Abstract

A closed-form expression of the force on an infinite lossless dielectric cylinder illuminated by a TM incidence (electric field parallel to the cylinder’s axis) is derived. The formula, expressed as a simple sum, is straightforward to compute and is shown to be faster converging than the direct application of the Maxwell stress tensor and the expansion of the fields in the cylindrical coordinate system. A generalization of the formula to multiple incidences is provided and is illustrated by studying the force due to a Gaussian beam on cylinders of various parameters. We show in this way that the effects of the gradient of the intensity profile on the transverse and longitudinal confinements are decoupled, due to the permittivity contrast and to the size of the particle. Since the formula we derive is exact and is therefore not limited to the Rayleigh or ray optics regime, we expect it to be important for the modeling of optical forces on elongated particles of arbitrary sizes.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  31. 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]
  32. 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]
  33. J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," Proc. SPIE 5930, 238-247 (2005).
  34. P. C. Chaumet and M. Nieto-Vesperinas, "Time-average total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2001).
    [CrossRef]
  35. 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]
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    [CrossRef]
  37. P. Zemánek, V. Karásek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004).
    [CrossRef]
  38. C. D. Mellor and C. D. Bain, "Array formation in evanescent waves," ChemPhysChem 7, 329-332 (2006).
    [CrossRef]
  39. L. Tsang, J. Kong, K. Ding, and C. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2006 (10)

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]

V. Wong and M. A. Ratner, "Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles," Phys. Rev. B 73, 075416 (2006).
[CrossRef]

J. Zhang, H. I. Kim, X. Sun, C. H. Oh, and H. Lee, "Optical trapping carbon nanotubes," Colloids Surf. A 284-285, 369-372 (2006).
[CrossRef]

D. Maystre and P. Vincent, "Making photonic crystals using trapping and binding optical forces on particles," J. Opt. A 8, 1059-1066 (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, "Optical momentum transfer to absorbing Mie particles," Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

C. D. Mellor and C. D. Bain, "Array formation in evanescent waves," ChemPhysChem 7, 329-332 (2006).
[CrossRef]

M. Pelton, M. Liu, H. Y. Kim, G. Smith, P. Guyot-Sionnest, and N. F. Scherer, "Optical trapping and alignment of single gold nanorods by using plasmon resonances," Opt. Lett. 31, 2075-2077 (2006).
[CrossRef] [PubMed]

V. V. Kotlyar and A. G. Nalimov, "Analytical expression for radiation forces on a dielectric cylinder illuminated by a cylindrical Gaussian beam," Opt. Express 14, 6316-6321 (2006).
[CrossRef] [PubMed]

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]

2005 (4)

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]

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," 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]

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]

2004 (3)

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

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]

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 6, 921-931 (2004).
[CrossRef]

2003 (1)

2001 (1)

2000 (1)

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

1999 (2)

1998 (2)

K. T. Gahagan and J. G. A. Swartzlander, "Trapping of low-index microparticles in an optical vortex," J. Opt. Soc. Am. B 15, 524-534 (1998).
[CrossRef]

P. Zemánek, A. Jonás, L. Srámek, and M. Liska, "Optical trapping of Rayleigh particles using a Gaussian standing wave," Opt. Commun. 151, 273-285 (1998).
[CrossRef]

1996 (2)

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

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

1995 (1)

1994 (2)

D. Felbacq, G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," J. Opt. Soc. Am. A 11, 2526-2538 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, and G. Gouesbet, "Radiation pressure forces exerted on a particle artbitrarily located in a Gaussian beam by using the generalized Lorentz-Mie theory, and associated resonance effects," Opt. Commun. 108, 343-354 (1994).
[CrossRef]

1992 (1)

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]

1989 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

1988 (1)

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

1986 (1)

1973 (1)

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

1971 (1)

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

1970 (1)

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

1905 (1)

J. H. Poynting, "Tangential stress of light obliquely incident on absorbing surface," Philos. Mag. 9, 169-171 (1905).

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

Ao, C.

