Abstract

The principle of optical trapping is conventionally based on the interaction of optical fields with linear-induced polarizations. However, the optical force originating from the nonlinear polarization becomes significant when nonlinear optical nanoparticles are trapped by femtosecond laser pulses. Herein we develop the time-averaged optical forces on a nonlinear optical nanoparticle using high-repetition-rate femtosecond laser pulses, based on the linear and nonlinear polarization effects. We investigate the dependence of the optical forces on the magnitudes and signs of the refractive nonlinearities. It is found that the self-focusing effect enhances the trapping ability, whereas the self-defocusing effect leads to the splitting of the potential well at the focal plane and destabilizes the optical trap. Our results show good agreement with the reported experimental observations and provide theoretical support for capturing nonlinear optical particles.

© 2018 Chinese Laser Press

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References

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    [Crossref]

2017 (1)

A. Devi and A. K. De, “Theoretical investigation on optical Kerr effect in femtosecond laser trapping of dielectric microspheres,” J. Opt. 19, 065504 (2017).
[Crossref]

2016 (2)

A. Devi and K. De, “Theoretical investigation on nonlinear optical effects in laser trapping of dielectric nanoparticles with ultrafast pulsed excitation,” Opt. Express 24, 21485–21496 (2016).
[Crossref]

T. H. Liu, W. Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120, 2392–2399 (2016).
[Crossref]

2015 (1)

2014 (5)

G. Rui and Q. Zhan, “Trapping of resonant metallic nanoparticles with engineered vectorial optical field,” Nanophotonics 3, 351–361 (2014).
[Crossref]

M. Gu, H. Bao, X. Gan, N. Stokes, and J. Wu, “Tweezing and manipulating micro- and nanoparticles by optical nonlinear endoscopy,” Light: Sci. Appl. 3, e126 (2014).
[Crossref]

I. Heller, T. P. Hoekstra, G. A. King, E. J. G. Peterman, and G. J. L. Wuite, “Optical tweezers analysis of DNA-protein complexes,” Chem. Rev. 114, 3087–3119 (2014).
[Crossref]

W. Chiang, T. Okuhata, A. Usman, N. Tamai, and H. Masuhara, “Efficient optical trapping of CdTe quantum dots by femtosecond laser pulses,” J. Phys. Chem. B 118, 14010–14016 (2014).
[Crossref]

I. S. Park, S. H. Park, S. W. Lee, D. S. Yoon, and B. Kim, “Quantitative characterization for dielectrophoretic behavior of biological cells using optical tweezers,” Appl. Phys. Lett. 104, 053701 (2014).
[Crossref]

2013 (3)

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref]

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88, 033831 (2013).
[Crossref]

W. Y. Chiang, A. Usman, and H. Masuhara, “Femtosecond pulse-width dependent trapping and directional ejection dynamics of dielectric nanoparticles,” J. Phys. Chem. C 117, 19182–19188 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (5)

J. C. Shane, M. Mazilu, W. M. Lee, and K. Dholakia, “Effect of pulse temporal shape on optical trapping and impulse transfer using ultrashort pulsed lasers,” Opt. Express 18, 7554–7568 (2010).
[Crossref]

Y. Jiang, T. Narushima, and H. Okamoto, “Nonlinear optical effects in trapping nanoparticles with femtosecond pulses,” Nat. Phys. 6, 1005–1009 (2010).
[Crossref]

E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18, 11428–11443 (2010).
[Crossref]

L. Jauffred and L. B. Oddershede, “Two-photon quantum dot excitation during optical trapping,” Nano Lett. 10, 1927–1930 (2010).
[Crossref]

2009 (2)

A. K. De, D. Roy, A. Dutta, and D. Goswami, “Stable optical trapping of latex nanoparticles with ultrashort pulsed illumination,” Appl. Opt. 48, G33–G37 (2009).
[Crossref]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Saenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102, 113602 (2009).
[Crossref]

2008 (1)

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

2007 (1)

2006 (1)

R. Pobre and C. Saloma, “Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam,” Opt. Commun. 267, 295–304 (2006).
[Crossref]

2005 (1)

2004 (1)

2000 (1)

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)

Agate, B.

