Abstract

We present a method for the precise calculation of optical forces due to a tightly-focused pulsed laser beam using generalized Lorenz–Mie theory or the T-matrix method. This method can be used to obtain the fields as a function of position and time, allowing the approximate calculation of weak non-linear effects, and provides a reference calculation for validation of calculations including non-linear effects. We calculate forces for femtosecond pulses of various widths, and compare with forces due to a continuous wave (CW) beam. The forces are similar enough so that the continuous beam case provides a useful approximation for the pulsed case, with trap parameters such as the radial spring constant usually differing by less than 1% for pulses of 100 fs or longer. For large high-index (e.g., polystyrene, with n = 1.59) particles, the difference can be as large as 3% for 100 fs pulses, and up to 8% for 25 fs pulses. A weighted average of CW forces for individual spectral components of the pulsed beam provides a simple improved approximation, which we use to illustrate the physical principles responsible for the differences between pulsed and CW beams.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. 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] [PubMed]
  4. A. Fontes, K. Ajito, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, A. M. de Paula, and C. L. Cesar, “Raman, hyper-Raman, hyper-Rayleigh, two-photon luminescence and morphology-dependent resonance modes in a single optical tweezers system,” Phys. Rev. E 72, 012903 (2005).
    [Crossref]
  5. F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, “Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser,” Opt. Commun. 256, 358–363 (2005).
    [Crossref]
  6. K.-B. Im, S.-B. Ju, S. Han, H. Park, B.-M. Kim, D. Jin, and S.-K. Kim, “Trapping efficiency of a femtosecond laser and damage thresholds for biological cells,” J. Korean Phys. Soc. 48, 968–973 (2006).
  7. Y. Jiang, T. Narushima, and H. Okamoto, “Nonlinear optical effects in trapping nanoparticles with femtosecond pulses,” Nat. Phys. 6, 1005–1009 (2010).
    [Crossref]
  8. A. Usman, W.-Y. Chiang, and H. Masuhara, “Femtosecond trapping efficiency enhanced for nano-sized silica spheres,” Proc. SPIE 8458, 845833 (2012).
    [Crossref]
  9. J. liao Deng, Q. Wei, Y. zhu Wang, and Y. qing Li, “Numerical modeling of optical levitation and trapping of the “stuck” particles with a pulsed optical tweezers,” Opt. Express 13, 3673–3680 (2005).
    [Crossref]
  10. Q. Xing, F. Mao, L. Chai, and Q. Wang, “Numerical modeling and theoretical analysis of femtosecond laser tweezers,” Opt. Laser Technol. 36, 635–639 (2004).
    [Crossref]
  11. P. A. Maia Neto and H. M. Nussenzweig, “Theory of optical tweezers,” Europhys. Lett. 50, 702–708 (2000).
    [Crossref]
  12. A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. A 459, 3021–3041 (2003).
    [Crossref]
  13. A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
    [Crossref] [PubMed]
  14. T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, “Optical tweezers: Theory and modelling,” J. Quant. Spectrosc. Radiat. Transf. 146, 59–80 (2014).
    [Crossref]
  15. T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1005–1017 (2003).
    [Crossref]
  16. G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer, 2011).
    [Crossref]
  17. T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
    [Crossref]
  18. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
    [Crossref]
  19. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
    [Crossref]
  20. G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521 (2010).
    [Crossref]
  21. Ø. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108–130 (1996).
    [Crossref]
  22. J. H. Crichton and P. L. Marston, “The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation,” Electron. J. Differ. Equ. Conf.  04, 37–50 (2000).

2014 (1)

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, “Optical tweezers: Theory and modelling,” J. Quant. Spectrosc. Radiat. Transf. 146, 59–80 (2014).
[Crossref]

2012 (1)

A. Usman, W.-Y. Chiang, and H. Masuhara, “Femtosecond trapping efficiency enhanced for nano-sized silica spheres,” Proc. SPIE 8458, 845833 (2012).
[Crossref]

2010 (3)

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

G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521 (2010).
[Crossref]

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] [PubMed]

2008 (2)

2007 (1)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

2006 (1)

K.-B. Im, S.-B. Ju, S. Han, H. Park, B.-M. Kim, D. Jin, and S.-K. Kim, “Trapping efficiency of a femtosecond laser and damage thresholds for biological cells,” J. Korean Phys. Soc. 48, 968–973 (2006).

