  We propose and demonstrate the effectual generation and control of
nonparaxial self-accelerating beams by using UV-resin pendant droplets. We show
that the geometrical shape of the hanging droplets formed as a result of the
interplay between surface tension and gravity offers a natural curvature
enabling the generation of nonparaxial self-accelerating beams. By simply
adjusting the tilt angle of the surface where the droplets reside, a passing
light beam is set to propagate along different curved trajectories, bending
into large angles with non-diffracting features superior to a conventional Airy
beam. Such self-accelerating beams are directly traced experimentally through
the scattered light in yeast-cell suspensions, along with extensive ray tracing
and numerical simulations. Furthermore, by modifying the shape of uncured
pendant resin droplets in real time, we showcase the dynamical trajectory
control of the self-accelerating beams. Our scheme and experimental method may
be adopted for droplet-based shaping of other waves such as microfluidic jets
and surface acoustic waves.
