Tailored radially self-accelerating beams

Radially self-accelerating beams are rotating shape-invariant solutions of the Helmholtz equation. As such, they exhibit continuous indefinitely spiraling trajectories. Here we present the possibility to tailor those beams to achieve almost any desired beam cross section, without sacrificing the unique propagation characteristics. We discuss analytical tailoring opportunities and highlight their inherent limitations. Following that, by way of example, a genetic optimization algorithm is applied to demonstrate the feasibility of heuristic computer optimization methods in general. The convergence towards several test-targets is demonstrated and the influence of the chosen fitness function is discussed.