2005 (3)

A. Fontes, K. Ajito, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, A. M. de Paula, and C. L. Cesar, “Raman, hyper-Raman, hyper-Rayleigh, two-photon luminescence and morphology-dependent resonance modes in a single optical tweezers system,” Phys. Rev. E 72, 012903 (2005).
[Crossref]

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, “Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser,” Opt. Commun. 256, 358–363 (2005).
[Crossref]

J. liao Deng, Q. Wei, Y. zhu Wang, and Y. qing Li, “Numerical modeling of optical levitation and trapping of the “stuck” particles with a pulsed optical tweezers,” Opt. Express 13, 3673–3680 (2005).
[Crossref]

2004 (1)

Q. Xing, F. Mao, L. Chai, and Q. Wang, “Numerical modeling and theoretical analysis of femtosecond laser tweezers,” Opt. Laser Technol. 36, 635–639 (2004).
[Crossref]

2003 (2)

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1005–1017 (2003).
[Crossref]

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. A 459, 3021–3041 (2003).
[Crossref]

2000 (2)

J. H. Crichton and P. L. Marston, “The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation,” Electron. J. Differ. Equ. Conf.  04, 37–50 (2000).

P. A. Maia Neto and H. M. Nussenzweig, “Theory of optical tweezers,” Europhys. Lett. 50, 702–708 (2000).
[Crossref]

1996 (1)

Ø. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108–130 (1996).
[Crossref]

1991 (1)

1986 (1)

1971 (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[Crossref]

Ajito, K.

A. Fontes, K. Ajito, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, A. M. de Paula, and C. L. Cesar, “Raman, hyper-Raman, hyper-Rayleigh, two-photon luminescence and morphology-dependent resonance modes in a single optical tweezers system,” Phys. Rev. E 72, 012903 (2005).
[Crossref]

Ashkin, A.

Barbosa, L. C.

A. Fontes, K. Ajito, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, A. M. de Paula, and C. L. Cesar, “Raman, hyper-Raman, hyper-Rayleigh, two-photon luminescence and morphology-dependent resonance modes in a single optical tweezers system,” Phys. Rev. E 72, 012903 (2005).
[Crossref]

Bjorkholm, J. E.

Branczyk, A. M.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Bui, A. A. M.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, “Optical tweezers: Theory and modelling,” J. Quant. Spectrosc. Radiat. Transf. 146, 59–80 (2014).
[Crossref]

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] [PubMed]

Cesar, C. L.

A. Fontes, K. Ajito, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, A. M. de Paula, and C. L. Cesar, “Raman, hyper-Raman, hyper-Rayleigh, two-photon luminescence and morphology-dependent resonance modes in a single optical tweezers system,” Phys. Rev. E 72, 012903 (2005).
[Crossref]

Chai, L.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, “Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser,” Opt. Commun. 256, 358–363 (2005).
[Crossref]

Q. Xing, F. Mao, L. Chai, and Q. Wang, “Numerical modeling and theoretical analysis of femtosecond laser tweezers,” Opt. Laser Technol. 36, 635–639 (2004).
[Crossref]

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] [PubMed]

Chiang, W.-Y.

A. Usman, W.-Y. Chiang, and H. Masuhara, “Femtosecond trapping efficiency enhanced for nano-sized silica spheres,” Proc. SPIE 8458, 845833 (2012).
[Crossref]

Chu, S.

Crichton, J. H.

J. H. Crichton and P. L. Marston, “The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation,” Electron. J. Differ. Equ. Conf.  04, 37–50 (2000).

de Paula, A. M.

A. Fontes, K. Ajito, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, A. M. de Paula, and C. L. Cesar, “Raman, hyper-Raman, hyper-Rayleigh, two-photon luminescence and morphology-dependent resonance modes in a single optical tweezers system,” Phys. Rev. E 72, 012903 (2005).
[Crossref]

de Thomaz, A. A.

