles of particular sizes and index contrasts with the background. Under these circumstances, the trajectories of the particles can be assimilated to spirals whose centers correspond to the points of undetermined phase in the optical landscape.

© 2007 Optical Society of America

1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992). [CrossRef] [PubMed]
2. J. F. Nye and J. V. Hajnal, "The wave structure of monochromatic electromagnetic radiation," Proc. R. Soc. London Ser. A 409, 21-36 (1987). [CrossRef]
3. D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003). [CrossRef] [PubMed]
4. M. V. Berry, "Optical vortices evolving from helicoidal integer and fractional phase steps," J. Opt. A: Pure Appl. Opt. 6, 259-268 (2004). [CrossRef]
5. L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, 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]
6. A. Jesacher, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, "Holographic optical tweezers for object manipulations at an air-liquid surface," Opt. Express 14, 6342-6352 (2006). [CrossRef] [PubMed]
7. K. T. Gahagan and J. G. A. Swartzlander, "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996). [CrossRef] [PubMed]
8. 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, 288-290 (1986). [CrossRef] [PubMed]
9. D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, "Laser trapping and micromanipulation using optical vortices," Microelectron. Eng. 78-79, 125-131 (2005). [CrossRef]
10. J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002). [CrossRef]
11. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical Matter: crystallization and binding in intense optical fields," Science 249, 749-754 (1990). [CrossRef] [PubMed]
12. J.-M. Fournier, G. Boer, G. Delacrétaz, P. Jacquot, J. Rohner, and R. Salathé, "Building optical matter with binding and trapping forces," Proc. SPIE 5514, 309-317 (2004). [CrossRef]
13. T. M. Grzegorczyk and J. A. Kong, "Analytical expression of the force due to multiple TM plane wave incidences on an infinite dielectric cylinder," J. Opt. Soc. Am. B 24, 644-652 (2006). [CrossRef]
14. J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001). [CrossRef]
15. B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988). [CrossRef]
16. P. C. Chaumet and M. Nieto-Vesperinas, "Coupled dipole method determination of the electromagnetic force on particle over a flat dielectric substrate," Phys. Rev. B 61, 14119-14127 (2000). [CrossRef]
17. T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006). [CrossRef] [PubMed]
18. T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field," J. Opt. Soc. Am. A 23, 2324-2330 (2006). [CrossRef]
19. D. Maystre and P. Vincent, "Making photonic crystals using trapping and binding optical forces on particles," J. Opt. A: Pure Appl. Opt. 8, 1059-1066 (2006). [CrossRef]
20. B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Optical momentum transfer to absorbing Mie particles," Phys. Rev. Lett. 97, 133902 (2006). [CrossRef] [PubMed]
21. P. Zemanek, V. Karasek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004). [CrossRef]
22. A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992). [CrossRef] [PubMed]

Appl. Phys. Lett.

• L. Paterson, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, 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]

Astrophys. J.

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

Biophys. J.

• A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992). [CrossRef] [PubMed]

J. Opt. A: Pure Appl. Opt.

• D. Maystre and P. Vincent, "Making photonic crystals using trapping and binding optical forces on particles," J. Opt. A: Pure Appl. Opt. 8, 1059-1066 (2006). [CrossRef]
• M. V. Berry, "Optical vortices evolving from helicoidal integer and fractional phase steps," J. Opt. A: Pure Appl. Opt. 6, 259-268 (2004). [CrossRef]

J. Opt. Soc. Am. A

• T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field," J. Opt. Soc. Am. A 23, 2324-2330 (2006). [CrossRef]

J. Opt. Soc. Am. B

• T. M. Grzegorczyk and J. A. Kong, "Analytical expression of the force due to multiple TM plane wave incidences on an infinite dielectric cylinder," J. Opt. Soc. Am. B 24, 644-652 (2006). [CrossRef]

Microelectron. Eng.

• D. Cojoc, V. Garbin, E. Ferrari, L. Businaro, F. Romanato, and E. Di Fabrizio, "Laser trapping and micromanipulation using optical vortices," Microelectron. Eng. 78-79, 125-131 (2005). [CrossRef]

Nature

• D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003). [CrossRef] [PubMed]

Opt. Commun.

• J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002). [CrossRef]
• J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001). [CrossRef]
• P. Zemanek, V. Karasek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004). [CrossRef]

Opt. Express

• A. Jesacher, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, "Holographic optical tweezers for object manipulations at an air-liquid surface," Opt. Express 14, 6342-6352 (2006). [CrossRef] [PubMed]

Opt. Lett.

• K. T. Gahagan and J. G. A. Swartzlander, "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996). [CrossRef] [PubMed]
• 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, 288-290 (1986). [CrossRef] [PubMed]

Phys. Rev. A

• L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992). [CrossRef] [PubMed]

Phys. Rev. B

• P. C. Chaumet and M. Nieto-Vesperinas, "Coupled dipole method determination of the electromagnetic force on particle over a flat dielectric substrate," Phys. Rev. B 61, 14119-14127 (2000). [CrossRef]

Phys. Rev. Lett.

• T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006). [CrossRef] [PubMed]
• B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Optical momentum transfer to absorbing Mie particles," Phys. Rev. Lett. 97, 133902 (2006). [CrossRef] [PubMed]

Proc. R. Soc. London Ser. A

• J. F. Nye and J. V. Hajnal, "The wave structure of monochromatic electromagnetic radiation," Proc. R. Soc. London Ser. A 409, 21-36 (1987). [CrossRef]

Proc. SPIE

• J.-M. Fournier, G. Boer, G. Delacrétaz, P. Jacquot, J. Rohner, and R. Salathé, "Building optical matter with binding and trapping forces," Proc. SPIE 5514, 309-317 (2004). [CrossRef]

Science

• M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical Matter: crystallization and binding in intense optical fields," Science 249, 749-754 (1990). [CrossRef] [PubMed]

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