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

Arias-González, J. R.

Asakura, T.

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

Ashkin, A

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]

Ashkin, A.

Ashman, M.

Bain, C. D.

C. D. Mellor and C. D. Bain, "Array formation in evanescent waves," ChemPhysChem 7, 329-332 (2006).
[CrossRef]

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

Bjorkholm, J. E.

Boer, G.

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]

Bryant, P. E.

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]

Chaumet, P. C.

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

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

Chu, S.

Delacrétaz, G.

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]

Dholakia, K.

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]

Ding, K.

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

L. Tsang, J. Kong, and K. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
[CrossRef]

Draine, B. T.

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

Dziedzic, J. M.

Felbacq, D.

Fournier, J.-M.

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," 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," Proc. SPIE 5514, 309-317 (2004).
[CrossRef]

Gahagan, K. T.

Garcés-Chávez, V.

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]

Gauthier, R. C.

Gordon, J. P.

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

Gouesbet, G.

L. Mees, K. F. Ren, G. Gréhan, and G. Gouesbet, "Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results," Appl. Opt. 38, 1867-1876 (1999).
[CrossRef]

K. F. Ren, G. Gréhan, and G. Gouesbet, "Radiation pressure forces exerted on a particle artbitrarily located in a Gaussian beam by using the generalized Lorentz-Mie theory, and associated resonance effects," Opt. Commun. 108, 343-354 (1994).
[CrossRef]

Gréhan, G.

L. Mees, K. F. Ren, G. Gréhan, and G. Gouesbet, "Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results," Appl. Opt. 38, 1867-1876 (1999).
[CrossRef]

K. F. Ren, G. Gréhan, and G. Gouesbet, "Radiation pressure forces exerted on a particle artbitrarily located in a Gaussian beam by using the generalized Lorentz-Mie theory, and associated resonance effects," Opt. Commun. 108, 343-354 (1994).
[CrossRef]

Grover, C. P.

Grzegorczyk, T. M.

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]

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, "Optical momentum transfer to absorbing Mie particles," Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

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]

Gunn-Moore, F. J.

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]

Guyot-Sionnest, P.

Harada, Y.

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

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 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," 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," 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," Proc. SPIE 5930, 238-247 (2005).

Jonás, A.

P. Zemánek, A. Jonás, L. Srámek, and M. Liska, "Optical trapping of Rayleigh particles using a Gaussian standing wave," Opt. Commun. 151, 273-285 (1998).
[CrossRef]

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, "Optical momentum transfer to absorbing Mie particles," Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

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]

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]

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]

Kim, H. I.

J. Zhang, H. I. Kim, X. Sun, C. H. Oh, and H. Lee, "Optical trapping carbon nanotubes," Colloids Surf. A 284-285, 369-372 (2006).
[CrossRef]

Kim, H. Y.

Kong, J.

L. Tsang, J. Kong, and K. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
[CrossRef]

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, "Optical momentum transfer to absorbing Mie particles," Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

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]

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]

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, 2005).

Kotlyar, V. V.

Lee, H.

J. Zhang, H. I. Kim, X. Sun, C. H. Oh, and H. Lee, "Optical trapping carbon nanotubes," Colloids Surf. A 284-285, 369-372 (2006).
[CrossRef]

Liska, M.

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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).
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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).
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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).
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J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," 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," Proc. SPIE 5514, 309-317 (2004).
[CrossRef]

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J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mias, and R. Salathé, "Assembling mesoscopic particles by various optical schemes," 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," Proc. SPIE 5514, 309-317 (2004).
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D. Maystre and P. Vincent, "Making photonic crystals using trapping and binding optical forces on particles," J. Opt. A 8, 1059-1066 (2006).
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V. Wong and M. A. Ratner, "Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles," Phys. Rev. B 73, 075416 (2006).
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J. Zhang, H. I. Kim, X. Sun, C. H. Oh, and H. Lee, "Optical trapping carbon nanotubes," Colloids Surf. A 284-285, 369-372 (2006).
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J. Zhang, H. I. Kim, X. Sun, C. H. Oh, and H. Lee, "Optical trapping carbon nanotubes," Colloids Surf. A 284-285, 369-372 (2006).
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J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
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D. Maystre and P. Vincent, "Making photonic crystals using trapping and binding optical forces on particles," J. Opt. A 8, 1059-1066 (2006).
[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 6, 921-931 (2004).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (1)

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

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[CrossRef]

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Opt. Lett. (4)

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J. H. Poynting, "Tangential stress of light obliquely incident on absorbing surface," Philos. Mag. 9, 169-171 (1905).

