A study of photophoretic trapping exploiting motional resonances of trapped particles induced by wideband excitation

Abstract

Photophoretic forces confine particles by a combination of levitation and active trapping. To generate the latter, the component of photophoretic force transverse to gravity generates a torque, which leads to complex rotation of the particle, thereby generating a restoring force. This force has not been understood quantitatively. In this paper, we study this component of photophoretic force by trapping a single absorbing particle using a loosely focused Gaussian laser beam and modulating the trap-center spatially using a superposition of multiple sinusoidal frequencies applied to the trapping beam. We vary the modulation amplitude in proportion to the excitation frequency so as to compensate for the reduced particle response at higher frequencies and thus obtain an almost constant response of the particle over the entire excitation range. We use the amplitude and phase response to determine the resonance frequency and the trap stiffness—which we study as a function of laser power and the intensity experienced by trapped particles of different sizes. We observe that, while the trapping stiffness is proportional to laser power, the optical intensity experienced by a particle at different powers is the same. This is reasonable in order to facilitate optical levitation but implies that the trap stiffness actually depends on an “effective intensity,” which may be a combination of the particle accommodation coefficient and the laser power.