A. Fontes, K. Ajito, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, A. M. de Paula, and C. L. Cesar, “Raman, hyper-Raman, hyper-Rayleigh, two-photon luminescence and morphology-dependent resonance modes in a single optical tweezers system,” Phys. Rev. E 72, 012903 (2005).
[Crossref]

Dholakia, K.

du Preez-Wilkinson, N.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, “Optical tweezers: Theory and modelling,” J. Quant. Spectrosc. Radiat. Transf. 146, 59–80 (2014).
[Crossref]

Dziedzic, J. M.

Farsund, Ø.

Ø. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108–130 (1996).
[Crossref]

Felderhof, B. U.

Ø. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108–130 (1996).
[Crossref]

Fontes, A.

A. Fontes, K. Ajito, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, A. M. de Paula, and C. L. Cesar, “Raman, hyper-Raman, hyper-Rayleigh, two-photon luminescence and morphology-dependent resonance modes in a single optical tweezers system,” Phys. Rev. E 72, 012903 (2005).
[Crossref]

Gouesbet, G.

G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521 (2010).
[Crossref]

G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer, 2011).
[Crossref]

Gréhan, G.

G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer, 2011).
[Crossref]

Han, S.

K.-B. Im, S.-B. Ju, S. Han, H. Park, B.-M. Kim, D. Jin, and S.-K. Kim, “Trapping efficiency of a femtosecond laser and damage thresholds for biological cells,” J. Korean Phys. Soc. 48, 968–973 (2006).

Heckenberg, N. R.

A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1005–1017 (2003).
[Crossref]

Im, K.-B.

K.-B. Im, S.-B. Ju, S. Han, H. Park, B.-M. Kim, D. Jin, and S.-K. Kim, “Trapping efficiency of a femtosecond laser and damage thresholds for biological cells,” J. Korean Phys. Soc. 48, 968–973 (2006).

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]

Jin, D.

K.-B. Im, S.-B. Ju, S. Han, H. Park, B.-M. Kim, D. Jin, and S.-K. Kim, “Trapping efficiency of a femtosecond laser and damage thresholds for biological cells,” J. Korean Phys. Soc. 48, 968–973 (2006).

Ju, S.-B.

K.-B. Im, S.-B. Ju, S. Han, H. Park, B.-M. Kim, D. Jin, and S.-K. Kim, “Trapping efficiency of a femtosecond laser and damage thresholds for biological cells,” J. Korean Phys. Soc. 48, 968–973 (2006).

Kim, B.-M.

K.-B. Im, S.-B. Ju, S. Han, H. Park, B.-M. Kim, D. Jin, and S.-K. Kim, “Trapping efficiency of a femtosecond laser and damage thresholds for biological cells,” J. Korean Phys. Soc. 48, 968–973 (2006).

Kim, S.-K.

K.-B. Im, S.-B. Ju, S. Han, H. Park, B.-M. Kim, D. Jin, and S.-K. Kim, “Trapping efficiency of a femtosecond laser and damage thresholds for biological cells,” J. Korean Phys. Soc. 48, 968–973 (2006).

Knöner, G.

A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Lang, L.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, “Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser,” Opt. Commun. 256, 358–363 (2005).
[Crossref]

Lee, W. M.

liao Deng, J.

Loke, V. L. Y.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, “Optical tweezers: Theory and modelling,” J. Quant. Spectrosc. Radiat. Transf. 146, 59–80 (2014).
[Crossref]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Maia Neto, P. A.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. A 459, 3021–3041 (2003).
[Crossref]

P. A. Maia Neto and H. M. Nussenzweig, “Theory of optical tweezers,” Europhys. Lett. 50, 702–708 (2000).
[Crossref]

Mao, F.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, “Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser,” Opt. Commun. 256, 358–363 (2005).
[Crossref]

Q. Xing, F. Mao, L. Chai, and Q. Wang, “Numerical modeling and theoretical analysis of femtosecond laser tweezers,” Opt. Laser Technol. 36, 635–639 (2004).
[Crossref]

Marston, P. L.

J. H. Crichton and P. L. Marston, “The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation,” Electron. J. Differ. Equ. Conf.  04, 37–50 (2000).

