Abstract

The Mie theory and the Foldy–Lax multiple-scattering equations are applied to compute the scattered field of an arbitrary number of infinite dielectric cylinders of arbitrary size, subject to in-plane incidences. The Maxwell stress tensor is then used to compute the force on each cylinder. Trapping and binding forces are studied as a function of particle size, number, permittivity, and separation. Finally, the formulation is applied to a system of 20 particles, and the results show clear similarities with known experimental reports. The formulation presented here extends the capabilities of modeling particle interaction and optical matter beyond the simple cases of the Rayleigh regime and two-particle systems.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
    [CrossRef]
  2. A. Ashkin and J. M. Dziedzic, "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283-285 (1971).
    [CrossRef]
  3. A. Ashkin and J. M. Dziedzic, "Optical levitation in high vacuum," Appl. Phys. Lett. 28, 333-335 (1976).
    [CrossRef]
  4. A. Ashkin, "Applications of laser radiation pressure," Science 210, 1081-1088 (1980).
    [CrossRef] [PubMed]
  5. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
    [CrossRef] [PubMed]
  6. 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]
  7. J.-M. Fournier, G. Boer, G. Delacrétaz, P. Jacquot, J. Rohner, and R. Salathé, "Building optical matter with binding and trapping forces," in Proc. SPIE 5514, 309-317 (2004).
    [CrossRef]
  8. A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
    [CrossRef]
  9. 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]
  10. J. Stratton, Electromagnetic Theory (McGraw-Hill,1941).
  11. J. A. Kong, Electromagnetic Wave Theory (EMW, 2000).
  12. A. R. Zakharian, M. Mansuripur, and J. V. Moloney, "Radiation pressure and the distribution of electromagnetic force in dielectric media," Opt. Express 13, 2321-2336 (2005).
    [CrossRef] [PubMed]
  13. A. Ashkin, "Trapping of atoms by resonance radiation pressure," Phys. Rev. Lett. 40, 729-732 (1978).
    [CrossRef]
  14. J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
    [CrossRef]
  15. P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2001).
    [CrossRef]
  16. J. R. Arias-González and M. Nieto-Vesperinas, "Optical forces on small particles: attractive and repulsive nature and plasmon-resonance conditions," J. Opt. Soc. Am. A 20, 1201-1209 (2003).
    [CrossRef]
  17. E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
    [CrossRef]
  18. P. C. Chaumet and M. Nieto-Vesperinas, "Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate," Phys. Rev. B 61, 14119-14127 (2000).
    [CrossRef]
  19. C. Rockstuhl and H. P. Herzig, "Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders," J. Opt. A, Pure Appl. Opt. 6, 921-931 (2004).
    [CrossRef]
  20. A. Madrazo and M. Nieto-Vesperinas, "Scattering of electromagnetic waves from a cylinder in front of a conducting plane," J. Opt. Soc. Am. A 12, 1298-1309 (1995).
    [CrossRef]
  21. A. Madrazo and M. Nieto-Vesperinas, "Surface structure and polariton interactions in the scattering of electromagnetic waves from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope," J. Opt. Soc. Am. A 13, 785-795 (1996).
    [CrossRef]
  22. F. Depasse and J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D 27, 914-919 (1994).
    [CrossRef]
  23. P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64, 035422 (2001).
    [CrossRef]
  24. L. Tsang, J. Kong, K. Ding, and C. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).
    [CrossRef]
  25. L. L. Foldy, "The multiple scattering of waves," Phys. Rev. 67, 107-119 (1945).
    [CrossRef]
  26. M. Lax, "Multiple scattering of waves. II. The effective field in dense systems," Phys. Rev. 85, 261-269 (1952).
    [CrossRef]
  27. M. Lester and M. Nieto-Vesperinas, "Optical forces on microparticles in an evanescent laser field," Opt. Lett. 24, 936-938 (1999).
    [CrossRef]
  28. B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Ab initio study of the radiation pressure on dielectric and magnetic media," Opt. Express 13, 9280-9291 (2005).
    [CrossRef] [PubMed]
  29. B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
    [CrossRef]
  30. P. Zemánek, V. Karásek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004).
    [CrossRef]
  31. J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," in Proc. SPIE 5930, 238-247 (2005).

2006

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, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

2005

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Ab initio study of the radiation pressure on dielectric and magnetic media," Opt. Express 13, 9280-9291 (2005).
[CrossRef] [PubMed]

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," in Proc. SPIE 5930, 238-247 (2005).

