We report the generation of two types of self-accelerating surface plasmon beams which are solutions of the nonparaxial Helmholtz equation in two dimensions. These beams preserve their shape while propagating along either elliptic (Mathieu beam) or parabolic (Weber beam) trajectories. We show that owing to the nonparaxial nature of the Weber beam, it maintains its shape over a much larger distance along the parabolic trajectory, with respect to the corresponding solution of the paraxial equation—the Airy beam. Dynamic control of the trajectory is realized by translating the position of the illuminating free-space beam. Finally, the ability of these beams to self-heal after blocking obstacles is demonstrated as well.

• Received 14 April 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.123902