Masuhara, H.

A. Usman, W.-Y. Chiang, and H. Masuhara, “Femtosecond trapping efficiency enhanced for nano-sized silica spheres,” Proc. SPIE 8458, 845833 (2012).
[Crossref]

Mazilu, M.

Mazolli, A.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. A 459, 3021–3041 (2003).
[Crossref]

Mishchenko, M. I.

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] [PubMed]

Moreira, W. L.

A. Fontes, K. Ajito, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, A. M. de Paula, and C. L. Cesar, “Raman, hyper-Raman, hyper-Rayleigh, two-photon luminescence and morphology-dependent resonance modes in a single optical tweezers system,” Phys. Rev. E 72, 012903 (2005).
[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]

Neves, A. A. R.

A. Fontes, K. Ajito, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, A. M. de Paula, and C. L. Cesar, “Raman, hyper-Raman, hyper-Rayleigh, two-photon luminescence and morphology-dependent resonance modes in a single optical tweezers system,” Phys. Rev. E 72, 012903 (2005).
[Crossref]

Nieminen, T. A.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, “Optical tweezers: Theory and modelling,” J. Quant. Spectrosc. Radiat. Transf. 146, 59–80 (2014).
[Crossref]

A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1005–1017 (2003).
[Crossref]

Nussenzveig, H. M.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. A 459, 3021–3041 (2003).
[Crossref]

Nussenzweig, H. M.

P. A. Maia Neto and H. M. Nussenzweig, “Theory of optical tweezers,” Europhys. Lett. 50, 702–708 (2000).
[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]

Park, H.

K.-B. Im, S.-B. Ju, S. Han, H. Park, B.-M. Kim, D. Jin, and S.-K. Kim, “Trapping efficiency of a femtosecond laser and damage thresholds for biological cells,” J. Korean Phys. Soc. 48, 968–973 (2006).

qing Li, Y.

Rubinsztein-Dunlop, H.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, “Optical tweezers: Theory and modelling,” J. Quant. Spectrosc. Radiat. Transf. 146, 59–80 (2014).
[Crossref]

A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1005–1017 (2003).
[Crossref]

Shane, J. C.

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] [PubMed]

Stilgoe, A. B.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, “Optical tweezers: Theory and modelling,” J. Quant. Spectrosc. Radiat. Transf. 146, 59–80 (2014).
[Crossref]

A. B. Stilgoe, T. A. Nieminen, G. Knöner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[Crossref] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

Usman, A.

A. Usman, W.-Y. Chiang, and H. Masuhara, “Femtosecond trapping efficiency enhanced for nano-sized silica spheres,” Proc. SPIE 8458, 845833 (2012).
[Crossref]

Wang, K.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, “Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser,” Opt. Commun. 256, 358–363 (2005).
[Crossref]

Wang, Q.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, “Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser,” Opt. Commun. 256, 358–363 (2005).
[Crossref]

Q. Xing, F. Mao, L. Chai, and Q. Wang, “Numerical modeling and theoretical analysis of femtosecond laser tweezers,” Opt. Laser Technol. 36, 635–639 (2004).
[Crossref]

Wang, Z.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, “Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser,” Opt. Commun. 256, 358–363 (2005).
[Crossref]

Waterman, P. C.

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[Crossref]

Wei, Q.

Xing, Q.

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, “Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser,” Opt. Commun. 256, 358–363 (2005).
[Crossref]

Q. Xing, F. Mao, L. Chai, and Q. Wang, “Numerical modeling and theoretical analysis of femtosecond laser tweezers,” Opt. Laser Technol. 36, 635–639 (2004).
[Crossref]

zhu Wang, Y.

Annu. Rev. Biochem. (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] [PubMed]

Electron. J. Differ. Equ. (1)

J. H. Crichton and P. L. Marston, “The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation,” Electron. J. Differ. Equ. Conf.  04, 37–50 (2000).