Albaladejo, S.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Saenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102, 113602 (2009).
[Crossref]

Alzaidi, T.

Ashkin, A.

Bao, H.

M. Gu, H. Bao, X. Gan, N. Stokes, and J. Wu, “Tweezing and manipulating micro- and nanoparticles by optical nonlinear endoscopy,” Light: Sci. Appl. 3, e126 (2014).
[Crossref]

Bjorkholm, J. E.

Brown, C.

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

Canaguier-Durand, A.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88, 033831 (2013).
[Crossref]

Chantada, L.

Chaumet, P.

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

Chiang, W.

W. Chiang, T. Okuhata, A. Usman, N. Tamai, and H. Masuhara, “Efficient optical trapping of CdTe quantum dots by femtosecond laser pulses,” J. Phys. Chem. B 118, 14010–14016 (2014).
[Crossref]

Chiang, W. Y.

T. H. Liu, W. Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120, 2392–2399 (2016).
[Crossref]

W. Y. Chiang, A. Usman, and H. Masuhara, “Femtosecond pulse-width dependent trapping and directional ejection dynamics of dielectric nanoparticles,” J. Phys. Chem. C 117, 19182–19188 (2013).
[Crossref]

Chu, S.

Cuche, A.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88, 033831 (2013).
[Crossref]

Dawkins, S. T.

E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

De, A. K.

A. Devi and A. K. De, “Theoretical investigation on optical Kerr effect in femtosecond laser trapping of dielectric microspheres,” J. Opt. 19, 065504 (2017).
[Crossref]

A. K. De, D. Roy, A. Dutta, and D. Goswami, “Stable optical trapping of latex nanoparticles with ultrashort pulsed illumination,” Appl. Opt. 48, G33–G37 (2009).
[Crossref]

De, K.

Deng, J. L.

Devi, A.

A. Devi and A. K. De, “Theoretical investigation on optical Kerr effect in femtosecond laser trapping of dielectric microspheres,” J. Opt. 19, 065504 (2017).
[Crossref]

A. Devi and K. De, “Theoretical investigation on nonlinear optical effects in laser trapping of dielectric nanoparticles with ultrafast pulsed excitation,” Opt. Express 24, 21485–21496 (2016).
[Crossref]

Dholakia, K.

Draine, B. T.

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

Du, L.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref]

Dutta, A.

Dziedic, J. M.

Ebbesen, T. W.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88, 033831 (2013).
[Crossref]

Fang, H.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref]

Feng, B.

Gan, X.

M. Gu, H. Bao, X. Gan, N. Stokes, and J. Wu, “Tweezing and manipulating micro- and nanoparticles by optical nonlinear endoscopy,” Light: Sci. Appl. 3, e126 (2014).
[Crossref]

Genet, C.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, “Force and torque on an electric dipole by spinning light fields,” Phys. Rev. A 88, 033831 (2013).
[Crossref]

Gómez-Medina, R.

Goswami, D.

Gu, M.

M. Gu, H. Bao, X. Gan, N. Stokes, and J. Wu, “Tweezing and manipulating micro- and nanoparticles by optical nonlinear endoscopy,” Light: Sci. Appl. 3, e126 (2014).
[Crossref]

M. Gu, Advanced Optical Imaging Theory (Springer, 2000), Chap. 6.

Guo, H.

Hanna, S.

Heller, I.

I. Heller, T. P. Hoekstra, G. A. King, E. J. G. Peterman, and G. J. L. Wuite, “Optical tweezers analysis of DNA-protein complexes,” Chem. Rev. 114, 3087–3119 (2014).
[Crossref]

Hoekstra, T. P.

I. Heller, T. P. Hoekstra, G. A. King, E. J. G. Peterman, and G. J. L. Wuite, “Optical tweezers analysis of DNA-protein complexes,” Chem. Rev. 114, 3087–3119 (2014).
[Crossref]

Huang, L.

Jauffred, L.

L. Jauffred and L. B. Oddershede, “Two-photon quantum dot excitation during optical trapping,” Nano Lett. 10, 1927–1930 (2010).
[Crossref]

Jiang, Y.