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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]

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

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

J. A. Kong, Electromagnetic Wave Theory (EMW, 2005).

L. Tsang, J. Kong, and K. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
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[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Comparison of the convergence rate of the summation involved in the force calculation. Solid line: closed-form expression of Eq. (27). Dashed curve: numerical evaluation based on Eqs. (1, 2). Obviously, the two methods eventually converge to the same value. Parameters: ε = 1.69 ε 0 , ε p = 2.56 ε 0 , λ = 1064 nm , k ̂ i = x ̂ .

Fig. 2
Fig. 2

Comparison between the force computed with N = 20 terms (solid curves) and N = 0 term (dashed curves) for various radii a and permittivities ε p . Other parameters are: ε b = 1.69 ε 0 , λ = 1064 nm . The single-term approximation is seen to be valid for particle sizes larger than the Rayleigh limit of λ 20 .

Fig. 3
Fig. 3

Force distributions in space (arrows) and potential (background pattern) in four difference configurations: (a) ε p = 2.56 ε 0 , a = 0.5 λ , (b) ε p = ε 0 , a = 0.5 λ , (c) ε p = 2.56 ε 0 , a = 0.01 λ , (d) ε p = ε 0 , a = 0.01 λ . Two effects can be distinguished: axial and transverse. Axially the large particle is pushed away by the beam while the small one is attracted toward the focus. Transversally the dense particle is attracted into the beam while the less dense one is expelled from it. Case (c) is a classical optical tweezer. Other parameters are: ε b = 1.69 ε 0 , λ = 1064 nm , g = λ 2 .

Fig. 4
Fig. 4

Evolution of the stable trapping position in an optical tweezer as function of particle radius a and tapering parameter g. Tighter focused beam (corresponding to smaller g) is seen to trap larger particles. Parameters are: ε b = 1.69 ε 0 , ε p = 2.56 ε 0 , λ = 1064 nm .

Equations (57)

