## Optical trapping of dielectric particles in arbitrary fields

JOSA A, Vol. 18, Issue 4, pp. 839-853 (2001)

http://dx.doi.org/10.1364/JOSAA.18.000839

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### Abstract

We present a new method to calculate trapping forces of dielectric particles with diameters D ≤ λ in arbitrary electromagnetic, time-invariant fields. The two components of the optical force, the gradient force and the scattering force, are determined separately. Both the arbitrary incident field and the scatterer are represented by plane-wave spectra. The scattering force is determined by means of the momentum transfer in either single- or double-scattering processes. Therefore the second-order Born series is evaluated and solved in the frequency domain by Ewald constructions. Numerical results of our two-force-component approach and an established calculation method are compared and show satisfying agreement. Our procedure is applied to investigate axial trapping by focused waves experiencing effects of aperture illumination and refractive-index mismatch.

© 2001 Optical Society of America

**OCIS Codes**

(180.0180) Microscopy : Microscopy

(260.0260) Physical optics : Physical optics

(290.0290) Scattering : Scattering

**Citation**

Alexander Rohrbach and Ernst H. K. Stelzer, "Optical trapping of dielectric particles in arbitrary fields," J. Opt. Soc. Am. A **18**, 839-853 (2001)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-4-839

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### References

- A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
- A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
- A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
- S. M. Block, D. F. Blair, and H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature (London) 338, 514–518 (1989).
- S. M. Block, L. S. Goldstein, and B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature (London) 348, 348–352 (1990).
- A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature (London) 348, 346–348 (1990).
- S. C. Kuo and M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260, 232–234 (1993).
- K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
- R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, and M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12, 505–510 (1991).
- M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, and R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. U.S.A. 86, 7914–7918 (1989).
- S. Seeger, S. Monajembashi, K. J. Hutter, G. Futterman, J. Wolfrum, and K. O. Greulich, “Application of laser optical tweezers in immunology and molecular genetics,” Cytometry 12, 497–504 (1991).
- L. P. Ghislain and W. W. Webb, “Scanning-force microscope based on an optical trap,” Opt. Lett. 18, 1678–1680 (1993).
- A. Pralle, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Local viscosity probed by photonic force microscopy,” Appl. Phys. A 66, P71–P73 (1998).
- E.-L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, “Photonic force microscope (PFM) based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202–211 (1997).
- E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys. A: Solids Surf. 66, S75–S78 (1998).
- A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional position tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
- P. Debye, “Der Lichtdruck auf Kugeln von beliebige Material,” Ann. Phys. 30, 57–136 (1909).
- G. Mie, “Beitraege zur Optik trueber Medien speziell Kolloidaler Metalloesungen,” Ann. Phys. 25, 377–445 (1908).
- J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 236.
- P. Mulser, “Radiation pressure on microscopic bodies,” J. Opt. Soc. Am. B 2, 1814–1829 (1985).
- 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).
- R. Gussgard, T. Lindmo, and I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. B 9, 1922–1930 (1992).
- T. Wohland, A. Rosin, and E. H. K. Stelzer, “Theoretical determination of the influence of the polarization on forces exerted by optical tweezers,” Optik 102, 181–190 (1996).
- J. S. Kim and S. S. Lee, “Scattering of laser beams and the optical potential well for a homogeneous sphere,” J. Opt. Soc. Am. 73, 303–312 (1983).
- J. P. Barton and D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
- 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).
- F. Ren, G. Gréhan, and G. Gouesbet, “Radiation pressure forces exerted on a particle located arbitrarily in a Gaussian beam by using the generalized Lorentz–Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994).
- W. H. Wright, G. J. Sonek, and M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993).
- W. H. Wright, G. J. Sonek and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
- Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996).
- 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).
- P. Zemánek, A. Jonás, L. Srámek, and M. Liska, “Opticaltrapping of nanoparticles and microparticles by a Gaussian standing wave,” Opt. Lett. 24, 1448–1450 (1999).
- M. Kerker, The Scattering of Light, 1st ed. (Academic, New York, 1969).
- K. S. Shifrin, Scattering of Light in a Turbid Medium, 1st ed. (Nauka, Moscow, 1951) N. T. t. T. F.-. (1968).
- C. Acquista, “Light Scattering by tenuous particles: a generalization of the Rayleigh–Gans–Rocard approach,” Appl. Opt. 15, 2932–2936 (1976).
- S. Colak, C. Yeh and L. W. Casperson, “Scattering of focused beams by tenuous particles,” Appl. Opt. 18, 294–302 (1979).
- M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074–1085 (1998).
- C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,” J. Opt. Soc. Am. 54, 240–244 (1964).
- J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, San Francisco, Calif., 1968), pp. 48–56.
- M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2093 (1986).
- M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989).
- C. J. R. Sheppard and K. G. Larkin, “Vectorial pupil functions and vectorial transfer functions,” Optik 107, 79–87 (1997).
- A. Rohrbach, www.embl-heidelberg.de/~rohrbach.
- J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
- J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. 8, 14–21 (1973).
- J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 239.
- K. Visscher and G. J. Brakenhoff, “Theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatterers,” Optik 89, 174–180 (1992).
- J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 151.
- C. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Science Paperback, New York, 1998), p. 137.
- E. Lalor and E. Wolf, “Exact solution of the equation of molecular optics for refraction and reflection of an electromagnetic wave on a semi-infinite dielectric,” J. Opt. Soc. Am. 62, 1165–1174 (1972).
- M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, New York, 1999).
- B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1498 (1994).
- T. Lemaire, “Coupled-multipole formulation for the treatment of electromagnetic scattering by a small dielectric particle of arbitrary shape,” J. Opt. Soc. Am. A 14, 470–474 (1997).
- M. Kerker, “Rayleigh–Debye scattering,” in The Scattering of Light, E. M. Loebl, ed., 1st ed. (Academic, New York, 1969), p. 414.
- W. Singer and K.-H. Brenner, “Transition of a scalar field at a refracting surface in the generalized Kirchhoff diffraction theory,” J. Opt. Soc. Am. A 12, 1913–1919 (1995).
- A. Rohrbach and W. Singer, “Scattering of a scalar field at dielectric surfaces by Born series expansion,” J. Opt. Soc. Am. A 15, 2651–2659 (1998).
- H. Weyl, “Ausbreitung elektromagnetischer Wellen ueber einem ebenen Leiter,” Ann. Phys. 60, 481–500 (1919).
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
- Mie scattering, www.omlc.ogi.edu/calc/mie_calc.html.
- P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995).
- H. Felgner, O. Müller, and M. Schliwa, “Calibration of light forces in optical tweezers,” Appl. Opt. 34, 977–982 (1995).
- M. Gu, P. C. Ke, and X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997).

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