Optical caustics and wavefronts of butterfly beams (BBs) derived by using a catastrophe theory determined by potential functions depending on the state and control variables are reported. Due to the high dimensionality for the control variables, BBs can be manipulated into various optical light structures. It is also demonstrated that these curious beams have relatively simple Fourier spectra that can be described as polynomials, and another way to generate BBs from the Fourier spectrum’s perspective is provided. The dynamics for BBs are investigated by potential functions. Our experimental results agree well with the theoretical predictions. In addition to micro-manipulation and machining, these novel, to the best of our knowledge, caustic beams will pave the way for creating waveguide structures since they display high-intensity formations that evolve along curved trajectories.

中文翻译：

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通过蝴蝶焦散的各种横截面的实验可视化

报告了蝶形光束 (BBs) 的光学焦散和波前，该理论使用突变理论推导出来，该理论由取决于状态和控制变量的势函数确定。由于控制变量的高维数，BBs 可以被操纵成各种光学结构。还证明了这些奇怪的光束具有相对简单的傅立叶光谱，可以描述为多项式，并提供了从傅立叶光谱的角度生成 BB 的另一种方法。BBs 的动力学通过势函数进行研究。我们的实验结果与理论预测非常吻合。除了微操作和机械加工，这些新颖的，据我们所知，