Y. Jiang, T. Narushima, and H. Okamoto, “Nonlinear optical effects in trapping nanoparticles with femtosecond pulses,” Nat. Phys. 6, 1005–1009 (2010).
[Crossref]

Kim, B.

I. S. Park, S. H. Park, S. W. Lee, D. S. Yoon, and B. Kim, “Quantitative characterization for dielectrophoretic behavior of biological cells using optical tweezers,” Appl. Phys. Lett. 104, 053701 (2014).
[Crossref]

King, G. A.

I. Heller, T. P. Hoekstra, G. A. King, E. J. G. Peterman, and G. J. L. Wuite, “Optical tweezers analysis of DNA-protein complexes,” Chem. Rev. 114, 3087–3119 (2014).
[Crossref]

Laroche, M.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Saenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102, 113602 (2009).
[Crossref]

Lee, S. W.

I. S. Park, S. H. Park, S. W. Lee, D. S. Yoon, and B. Kim, “Quantitative characterization for dielectrophoretic behavior of biological cells using optical tweezers,” Appl. Phys. Lett. 104, 053701 (2014).
[Crossref]

Lee, W. M.

Lei, T.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref]

Li, J.

Li, Z. Y.

Ling, L.

Liu, T. H.

T. H. Liu, W. Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120, 2392–2399 (2016).
[Crossref]

Marqués, M. I.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Saenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102, 113602 (2009).
[Crossref]

Masuhara, H.

T. H. Liu, W. Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120, 2392–2399 (2016).
[Crossref]

W. Chiang, T. Okuhata, A. Usman, N. Tamai, and H. Masuhara, “Efficient optical trapping of CdTe quantum dots by femtosecond laser pulses,” J. Phys. Chem. B 118, 14010–14016 (2014).
[Crossref]

W. Y. Chiang, A. Usman, and H. Masuhara, “Femtosecond pulse-width dependent trapping and directional ejection dynamics of dielectric nanoparticles,” J. Phys. Chem. C 117, 19182–19188 (2013).
[Crossref]

Mazilu, M.

Min, C.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref]

Moffitt, J. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

Narushima, T.

Y. Jiang, T. Narushima, and H. Okamoto, “Nonlinear optical effects in trapping nanoparticles with femtosecond pulses,” Nat. Phys. 6, 1005–1009 (2010).
[Crossref]

Nieminen, T. A.

Nieto-Vesperinas, M.

Oddershede, L. B.

L. Jauffred and L. B. Oddershede, “Two-photon quantum dot excitation during optical trapping,” Nano Lett. 10, 1927–1930 (2010).
[Crossref]

Okamoto, H.

Y. Jiang, T. Narushima, and H. Okamoto, “Nonlinear optical effects in trapping nanoparticles with femtosecond pulses,” Nat. Phys. 6, 1005–1009 (2010).
[Crossref]

Okuhata, T.

W. Chiang, T. Okuhata, A. Usman, N. Tamai, and H. Masuhara, “Efficient optical trapping of CdTe quantum dots by femtosecond laser pulses,” J. Phys. Chem. B 118, 14010–14016 (2014).
[Crossref]

Park, I. S.

I. S. Park, S. H. Park, S. W. Lee, D. S. Yoon, and B. Kim, “Quantitative characterization for dielectrophoretic behavior of biological cells using optical tweezers,” Appl. Phys. Lett. 104, 053701 (2014).
[Crossref]

Park, S. H.

I. S. Park, S. H. Park, S. W. Lee, D. S. Yoon, and B. Kim, “Quantitative characterization for dielectrophoretic behavior of biological cells using optical tweezers,” Appl. Phys. Lett. 104, 053701 (2014).
[Crossref]

Peterman, E. J. G.

I. Heller, T. P. Hoekstra, G. A. King, E. J. G. Peterman, and G. J. L. Wuite, “Optical tweezers analysis of DNA-protein complexes,” Chem. Rev. 114, 3087–3119 (2014).
[Crossref]

Pobre, R.

R. Pobre and C. Saloma, “Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam,” Opt. Commun. 267, 295–304 (2006).
[Crossref]

Preez-Wilkinson, N.

Rauschenbeutel, A.

E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

Reitz, D.

E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

Roy, D.

Rubinsztein-Dunlop, H.

Rui, G.

