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.
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