Europhys. Lett. (1)

P. A. Maia Neto and H. M. Nussenzweig, “Theory of optical tweezers,” Europhys. Lett. 50, 702–708 (2000).
[Crossref]

J. Korean Phys. Soc. (1)

K.-B. Im, S.-B. Ju, S. Han, H. Park, B.-M. Kim, D. Jin, and S.-K. Kim, “Trapping efficiency of a femtosecond laser and damage thresholds for biological cells,” J. Korean Phys. Soc. 48, 968–973 (2006).

J. Opt. A (1)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).
[Crossref]

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

J. Quant. Spectrosc. Radiat. Transf. (2)

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, “Optical tweezers: Theory and modelling,” J. Quant. Spectrosc. Radiat. Transf. 146, 59–80 (2014).
[Crossref]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1005–1017 (2003).
[Crossref]

Nat. Phys. (1)

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

Opt. Commun. (2)

F. Mao, Q. Xing, K. Wang, L. Lang, Z. Wang, L. Chai, and Q. Wang, “Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser,” Opt. Commun. 256, 358–363 (2005).
[Crossref]

G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521 (2010).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (1)

Q. Xing, F. Mao, L. Chai, and Q. Wang, “Numerical modeling and theoretical analysis of femtosecond laser tweezers,” Opt. Laser Technol. 36, 635–639 (2004).
[Crossref]

Opt. Lett. (1)

Phys. Rev. D (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[Crossref]

Phys. Rev. E (1)

A. Fontes, K. Ajito, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, A. M. de Paula, and C. L. Cesar, “Raman, hyper-Raman, hyper-Rayleigh, two-photon luminescence and morphology-dependent resonance modes in a single optical tweezers system,” Phys. Rev. E 72, 012903 (2005).
[Crossref]

Physica A (1)

Ø. Farsund and B. U. Felderhof, “Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field,” Physica A 227, 108–130 (1996).
[Crossref]

Proc. R. Soc. Lond. A (1)

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. A 459, 3021–3041 (2003).
[Crossref]

Proc. SPIE (1)

A. Usman, W.-Y. Chiang, and H. Masuhara, “Femtosecond trapping efficiency enhanced for nano-sized silica spheres,” Proc. SPIE 8458, 845833 (2012).
[Crossref]

Other (1)

