  We report for the first time the theory of optical tweezers of spherical
dielectric particles embedded in a chiral medium. We develop a partial-wave
(Mie) expansion to calculate the optical force acting on a dielectric
microsphere illuminated by a circularly-polarized, highly focused laser beam.
When choosing a polarization with the same handedness of the medium, the axial
trap stability is improved, thus allowing for tweezing of high-refractive-index
particles. When the particle is displaced off-axis by an external force, its
equilibrium position is rotated around the optical axis by the mechanical
effect of an optical torque. Both the optical torque and the angle of rotation
are greatly enhanced in the presence of a chiral host medium when considering
radii a few times larger than the wavelength. In this range, the angle of
rotation depends strongly on the microsphere radius and the chirality parameter
of the host medium, opening the way for a quantitative characterization of both
parameters. Measurable angles are predicted even in the case of naturally
occurring chiral solutes, allowing for a novel all-optical method to locally
probe the chiral response at the nanoscale.