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F = C d l [ ε 2 R ( ( E n ̂ ) E * ) + μ 2 R ( ( H n ̂ ) H * ) ε 4 E E * n ̂ μ 4 H H * n ̂ ] ,
E inc ( ρ ) = ( v ̂ i E v i + h ̂ i E h i ) e i k ρ = n [ a n ( M ) R g M n ( k , ρ ) + a n ( N ) R g N n ( k , ρ ) ] ,
E scat ( ρ ) = n [ a n ( M ) s M n ( k , ρ ) + a n ( N ) s N n ( k , ρ ) ] ,
E int ( ρ ) = n [ c n ( M ) R g M n ( k p , ρ ) + c n ( N ) R g N n ( k p , 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 H n ( 1 ) ( k ρ ) e i n ϕ ,
a n ( M ) = i n + 1 e i n ϕ i k ρ E h i , a n ( N ) = i n e i n ϕ i k ρ E v i ,
a n ( M ) s = T n M a n ( M ) , a n ( N ) s = T n N a n ( N ) ,
T n M = k p J n ( k p a ) J n ( k a ) k J n ( k a ) J n ( k p a ) k H n ( 1 ) ( k a ) J n ( k p a ) k p H n ( 1 ) ( k a ) J n ( k p a ) ,
T n N = k p J n ( k a ) J n ( k p a ) k J n ( k p a ) J n ( k a ) k H n ( 1 ) ( k a ) J n ( k p a ) k p H n ( 1 ) ( k a ) J n ( k p a ) .
E = E inc + E scat = ρ ̂ n i n ρ [ a n ( M ) s H n ( a ) ( k ρ ) + a n ( M ) J n ( k ρ ) ] e i n ϕ ϕ ̂ n k [ a n ( M ) s H n ( 1 ) ( k ρ ) + a n ( M ) J n ( k ρ ) ] e i n ϕ + z ̂ n k [ a n ( N ) s H n ( 1 ) ( k ρ ) + a n ( N ) J n ( k ρ ) ] e in ϕ ,
i η H = i η ( H inc + H scat ) = ρ ̂ n i n ρ [ a n ( N ) s H n ( 1 ) ( k ρ ) + a n ( N ) J n ( k ρ ) ] e i n ϕ ϕ ̂ n k [ a n ( N ) s H n ( 1 ) ( k ρ ) + a n ( N ) J n ( k ρ ) ] e i n ϕ + z ̂ n k [ a n ( M ) s H n ( 1 ) ( k ρ ) + a n ( M ) J n ( k ρ ) ] e i n ϕ ,
E = ρ ̂ n E ρ n e i n ϕ ϕ ̂ n E ϕ n e i n ϕ + z ̂ n E z n e i n ϕ ,
i η H = ρ ̂ n H ρ n e i n ϕ ϕ ̂ n H ϕ n e i n ϕ + z ̂ n H z n e i n ϕ ,
E ρ n = i n ρ [ a n ( M ) s H n ( 1 ) ( k ρ ) + a n ( M ) J n ( k ρ ) ] = i n k ρ H z n ,
E ϕ n = k [ a n ( M ) s H n ( 1 ) ( k ρ ) + a n ( M ) J n ( k ρ ) ] ,
H ρ n = in ρ [ a n ( N ) s H n ( 1 ) ( k ρ ) + a n ( N ) J n ( k ρ ) ] = i n k ρ E z n ,
H ϕ n = k [ a n ( N ) s H n ( 1 ) ( k ρ ) + a n ( N ) J n ( k ρ ) ] .
( E n ̂ ) E * = ρ ̂ n , n E ρ n E ρ n * e i ( n n ) ϕ ϕ ̂ n , n E ρ n E ϕ n * e i ( n n ) ϕ + z ̂ n , n E ρ n E z n * e i ( n n ) ϕ ,
( H n ̂ ) H * = ρ ̂ 1 η 2 n , n H ρ n H ρ n * e i ( n n ) ϕ ϕ ̂ 1 η 2 n , n H ρ n H ϕ n * e i ( n n ) ϕ + z ̂ 1 η 2 n , n H ρ n H z n * e i ( n n ) ϕ ,
E E * = n , n E ρ n E ρ n * e i ( n n ) ϕ + n , n E ϕ n E ϕ n * e i ( n n ) ϕ + n , n E z n E z n * e i ( n n ) ϕ ,