G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer, 2011).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Numerical convergence test for the calculated force for a pulsed beam as a function of pulse spacing and truncation frequency. The force acting on a particle at the focus is given in terms of the axial force efficiency. The asterisk shows the parameters used; this point is well within the region of good convergence. The smallest pulse spacing tested was 500 fs, with other pulse spacings being 500 fs times powers of two. The truncation frequency is given in terms of the 1/e half-width of the Gaussian envelope of the pulse.
Fig. 2
Fig. 2 (a) Axial equilibrium position of particle as a function of particle size and refractive index, for CW beam. The white region indicates that particles with the specified properties were untrappable. (b) Axial equilibrium position of particle as a function of particle size and refractive index, for pulsed beam. (c) Regions where particle can be trapped with one type of beam, but not the other.
Fig. 3
Fig. 3 Equilibrium positions (left) and radial spring constants (right) for CW beams and pulses of different widths. The axial equilibrium positions and radial spring constants are shown for particles of refractive index (a)–(b) n = 1.45, (c)–(d) n = 1.48, and (e)–(f) n = 1.58.
Fig. 4
Fig. 4 Variation of scattering force with frequency and effect on pulsed-beam force. (a) The variation with frequency of the scattering force due to a CW beam is shown (green). The frequencies of the spectral components of the pulsed beam are also shown (circles), and the envelope of the pulsed spectrum (red). The pulsed-beam force is approximated a weighted average of the CW curve, using this envelope as the weighting function at the frequency components. (b) The variation of the pulsed-beam force with position and width of the pulse spectrum; shifting the position of the pulse spectrum relative to the scattering force versus frequency curve is analogous to varying the particle size. This is calculated using an idealised sin2 variation of scattering force with frequency, and pulses of the same duration, and half and double the durations of the pulse shown in (a). As the envelope of the spectrum broadens, the variation with particle size becomes smaller.
Fig. 5
Fig. 5 Difference in equilibrium position for pulses of different widths. The differences in equilibrium position between particles trapped in CW beams and pulsed beams are shown. The differences are shown for particles of refractive index (a) n = 1.45, (b) n = 1.48, and (c) n = 1.58. The RMS and maximum differences are shown in (d).
Fig. 6
Fig. 6 Difference in radial spring constant for pulses of different widths. The differences in time-averaged radial spring constant between particles trapped in CW beams and pulsed beams are shown. The absolute (left; (a), (c), (e)) and relative (right, (b), (d), (f)) differences are shown for particles of refractive index n = 1.45 ((a), (b)), n = 1.48 ((c), (d)), and n = 1.58 ((e), (f)). Legends are omitted where curves would be obscured, but note that legends for (a)–(f) are identical. The RMS and maximum differences are shown for (g) absolute and (h) relative differences.
Fig. 7
Fig. 7 Trap strengths and differences in trap strength for pulses of different widths. The trap strength is the maximum axial reverse restoring force. We show the trap strength (left; (a), (c), (e)) and the differences in trap strength between CW beams and pulsed beams, for particles of refractive index n = 1.45 ((a), (b)), n = 1.48 ((c), (d)), and n = 1.58 ((e), (f)). The RMS and maximum differences are shown for (g) absolute and (h) relative differences.
Fig. 8
Fig. 8 Axial spring constants and differences in axial spring constant for pulses of different widths. We show the axial spring constant (left; (a), (c), (e)) and the differences in axial spring constant between CW beams and pulsed beams, for particles of refractive index n = 1.45 ((a), (b)), n = 1.48 ((c), (d)), and n = 1.58 ((e), (f)). The RMS and maximum differences are shown for (g) absolute and (h) relative differences.
Fig. 9
Fig. 9 Error in equilibrium position and radial spring constant due to approximating force of pulsed beam as sum of forces of spectral components. (a) Error in equilibrium position. (b) Absolute error in radial spring constant. (c) Relative error in spring constant. The RMS and maximum differences between the pulsed beam calculation and the sum of forces of spectral components are shown.
Fig. 10
Fig. 10 Difference in equilibrium position and radial spring constant for pulses stretched by dispersion. The differences between the initial unstretched and undistorted pulse, of pulse width 25 fs, and the pulses stretched or distorted by dispersion are shown. We show the differences in equilibrium position (left) and radial spring constant (right) for quadratic phase shifts (i.e., linear dispersion), (top, (a) and (b)), and cubic phase shifts (bottom, (c) and (d)).
Fig. 11
Fig. 11 Change in time-averaged angular distribution of scattered light. Solid blue lines show the scattered light from the original beam, and dashed red lines with the upper sideband phase-shifted by a quarter-wave. Note that the forward scattering is almost the same in both cases (b), but the difference in backscattering is clearly visible (c).

Equations (17)

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F = S T d A ε μ d d t V S d V ,
t 1 t 2 F d t = t 1 t 2 S T d A d t ε μ V S ( t 2 ) d V + ε μ V S ( t 1 ) d V ,
t 1 t 2 F d t = t 1 t 2 S T d A d t .
E inc = n = 1 m = n n a n m M n m ( 3 ) ( k r ) + b n m N n m ( 3 ) ( k r ) ,
E scat = n = 1 m = n n p n m M n m ( 1 ) ( k r ) + q n m N n m ( 1 ) ( k r ) ,
p = T a ,
E inc = j N n = 1 m = n n a n m j M n m ( 3 ) ( k j r ) + b n m j N n m ( 3 ) ( k j r )
E scat = j N n = 1 n = 1 m = n n p n m j M n m ( 1 ) ( k j r ) + q n m j N n m ( 1 ) ( k j r ) ,
a n m = a n m j = 0 N A j exp ( i ω j t ) ,
b n m = b n m j = 0 N A j exp ( i ω j t ) .
p n m = j = 0 N p n m j exp ( i ω j t ) ,
q n m = j = 0 N q n m j exp ( i ω j t ) .
F = n medium P Q c ,
f = j N | A j | 2 f j ,
P = j N | A j | 2
P = j N n m = n n | A j | 2 ( | a m n | 2 + | b n m | 2 ) .
| p | = n medium P / c ,

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