Abstract
We theoretically study the evolution of ring-Airy beams during harmonic generation with the focus on the regime of pump energy depletion. We demonstrate that in this regime, ring-Airy beams still preserve their abrupt autofocusing properties, while transforming to a multiple ring-Airy structure. A similar transformation is observed on the beam of the generated harmonic. We suggest a simple analytical model that explains and predicts with precision our numerical findings.
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