A. R. Zakharian, M. Mansuripur, and J. V. Moloney, "Radiation pressure and the distribution of electromagnetic force in dielectric media," Opt. Express 13, 2321-2336 (2005).
[CrossRef] [PubMed]

A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
[CrossRef]

2004

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

P. Zemánek, V. Karásek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004).
[CrossRef]

C. Rockstuhl and H. P. Herzig, "Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders," J. Opt. A, Pure Appl. Opt. 6, 921-931 (2004).
[CrossRef]

2003

2001

P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2001).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64, 035422 (2001).
[CrossRef]

2000

L. Tsang, J. Kong, K. Ding, and C. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).
[CrossRef]

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

J. A. Kong, Electromagnetic Wave Theory (EMW, 2000).

1999

1996

1995

1994

F. Depasse and J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D 27, 914-919 (1994).
[CrossRef]

1990

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]

1989

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

1980

A. Ashkin, "Applications of laser radiation pressure," Science 210, 1081-1088 (1980).
[CrossRef] [PubMed]

1978

A. Ashkin, "Trapping of atoms by resonance radiation pressure," Phys. Rev. Lett. 40, 729-732 (1978).
[CrossRef]

1976

A. Ashkin and J. M. Dziedzic, "Optical levitation in high vacuum," Appl. Phys. Lett. 28, 333-335 (1976).
[CrossRef]

1973

J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

1971

A. Ashkin and J. M. Dziedzic, "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283-285 (1971).
[CrossRef]

1970

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

1952

M. Lax, "Multiple scattering of waves. II. The effective field in dense systems," Phys. Rev. 85, 261-269 (1952).
[CrossRef]

1945

L. L. Foldy, "The multiple scattering of waves," Phys. Rev. 67, 107-119 (1945).
[CrossRef]

1941

J. Stratton, Electromagnetic Theory (McGraw-Hill,1941).

Ao, C.

L. Tsang, J. Kong, K. Ding, and C. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).
[CrossRef]

Arias-González, J. R.

Ashkin, A.

A. Ashkin, "Applications of laser radiation pressure," Science 210, 1081-1088 (1980).
[CrossRef] [PubMed]

A. Ashkin, "Trapping of atoms by resonance radiation pressure," Phys. Rev. Lett. 40, 729-732 (1978).
[CrossRef]

A. Ashkin and J. M. Dziedzic, "Optical levitation in high vacuum," Appl. Phys. Lett. 28, 333-335 (1976).
[CrossRef]

A. Ashkin and J. M. Dziedzic, "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283-285 (1971).
[CrossRef]

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

Boer, G.

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

Burns, M. M.

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]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Casaburi, A.

A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
[CrossRef]

Chaumet, P. C.

P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2001).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64, 035422 (2001).
[CrossRef]

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

Delacrétaz, G.

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

Depasse, F.

F. Depasse and J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D 27, 914-919 (1994).
[CrossRef]

Ding, K.

L. Tsang, J. Kong, K. Ding, and C. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).
[CrossRef]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, "Optical levitation in high vacuum," Appl. Phys. Lett. 28, 333-335 (1976).
[CrossRef]

A. Ashkin and J. M. Dziedzic, "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283-285 (1971).
[CrossRef]

Foldy, L. L.

L. L. Foldy, "The multiple scattering of waves," Phys. Rev. 67, 107-119 (1945).
[CrossRef]

Fournier, J.-M.

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," in Proc. SPIE 5930, 238-247 (2005).

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

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]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Golovchenko, J. A.

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]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Gordon, J. P.

J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

Grzegorczyk, T. M.

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, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Ab initio study of the radiation pressure on dielectric and magnetic media," Opt. Express 13, 9280-9291 (2005).
[CrossRef] [PubMed]

Herzig, H. P.

C. Rockstuhl and H. P. Herzig, "Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders," J. Opt. A, Pure Appl. Opt. 6, 921-931 (2004).
[CrossRef]

Jacquot, P.

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," in Proc. SPIE 5930, 238-247 (2005).

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

Johann, R.

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," in Proc. SPIE 5930, 238-247 (2005).

Karásek, V.

P. Zemánek, V. Karásek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004).
[CrossRef]

Kemp, B. A.

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

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, "Ab initio study of the radiation pressure on dielectric and magnetic media," Opt. Express 13, 9280-9291 (2005).
[CrossRef] [PubMed]

Kong, J.

L. Tsang, J. Kong, K. Ding, and C. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).
[CrossRef]

Kong, J. A.

