  We demonstrate the generation of self-accelerating surface plasmon beams
along arbitrary caustic curvatures. These plasmonic beams are excited by
free-space beams through a two-dimensional binary plasmonic phase mask, which
provides the missing momentum between the two beams in the direction of
propagation, and sets the required phase for the plasmonic beam in the
transverse direction. We examine the cases of paraxial and non-paraxial
curvatures and show that this highly versatile scheme can be designed to
produce arbitrary plasmonic self-accelerating beams. Several different
plasmonic beams, which accelerate along polynomial and exponential
trajectories, are demonstrated both numerically and experimentally, with a
direct measurement of the plasmonic light intensity using a
near-field-scanning-optical-microscope.
