  We present a new approach for electronic control of optical tweezers by using
space-time-wavelength mapping (STWM), a technique that uses time-domain
modulation to control local intensity values, and hence the resulting optical
force, in space. The proposed technique enables direct control of magnitude,
location, and polarity of force hot-spots created by Lorentz force (gradient
force). In this paper, we develop an analytical formulation of the proposed
STWM technique for optical tweezing. In the case study presented here, we show
that 150 fs optical pulses are dispersed in time and space to achieve a focused
elliptical beam that is ~20 {\mu}m long and ~2 {\mu}m wide. By choosing the
appropriate RF waveform and electro-optic modulator, we can generate multiple
hot-spots with >200 pN force per pulse.
