According to singular optics, the phase and intensity that characterize structured electromagnetic beams can be understood in terms of concepts that involve subspaces where they or their derivatives exhibit a particular behavior, such as giving rise to extreme values or not being well defined. Caustics are a paradigmatic example of the former, while helical dislocation lines exemplify the latter. In this work the interrelation of the morphology of caustics and the morphology of dislocation lines is theoretically studied. The analysis for highly structured beams requires an efficient methodology that allows the identification of optical vortices, their topological charge, and the helical dislocation lines they belong to. Such a methodology is introduced and applied to paraxial elliptic umbilic beams and nonparaxial Airy symmetric three-dimensional beams. Nonparaxial beams exhibit caustic surfaces that delimit regions with a finite volume and different intensity average. It is shown that in the high intensity region so defined, the dislocation lines play the role of an internal skeleton, i.e., an endoskeleton, of the beam. The exoskeleton created in the low intensity regions shows subtle and interesting features that complement those of the endoskeleton; the caustics that delimit low intensity regions have a strong influence on the morphology of the exoskeleton.

中文翻译：

---

焦散线和位错线的形态：关于它们相互关系的一些线索

根据奇异光学，表征结构化电磁波束的相位和强度可以根据涉及子空间的概念来理解，在这些子空间中，它们或其衍生物表现出特定行为，例如产生极值或未明确定义。焦散线是前者的典型例子，而螺旋位错线是后者的例证。在这项工作中，从理论上研究了焦散形态与位错线形态的相互关系。对高度结构化光束的分析需要一种有效的方法来识别光学涡流、它们的拓扑电荷以及它们所属的螺旋位错线。这种方法被引入并应用于近轴椭圆脐带束和非近轴艾里对称三维梁。非近轴光束表现出焦散表面，用有限的体积和不同的强度平均值来界定区域。结果表明，在如此定义的高强度区域中，位错线起到了光束内部骨架，即内骨架的作用。在低强度区域创建的外骨骼显示出微妙而有趣的特征，与内骨骼的特征互补；界定低强度区域的焦散对外骨骼的形态有很大影响。位错线起到梁的内部骨架，即内骨架的作用。在低强度区域创建的外骨骼显示出微妙而有趣的特征，与内骨骼的特征互补；界定低强度区域的焦散对外骨骼的形态有很大影响。位错线起到梁的内部骨架，即内骨架的作用。在低强度区域创建的外骨骼显示出微妙而有趣的特征，与内骨骼的特征互补；界定低强度区域的焦散对外骨骼的形态有很大影响。