H H * = 1 η 2 n , n H ρ n H ρ n * e i ( n n ) ϕ + 1 η 2 n , n H ϕ n H ϕ n * e i ( n n ) ϕ + 1 η 2 n , n H z n H z n * e i ( n n ) ϕ ,
ε 2 ( E n ̂ ) E * + μ 2 ( H n ̂ ) H * ε 4 ( E E * ) n ̂ μ 4 ( H H * ) n ̂ = ρ ̂ ε 4 n , n [ ( E ρ n E ρ n * + H ρ n H ρ n * ) ( E ϕ n E ϕ n * + H ϕ n H ϕ n * ) ( E z n E z n * + H z n H z n * ) ] e i ( n n ) ϕ ϕ ̂ ε 2 n , n [ E ρ n E ϕ n * + H ϕ n H ρ n * ] e i ( n n ) ϕ + z ̂ ε 2 n , n [ E ρ n E z n * + H z n H ρ n * ] e i ( n n ) ϕ .
0 2 π d ϕ ρ ̂ e i ( n n ) ϕ = 0 2 π d ϕ [ x ̂ cos ϕ + y ̂ sin ϕ ] e i ( n n ) ϕ ,
0 2 π d ϕ ϕ ̂ e i ( n n ) ϕ = 0 2 π d ϕ [ x ̂ cos ϕ + y ̂ sin ϕ ] e i ( n n ) ϕ ,
0 2 π d ϕ z ̂ e i ( n n ) ϕ .
0 2 π d ϕ cos ϕ e i ( n n ) ϕ = { 0 , if n n ± 1 π if n = n ± 1 ,
0 2 π d ϕ sin ϕ e i ( n n ) ϕ = { 0 , if n n ± 1 i π if n = n + 1 i π , if n = n 1 ,
0 2 π d ϕ ρ ̂ e i ( n n ) ϕ = ( x ̂ i y ̂ ) π δ n , n + 1 + ( x ̂ + i y ̂ ) π δ n , n 1 ,
0 2 π d ϕ ϕ ̂ e i ( n n ) ϕ = ( x ̂ i y ̂ ) i π δ n , n + 1 ( x ̂ + i y ̂ ) i π δ n , n 1 ,
0 2 π d ϕ z ̂ e i ( n n ) ϕ = z ̂ 2 π δ n , n ,
0 2 π d ϕ [ ε 2 ( E n ̂ ) E * ε 4 ( E E * ) n ̂ + μ 2 ( H n ̂ ) H * μ 4 ( H H * ) n ̂ ] = x ̂ π ε 2 R ( n [ E ρ n E ρ n + 1 * + H ρ n H ρ n + 1 * E ϕ n E ϕ n + 1 * H ϕ n H ϕ n + 1 * E z n E z n + 1 * H z n H z n + 1 * ] ) + y ̂ π ε 2 I ( n [ E ρ n E ρ n + 1 * + H ρ n H ρ n + 1 * E ϕ n E ϕ n + 1 * H ϕ n H ϕ n + 1 * E z n E z n + 1 * H z n H z n + 1 * ] ) x ̂ i π ε 2 n E ρ n [ E ϕ n + 1 * E ϕ n 1 * ] x ̂ i π ε 2 n H ϕ n [ H ρ n + 1 * H ρ n 1 * ] y ̂ π ε 2 n H ϕ n [ H ρ n + 1 * + H ρ n 1 * ] y ̂ π ε 2 n E ρ n [ E ϕ n + 1 * + E ϕ n 1 * ] ,
H ρ n = i n k ρ E z n , E ρ n = i n k ρ H z n ,
F T M = x ̂ a π ε 2 R ( n ( n ( n + 1 ) ( k a ) 2 1 ) E z n E z n + 1 * H ϕ n H ϕ n + 1 * ) + y ̂ a π ε 2 I ( n ( n ( n + 1 ) ( k a ) 2 1 ) E z n E z n + 1 * H ϕ n H ϕ n + 1 * ) + x ̂ π ε 2 k R ( n ( H ϕ n ) [ ( n + 1 ) E z n + 1 * ( n 1 ) E z n 1 * ] ) y ̂ π ε 2 k I ( n ( H ϕ n ) [ ( n + 1 ) E z n + 1 * + ( n 1 ) E z n 1 * ] ) ,
F T E = x ̂ a π ε 2 R ( n ( n ( n + 1 ) ( k a ) 2 1 ) H z n H z n + 1 * E ϕ n E ϕ n + 1 * ) + y ̂ a π ε 2 I ( n ( n ( n + 1 ) ( k a ) 2 1 ) H z n H z n + 1 * E ϕ n E ϕ n + 1 * ) + x ̂ π ε 2 k R ( n n H z n ( E ϕ n + 1 * E ϕ n 1 * ) ) y ̂ π ε 2 k I ( n n H z n ( E ϕ n + 1 * + E ϕ n 1 * ) ) .
