We investigate the fundamental properties of the caustic curve associated with an optical beam by performing a kinematic analysis of its spectral phase. By parametrizing the caustic curve in terms of the first and second derivatives of the phase, we characterize the kinematic behavior of the trajectory and identify the conditions under which singularities arise—specifically, when the caustic velocity vector either vanishes or becomes undefined. Our results show that the third derivative of the spectral phase plays a central role: Its roots and discontinuities determine the occurrence of singularities. A detailed analysis distinguishes two classes of singularities: avoidable and unavoidable. Avoidable singularities preserve the smoothness of the caustic trajectory, whereas unavoidable ones disrupt it, giving rise to cusp points. Both classes of singularities strongly influence the mapping from spectral to spatial coordinates that governs the generation of the optical beam. Consequently, the light intensity distribution undergoes pronounced modifications in the vicinity of these points, potentially producing regions of enhanced intensity and steep intensity gradients. These findings provide a kinematic extension to the standard catastrophe classification by introducing the concepts of avoidable and unavoidable singularities, thereby broadening the potential of caustic beams in structured light applications.

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• Beam control
• Classical optics
• Near-field optics
• Optical coherence
• Optics & lasers