RESUMO
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.