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

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, "Ab initio study of the radiation pressure on dielectric and magnetic media," Opt. Express 13, 9280-9291 (2005).
[CrossRef] [PubMed]

J. A. Kong, Electromagnetic Wave Theory (EMW, 2000).

Lax, M.

M. Lax, "Multiple scattering of waves. II. The effective field in dense systems," Phys. Rev. 85, 261-269 (1952).
[CrossRef]

Lester, M.

Madrazo, A.

Mansuripur, M.

Mias, S.

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," in Proc. SPIE 5930, 238-247 (2005).

Moloney, J. V.

Nieto-Vesperinas, M.

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Pesce, G.

A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
[CrossRef]

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Rockstuhl, C.

C. Rockstuhl and H. P. Herzig, "Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders," J. Opt. A, Pure Appl. Opt. 6, 921-931 (2004).
[CrossRef]

Rohner, J.

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," in Proc. SPIE 5930, 238-247 (2005).

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

Salathé, R.

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," in Proc. SPIE 5930, 238-247 (2005).

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

Sasso, A.

A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
[CrossRef]

P. Zemánek, V. Karásek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004).
[CrossRef]

Stratton, J.

J. Stratton, Electromagnetic Theory (McGraw-Hill,1941).

Tsang, L.

L. Tsang, J. Kong, K. Ding, and C. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).
[CrossRef]

Vigoureux, J.-M.

F. Depasse and J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D 27, 914-919 (1994).
[CrossRef]

Zakharian, A. R.

Zemánek, P.

A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
[CrossRef]

P. Zemánek, V. Karásek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004).
[CrossRef]

Appl. Phys. Lett.

A. Ashkin and J. M. Dziedzic, "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283-285 (1971).
[CrossRef]

A. Ashkin and J. M. Dziedzic, "Optical levitation in high vacuum," Appl. Phys. Lett. 28, 333-335 (1976).
[CrossRef]

Astrophys. J.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

J. Electromagn. Waves Appl.

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Lorentz force on dielectric and magnetic particles," J. Electromagn. Waves Appl. 20, 827-839 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

C. Rockstuhl and H. P. Herzig, "Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders," J. Opt. A, Pure Appl. Opt. 6, 921-931 (2004).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. D

F. Depasse and J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D 27, 914-919 (1994).
[CrossRef]

Opt. Commun.

P. Zemánek, V. Karásek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004).
[CrossRef]

A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, "Two- and three-beam interferometric optical tweezers," Opt. Commun. 251, 393-404 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

L. L. Foldy, "The multiple scattering of waves," Phys. Rev. 67, 107-119 (1945).
[CrossRef]

M. Lax, "Multiple scattering of waves. II. The effective field in dense systems," Phys. Rev. 85, 261-269 (1952).
[CrossRef]

Phys. Rev. A

J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

Phys. Rev. B

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

P. C. Chaumet and M. Nieto-Vesperinas, "Optical binding of particles with or without the presence of a flat dielectric surface," Phys. Rev. B 64, 035422 (2001).
[CrossRef]

Phys. Rev. Lett.

A. Ashkin, "Trapping of atoms by resonance radiation pressure," Phys. Rev. Lett. 40, 729-732 (1978).
[CrossRef]

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

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]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef] [PubMed]

Proc. SPIE

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

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," in Proc. SPIE 5930, 238-247 (2005).

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]

A. Ashkin, "Applications of laser radiation pressure," Science 210, 1081-1088 (1980).
[CrossRef] [PubMed]

Other

J. Stratton, Electromagnetic Theory (McGraw-Hill,1941).

J. A. Kong, Electromagnetic Wave Theory (EMW, 2000).

L. Tsang, J. Kong, K. Ding, and C. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Force (represented by the black arrows) on a single cylinder due to the interference of three plane waves (represented by the background pattern) of identical amplitude E 0 = 1 ( V m ) , wavelength λ = 546 nm , and incident angles { π 2 , 7 π 6 , 11 π 6 } (rad). Other parameters are ϵ c = 2.56 ϵ 0 , ϵ = 1.69 ϵ 0 , N = 5 , and the radius a of the cylinder is as indicated. The background pattern shows the absolute value of the electric field on a scale from 0 ( V m ) (black) to 3 ( V m ) (white) (a) a = 0.15 λ , (b) a = 0.3 λ .

