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.

中文翻译：

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定制的径向自加速梁

径向自加速光束是亥姆霍兹方程的旋转形状不变解。因此，它们表现出连续的无限螺旋轨迹。在这里，我们提出了定制这些光束以实现几乎任何所需的光束横截面的可能性，而不会牺牲独特的传播特性。我们讨论了分析剪裁机会并强调了它们的固有局限性。之后，通过举例的方式，应用遗传优化算法来证明一般启发式计算机优化方法的可行性。证明了对几个测试目标的收敛，并讨论了所选适应度函数的影响。