  Difference-sideband generation in an optomechanical system coupled to a
charged object is investigated beyond the conventional linearized description
of optomechanical interactions. An exponential decay law for
difference-sideband generation in the presence of electric interaction is
identified which exhibits more sensitivity to electrical charges than the
conventional linearized effects. Using exact the same parameters with previous
work based on the linearized dynamics of the optomechanical interactions, we
show that optomechanically induced difference-sideband generation may enable an
all-optical sensor for precision measurement of electrical charges with higher
precision and lower power. The proposed mechanism is especially suited for
on-chip optomechanical devices, where nonlinear optomechanical interaction in
the weak coupling regime is within current experimental reach.