G. Rui and Q. Zhan, “Trapping of resonant metallic nanoparticles with engineered vectorial optical field,” Nanophotonics 3, 351–361 (2014).
[Crossref]

Saenz, J. J.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Saenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102, 113602 (2009).
[Crossref]

Sáenz, J. J.

Sague, G.

E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

Saloma, C.

R. Pobre and C. Saloma, “Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam,” Opt. Commun. 267, 295–304 (2006).
[Crossref]

Schmidt, R.

E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

Shane, J. C.

Shen, J.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref]

Shen, Z.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
[Crossref]

Sibbett, W.

Simpson, S.

Smith, S. B.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

Stilgoe, A. B.

Stokes, N.

M. Gu, H. Bao, X. Gan, N. Stokes, and J. Wu, “Tweezing and manipulating micro- and nanoparticles by optical nonlinear endoscopy,” Light: Sci. Appl. 3, e126 (2014).
[Crossref]

Tamai, N.

W. Chiang, T. Okuhata, A. Usman, N. Tamai, and H. Masuhara, “Efficient optical trapping of CdTe quantum dots by femtosecond laser pulses,” J. Phys. Chem. B 118, 14010–14016 (2014).
[Crossref]

Usman, A.

T. H. Liu, W. Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120, 2392–2399 (2016).
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W. Chiang, T. Okuhata, A. Usman, N. Tamai, and H. Masuhara, “Efficient optical trapping of CdTe quantum dots by femtosecond laser pulses,” J. Phys. Chem. B 118, 14010–14016 (2014).
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W. Y. Chiang, A. Usman, and H. Masuhara, “Femtosecond pulse-width dependent trapping and directional ejection dynamics of dielectric nanoparticles,” J. Phys. Chem. C 117, 19182–19188 (2013).
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Vetsch, E.

E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
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Wang, L.

Wang, Y. Z.

Wei, Q.

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M. Gu, H. Bao, X. Gan, N. Stokes, and J. Wu, “Tweezing and manipulating micro- and nanoparticles by optical nonlinear endoscopy,” Light: Sci. Appl. 3, e126 (2014).
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I. Heller, T. P. Hoekstra, G. A. King, E. J. G. Peterman, and G. J. L. Wuite, “Optical tweezers analysis of DNA-protein complexes,” Chem. Rev. 114, 3087–3119 (2014).
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Yoon, D. S.

I. S. Park, S. H. Park, S. W. Lee, D. S. Yoon, and B. Kim, “Quantitative characterization for dielectrophoretic behavior of biological cells using optical tweezers,” Appl. Phys. Lett. 104, 053701 (2014).
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Yuan, G.

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
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C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
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G. Rui and Q. Zhan, “Trapping of resonant metallic nanoparticles with engineered vectorial optical field,” Nanophotonics 3, 351–361 (2014).
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C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
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C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
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I. S. Park, S. H. Park, S. W. Lee, D. S. Yoon, and B. Kim, “Quantitative characterization for dielectrophoretic behavior of biological cells using optical tweezers,” Appl. Phys. Lett. 104, 053701 (2014).
[Crossref]

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Chem. Rev. (1)

I. Heller, T. P. Hoekstra, G. A. King, E. J. G. Peterman, and G. J. L. Wuite, “Optical tweezers analysis of DNA-protein complexes,” Chem. Rev. 114, 3087–3119 (2014).
[Crossref]

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A. Devi and A. K. De, “Theoretical investigation on optical Kerr effect in femtosecond laser trapping of dielectric microspheres,” J. Opt. 19, 065504 (2017).
[Crossref]

J. Phys. Chem. B (1)

W. Chiang, T. Okuhata, A. Usman, N. Tamai, and H. Masuhara, “Efficient optical trapping of CdTe quantum dots by femtosecond laser pulses,” J. Phys. Chem. B 118, 14010–14016 (2014).
[Crossref]

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W. Y. Chiang, A. Usman, and H. Masuhara, “Femtosecond pulse-width dependent trapping and directional ejection dynamics of dielectric nanoparticles,” J. Phys. Chem. C 117, 19182–19188 (2013).
[Crossref]

