Optical Gradient Forces of Strongly Localized Fields

Tsvi Tlusty; Amit Meller; Roy Bar-Ziv

doi:10.1103/PhysRevLett.81.1738

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Optical Gradient Forces of Strongly Localized Fields

Tsvi Tlusty¹, Amit Meller^2,3, and Roy Bar-Ziv⁴

¹Department of Materials and Interfaces, The Weizmann Institute of Science, Rehovot, 76100, Israel
²Rowland Institute for Science, 100 Edwin Land Boulevard, Cambridge, Massachusetts 02142
³and Center for Advanced Biotechnology, Boston University, Boston, Massachusetts 02215
⁴Center for Studies in Physics and Biology, The Rockefeller University, 1230 York Avenue, New York, New York 10021

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Phys. Rev. Lett. 81, 1738 – Published 24 August, 1998

DOI: https://doi.org/10.1103/PhysRevLett.81.1738

Abstract

We present a new approach for determining optical gradient forces applied by strongly focused laser beams on dielectric particles. We show that when the electromagnetic field is focused to a diffraction limited spot a dipole approximation is valid for any particle size. We derive intuitive predictions for force-displacement curves, maximal trapping forces, and force constants. The theory fits well with recent measurements of particles trapped by laser tweezers. We also discuss effects of radiation pressure and gravity.

References (14)

A. Ashkin, Phys. Rev. Lett. 24, 156–159 (1970).
A. Ashkin, Science 210, 1081–1088 (1980).
A. Ashkin, J. M. Dziedzic, and T. Yamane, Nature (London) 330, 769–771 (1987).
K. Svoboda and S. M. Block, Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, Biophys. J. 70, 1813–1822 (1996).
A. Ashkin, Proc. Natl. Acad. Sci. U.S.A. 94, 4853–4860 (1997); Methods Cell Biol. 55, 1–27 (1998).
M. Kerker, The Scattering of Light and other Electromagnetic Radiation (Academic, New York, 1969).
A. Ashkin, Biophys. J. 61, 569–582 (1992).
L. P. Ghislain, N. A. Switz, and W. W. Webb, Rev. Sci. Instrum. 65, 2762–2768 (1994).
R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, and S. A. Safran, Phys. Rev. Lett. 78, 154–157 (1997).
A. Meller, R. Bar-Ziv, T. Tlusty, E. Moses, J. Stavans, and S. A. Safran, Biophys. J. 74, 1541–1548 (1998).
L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1982).
Similarly, we obtain the same spatial dependence for the axial force, $F_{z} (z) / α I_{0} ω^{2} {= A}_{z} (ε) \sinh (a_{c} u_{z}) e^{- (1 / 2) u_{z}^{2}}$ , where the coordinate is $u_{z} = z / ω ε$ and the prefactor $A_{z} (ε) = 4 π \erf (b_{c} / \sqrt{2})^{2} e^{- (1 / 2) (a_{c} / ε)^{2}}$ .
To improve the compatibility with the exact calculation for very large spheres we integrate instead over a rectangular box having the same volume yielding the same expression 4 but with $b_{c} = \sqrt{π / 6} a_{c} = \frac{R}{ω}$ .

[c1] A. Ashkin, Phys. Rev. Lett. 24, 156–159 (1970).

[c2] A. Ashkin, Science 210, 1081–1088 (1980).

[c3] A. Ashkin, J. M. Dziedzic, and T. Yamane, Nature (London) 330, 769–771 (1987).

[c4] K. Svoboda and S. M. Block, Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).

[c5] R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, Biophys. J. 70, 1813–1822 (1996).

[c6] A. Ashkin, Proc. Natl. Acad. Sci. U.S.A. 94, 4853–4860 (1997); Methods Cell Biol. 55, 1–27 (1998).

[c7] M. Kerker, The Scattering of Light and other Electromagnetic Radiation (Academic, New York, 1969).

[c8] A. Ashkin, Biophys. J. 61, 569–582 (1992).

[c9] L. P. Ghislain, N. A. Switz, and W. W. Webb, Rev. Sci. Instrum. 65, 2762–2768 (1994).

[c10] R. Bar-Ziv, A. Meller, T. Tlusty, E. Moses, J. Stavans, and S. A. Safran, Phys. Rev. Lett. 78, 154–157 (1997).

[c11] A. Meller, R. Bar-Ziv, T. Tlusty, E. Moses, J. Stavans, and S. A. Safran, Biophys. J. 74, 1541–1548 (1998).

[c12] L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1982).

[c13] Similarly, we obtain the same spatial dependence for the axial force, $F_{z} (z) / α I_{0} ω^{2} {= A}_{z} (ε) \sinh (a_{c} u_{z}) e^{- (1 / 2) u_{z}^{2}}$ , where the coordinate is $u_{z} = z / ω ε$ and the prefactor $A_{z} (ε) = 4 π \erf (b_{c} / \sqrt{2})^{2} e^{- (1 / 2) (a_{c} / ε)^{2}}$ .

[c14] To improve the compatibility with the exact calculation for very large spheres we integrate instead over a rectangular box having the same volume yielding the same expression 4 but with $b_{c} = \sqrt{π / 6} a_{c} = \frac{R}{ω}$ .

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Optical Gradient Forces of Strongly Localized Fields

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