We introduce a new family of light beams with pre-engineered abruptly autofocusing properties. These beams have a circularly symmetric input profile that develops outward of a dark disk and oscillates radially as a sublinear-chirp signal, creating a series of concentric intensity rings with gradually decreasing width. The light rays involved in this process form a caustic surface of revolution that bends toward the beam axis at an acceleration rate that is determined by the radial chirp itself. The collapse of the caustic on the axis leads to a large intensity buildup right before the intended focus. This ray-optics interpretation provides valuable insight into the dynamics of abruptly autofocusing waves.
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