Theory of optical-tweezers forces near a plane interface

R. S. Dutra, P. A. Maia Neto, H. M. Nussenzveig, and H. Flyvbjerg
Optical-tweezers experiments in molecular and cell biology often take place near the surface of the microscope slide that defines the bottom of the sample chamber. There, as elsewhere, force measurements require force-calibrated tweezers. In bulk, one can calculate the tweezers force from first principles, as recently demonstrated. Near the surface of the microscope slide, this absolute calibration method fails because it does not account for reverberations from the slide of the laser beam scattered by the trapped microsphere. Nor does it account for evanescent waves arising from total internal reflection of wide-angle components of the strongly focused beam. In the present work we account for both of these phenomena. We employ Weyl's angular spectrum representation of spherical waves in terms of real and complex rays and derive a fast-converging recursive series of multiple reflections that describes the reverberations, including also evanescent waves. Numerical simulations for typical setup parameters evaluate these effects on the optical force and trap stiffness, with emphasis on axial trapping. Results are in good agreement with available experimental data. Thus, absolute calibration now applies to all situations encountered in practice.

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