Regular papers

Optical trapping at low numerical aperture

Department of Imaging Science and Technology, Technical University of Delft, Lorentzweg 1, 2628 CJ Delft, The Netherlands

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Received: 4 January 2011

Abstract

A theory of optical trapping at low Numerical Aperture (NA) is presented. The theory offers an analytical description of the competition between the stabilizing gradient and destabilizing scattering force. The trade-off can be characterized by a single dimensionless trapping parameter, which increases with bead radius to wavelength ratio a/λ and refractive index contrast m and decreases with NA. The gradient force dominates for small trapping parameters, the scattering force for large trapping parameters. The potential well depth, maximum forces and trap stiffness as a function of the three parameters (a/λ, m, NA) can be mapped onto universal functions of the trapping parameter. These functions do not depend on any free parameter. The universal well depth and maximum force curves match with numerical results based on the exact multipole expansion of the optical trapping force. The paraxial limit of low NA is relevant for compact optical tweezers based on Optical Pickup Units known from optical data storage.