Theory of trapping forces in optical tweezers

Starting from a Debye–type integral representation valid for a laser beam focused through a high numerical aperture objective, we derive an explicit partial–wave (Mie) representation for the force exerted on a dielectric sphere of arbitrary radius, position and refractive index. In the semi–classical limit, the ray–optics result is shown to follow from the Mie expansion, holding in the sense of a size average. The equilibrium position and trap stiffness oscillate as functions of the circumference–to–wavelength ratio, a signature of interference, not predicted by previous theories. We also present comparisons with experimental results.

[1]  A. Mehta,et al.  Single-molecule biomechanics with optical methods. , 1999, Science.

[2]  A. Ashkin.  Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime. , 1992, Methods in cell biology.

[3]  X. Gan,et al.  Trapping force by a high numerical-aperture microscope objective obeying the sine condition , 1997 .

[4]  K Bergman,et al.  Characterization of photodamage to Escherichia coli in optical traps. , 1999, Biophysical journal.

[5]  Arthur Ashkin,et al.  Optical Trapping and Manipulation of Neutral Particles Using Lasers , 1999 .

[6]  M. Schliwa,et al.  Calibration of light forces in optical tweezers. , 1995, Applied optics.

[7]  Warren J. Wiscombe,et al.  Efficiency factors in Mie scattering , 1980 .

[8]  E. Wolf,et al.  Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[9]  N. B. Viana,et al.  In situ measurement of laser power at the focus of a high numerical aperture objective using a microbolometer , 2002 .

[10]  G Gouesbet,et al.  Prediction of reverse radiation pressure by generalized Lorenz-Mie theory. , 1996, Applied optics.

[11]  H. M. Nussenzveig,et al.  Theory of optical tweezers , 1999 .

[12]  Dynamic light scattering from an optically trapped microsphere. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  J. B. Bateman,et al.  Determination of particle size and concentration from spectrophotometric transmission , 1959 .

[14]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[15]  Michael V Berry,et al.  Semiclassical approximations in wave mechanics , 1972 .

[16]  B. U. Felderhof,et al.  Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field , 1996 .

[17]  J. P. Barton,et al.  Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam , 1989 .

[18]  H. A. Tolhoek,et al.  Classical limits of clebsch-gordan coefficients, racah coefficients and Dmnl (φ, ϑ, ψ)-functions , 1957 .

[19]  Michelle D. Wang,et al.  Force and velocity measured for single molecules of RNA polymerase. , 1998, Science.

[20]  A. R. Edmonds.  Angular Momentum in Quantum Mechanics , 1957 .

[21]  Herch Moyses Nussenzveig.  Diffraction Effects in Semiclassical Scattering , 1992 .

[22]  T. Lindmo,et al.  Calculation of the trapping force in a strongly focused laser beam , 1992 .

[23]  Yao Xin-cheng,et al.  Effects of spherical aberration on optical trapping forces for Rayleigh particles , 2001 .

[24]  H. V. Hulst.  Light Scattering by Small Particles , 1957 .

[25]  W. Steen.  Absorption and Scattering of Light by Small Particles , 1999 .

[26]  K. Svoboda,et al.  Biological applications of optical forces. , 1994, Annual review of biophysics and biomolecular structure.

[27]  Watt W. Webb,et al.  Measurement of small forces using an optical trap , 1994 .

[28]  R. C. Thorne.  The asymptotic expansion of legendre function of large degree and order , 1957, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[29]  G. Roosen.  La lévitation optique de sphères , 1979 .