E ρ n = i n ρ [ T n M H n ( 1 ) ( k ρ ) + J n ( k ρ ) ] a n ( M ) = 2 n π ρ a k p k J n ( k p a ) k H n ( 1 ) ( k a ) J n ( k p a ) k p H n ( 1 ) ( k a ) J n ( k p a ) a n ( M ) ,
E ϕ n = 2 k i π a J n ( k p a ) k H n ( 1 ) ( k a ) J n ( k p a ) k p H n ( 1 ) ( k a ) J n ( k p a ) a n ( M ) ,
H ρ n = 2 n π ρ a J n ( k p a ) k H n ( 1 ) ( k a ) J n ( k p a ) k p H n ( 1 ) ( k a ) J n ( k p a ) a n ( N ) ,
H ϕ n = 2 i π a k p J n ( k p a ) k H n ( 1 ) ( k a ) J n ( k p a ) k p H n ( 1 ) ( k a ) J n ( k p a ) a n ( N ) ,
F T M = k ̂ i 4 ε π a k 2 k p 2 k 2 E v i 2 n = 0 + J n ( k p a ) J n + 1 ( k p a ) D n T M 2 D n + 1 T M 2 I ( D n T M D n + 1 T M * ) ,
k ̂ i = x cos ϕ i + y ̂ sin ϕ i ,
D n T M = k H n ( 1 ) ( k a ) J n ( k p a ) k p H n ( 1 ) ( k a ) J n ( k p a ) = k H n + 1 ( 1 ) ( k a ) J n ( k p a ) + k p H n ( 1 ) ( k a ) J n + 1 ( k p a ) ,
D n + 1 T M = k H n ( 1 ) ( k a ) J n + 1 ( k p a ) k p H n + 1 ( 1 ) ( k a ) J n ( k p a ) .
I ( D n T M D n + 1 T M * ) = ( k 2 k p 2 ) J n ( k p a ) J n + 1 ( k p a ) I ( H n ( 1 ) ( k a ) H n + 1 ( 1 ) * ( k a ) ) ,
I ( H n ( 1 ) ( k a ) H n + 1 ( 1 ) * ( k a ) ) = J n + 1 ( k a ) Y n ( k a ) J n ( k a ) Y n + 1 ( k a ) = 2 π k a ,
F T M = k ̂ i 8 ε k ( k p 2 k 2 π k a ) 2 E v i 2 n = 0 + J n 2 ( k p a ) J n + 1 2 ( k p a ) D n T M 2 D n + 1 T M 2 .
a n ( N ) = i n e i n ϕ i k E v i a n ( N ) = i n e i n ϕ i k E v i e i k ρ .
( E n ̂ ) E * = [ ( E 1 + E 2 ) n ̂ ] ( E 1 * + E 2 * ) = ( E 1 n ̂ ) E 1 * + ( E 2 n ̂ ) E 2 * + ( E 1 n ̂ ) E 2 * + ( E 2 n ̂ ) E 1 * .
F T M = F 11 T M + F 22 T M + F 12 T M + F 21 T M ,
F T M = i , j = 1 J F i j T M .
a n ( N ) a n + 1 ( N ) * = i E v i 2 k 2 e i ( n + 1 ) ϕ 2 i n ϕ 1 e i ( k 1 k 2 ) ρ ,
F i j T M = 4 ε π a k p 2 k 2 k 2 E v i 2 ( x ̂ cos Φ i j + y ̂ sin Φ i j ) n = 0 + J n ( k p a ) J n + 1 ( k p a ) D n T M 2 D n + 1 T M 2 I ( D n T M * D n + 1 T M e i ( n + 1 2 ) ( ϕ i ϕ j ) ) ,
Φ i j = ( k i k j ) ρ + ϕ i + ϕ j 2 .
E z ( x , y ) = g 2 π + d k y e i k x x + i k y y e k y 2 g 2 4 ,
E z ( x , y ) = j = 0 J 1 E v j e i k j ρ ,
E v j = g 2 π Δ k y e k y j 2 g 2 4 ,
k y j = j 2 k N 1 k , Δ k y = k y j + 1 k y j , k x j 2 + k y j 2 = k 2 ,

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