Fig. 2
Fig. 2

Two infinite cylinders of radius a and permittivity ϵ c are embedded in a background medium of permittivity ϵ = 1.69 ϵ 0 and subject to an incident field propagating in the y ̂ direction as indicated.

Fig. 3
Fig. 3

Force in the x ̂ direction for the configuration of Fig. 2 as a function of the relative distance between particles. The parameters are λ = 546 nm , ϵ c = 2.56 ϵ 0 , ϵ = 1.69 ϵ 0 , N = 10 , and radius a as indicated in the labels.

Fig. 4
Fig. 4

Force in the x ̂ direction for the configuration of Fig. 2 as a function of the relative distance between particles. The parameters are λ = 546 nm , ϵ = 1.69 ϵ 0 , a = 0.3 λ , and N = 10 . The relative permittivity of the cylinders is as indicated in the labels.

Fig. 5
Fig. 5

Force in the x ̂ direction for varying number of cylinders on the left (the force and the positions are for the particle on the right). The case of one cylinder corresponds to Fig. 2, the cases of two and four cylinders correspond to the situations shown in the insets. The positions of the fixed cylinders are ( x , y ) = ( 0 , ± 170 nm ) and ( x , y ) = { ( 170 nm , ± 170 nm ) , ( 0 , ± 170 nm ) } in the cases of two and four particles, respectively. The parameters are λ = 546 nm , ϵ c = 2.56 ϵ 0 , ϵ = 1.69 ϵ 0 , a = 0.3 λ , and N = 20 .

Fig. 6
Fig. 6

Positions of 20 dielectric cylinders and field distributions (shown in the background) for various cases: (a) random initial position in a three-plane-wave interference pattern (incident field shown); (b) organized final position due to trapping and binding forces (incident field shown); (c) same as case (b) but with the total field shown; (d) organized final position corresponding to another set of initial positions different from that in case (a). In all cases, the parameters are λ = 546 nm , ϵ c = 256 ϵ 0 , ϵ = 169 ϵ 0 , a = 0.15 λ , and N = 10 . The background patterns show the absolute value of the electric field (either incident or total field) on a scale from 0 (black) to 3 V m (white).

Tables (1)

Tables Icon

Table 1 Initial Positions ( x i , y i ) and Final Positions ( x f , y f ) of 20 Particles in a Three-Plane-Wave Interference Pattern a

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

E inc ( ρ ) = z ̂ E 0 e i k ρ = n = + a n R g N n ( k , ρ ) ,
H inc ( ρ ) = z ̂ × k ̂ z ̂ × k ̂ E 0 η 0 e i k ρ ,
E scat ( ρ ) = n = + a n s N n ( k , ρ ) ,
H scat ( ρ ) = 1 i η n = + a n s M n ( k , ρ ) ,
M n ( k , ρ ) = ρ ̂ i n ρ H n ( 1 ) ( k ρ ) e i n ϕ ϕ ̂ k H n ( 1 ) ( k ρ ) e i n ϕ ,
N n ( k , ρ ) = z ̂ k N n ( 1 ) ( k ρ ) e i n ϕ ,
E ex ( q ) ( ρ ) = E inc ( ρ ) + = 1 l q L E scat ( ) ( ρ ) .
E scat ( q ) ( ρ ) = n = + a n s ( q ) N n ( k , ρ ρ q ) ,
a n s ( q ) = T n w n ( q ) ,
T n = k c k J n ( k c a ) H n ( 1 ) ( k a ) B n J n ( k a ) H n ( 1 ) ( k a ) ,
B n = 2 i k π a k c [ k H n ( 1 ) ( k a ) J n ( k c a ) k c J n ( k c a ) H n ( 1 ) ( k a ) ] 1 ,
w n ( q ) = e i k ρ q a n + n = + = 1 l q L H n n ( 1 ) ( k ρ l ρ q ) e i ( n n ) ϕ l q T n w n ( ) ,
H n ( 1 ) ( k ρ ρ p ) e i n ϕ l p = n = + J n ( k ρ ρ q ) e i n ϕ l q H n n ( 1 ) ( k ρ p ρ q ) e i ( n n ) ϕ p q .
E scat ( ρ ) = q = 1 L E scat ( q ) ( ρ ) .
F = C d [ ϵ 2 Re { ( E n ̂ ) E * } + μ 2 Re { ( H n ̂ ) H ̂ * } ϵ 4 ( E E * ) n ̂ μ 4 ( H H * ) n ̂ ] .
x l i + 1 = x l i + α f x l i ,
y l i + 1 = y l i + α f y l i ,

Metrics