Young's boundary wave theory provides an alternative view of diffraction being an interference of a geometric wave and a boundary wave. Here, we show theoretically and experimentally that the transverse structure of a plane wave diffracted through slits originates solely from the boundary waves. For polygonal slits, we demonstrate that the concept of the ordinary evolute is ill-defined, and we solve this problem by taking the limit of the evolute as the curvature goes to zero. We show that light focuses not on caustic as ordinarily described in catastrophe optics but on regions which we define as second order evolutes. Experimentally, we show that these second order evolutes still correspond to the brightest regions of the diffraction because of the boundary waves at the vertices of the polygon. This research is valuable in the study of diffraction of slits in general and in optical self-healing where the reconstruction of the transverse structure is investigated.

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