T. H. Liu, W. Y. Chiang, A. Usman, and H. Masuhara, “Optical trapping dynamics of a single polystyrene sphere: continuous wave versus femtosecond lasers,” J. Phys. Chem. C 120, 2392–2399 (2016).
[Crossref]

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M. Gu, H. Bao, X. Gan, N. Stokes, and J. Wu, “Tweezing and manipulating micro- and nanoparticles by optical nonlinear endoscopy,” Light: Sci. Appl. 3, e126 (2014).
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L. Jauffred and L. B. Oddershede, “Two-photon quantum dot excitation during optical trapping,” Nano Lett. 10, 1927–1930 (2010).
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G. Rui and Q. Zhan, “Trapping of resonant metallic nanoparticles with engineered vectorial optical field,” Nanophotonics 3, 351–361 (2014).
[Crossref]

Nat. Commun. (1)

C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 2891 (2013).
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E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104, 203603 (2010).
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Figures (4)

Fig. 1.
Fig. 1. Transverse force distributions produced by tightly focused laser pulses for the particle with self-focusing (n2=5.9×1017  m2/W), without nonlinearity (n2=0), and with self-defocusing (n2=5.9×1017  m2/W) in the x-y plane (z=0), by taking NA=0.85 and a=40  nm. The magnitudes and directions of the transverse forces are illustrated by the colorbar and arrows in (a)–(i), respectively. (j)–(l) give the force profiles along the x direction shown in the above three rows.
Fig. 2.
Fig. 2. Longitudinal force distributions produced by tightly focused laser pulses for the particle with self-focusing (n2=5.9×1017  m2/W), without nonlinearity (n2=0), and with self-defocusing (n2=5.9×1017  m2/W) in the x-z plane (y=0), by taking NA=0.85 and a=40  nm. The bottom row gives the force profiles along the z direction shown in the above three rows. Arrows in the figures denote the directions of the longitudinal forces.
Fig. 3.
Fig. 3. Force profiles along the x direction for y=0 and z=0. (a) Different values of n2, NA=0.85, and a=40  nm. (c) Different values of NA, n2=6×1017  m2/W, and a=40  nm. (e) Different values of a, n2=6×1017  m2/W, and NA=0.85. (b), (d), and (f) are the maximum force Fmax versus n2, NA, and a, respectively.
Fig. 4.
Fig. 4. Trapping potential along (a) x direction and (b) z direction with three different values of n2 (i.e., 5.9×1017, 0, 5.9×1017  m2/W), NA=0.85, and a=40  nm.

Equations (19)

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E(r,t)=E0(r)exp(iωt)exp[2(ln2)t2/τF2],
B(r,t)=1iω×E(r,t),
p(r,t)=αe(r,t)1iαe(r,t)k3/(6πϵ0)E(r,t),
αe(r,t)=4πϵ0a3(χ1+χ3|E(r,t)|2)χ1+χ3|E(r,t)|2+3,
F=14TT/2T/2[(p+p*)·(E+E*)+(pt+p*t)×(B+B*)]dt,
F=πϵ0a3τFνln2Re[β(E0·E0*+E0××E0*)],
β=(χ1+χ3|E0|2eζ2)eζ23+(12ik3a3/3)(χ1+χ3|E0|2eζ2)dζ.
F=14Re(α)|E0|2+kϵ0cIm(α)SOrb,
SOrb=S+ϵ0c2kIm[(E0*·)E0],
S=12μ0ωIm[E0×(×E0*)],
α=πτFν2ln2(γL+γNL),
γL=α01iα0k3/(6πϵ0),
α0=4πϵ0a3ϵ20/ϵ101ϵ20/ϵ10+2,
γNL=12πϵ0a3ηm=2(1)mm1/2(χ3η|E0|2)m1[3+η(ϵ20/ϵ101)]m,
η=12ik3a3/3.
E0(r)=E00iλ{[I0+cos(2φ)I2]exsin(2φ)I2ey2i cosφI1ez}
I0=0ϑl(θ)eikzcosθ(1+cosθ)J0(krsinθ)dθ,
I1=0ϑl(θ)sinθeikzcosθJ1(krsinθ)dθ,
I2=0ϑl(θ)eikzcosθ(1cosθ)J2(krsinθ)dθ.

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