Axial optical trapping efficiency through a dielectric interface

Axial trapping through a dielectric interface is investigated in the framework of the angular spectrum representation and of the generalized Lorenz-Mie theory. We determine the optical force for an arbitrarily polarized non-paraxial, strongly aberrated, axially symmetric focusing beam and apply this description to the case of an arbitrarily positioned dielectric microsphere, commonly employed in optical tweezers, not taking into account the contribution of evanescent waves at the interface. We derive the analytical expression of the force profile, finding that the incident polarization does not affect the axial optical force. In addition, we derive an approximated expression for the axial force as a function of beam displacement just outside the microsphere and we show how the information provided by the ripple structure of the optical trapping efficiency versus sphere displacement curve, due to the aberration effect, could be exploited to calibrate the bead axial position versus the experimental beam positioning controls.