Abstract
We find the exact solution of the (1+1)-dimensional optical paraxial diffractive system by implementing the self-similarity method, leading to the discovery of a beam solution composed of Scorer functions, which we refer to as the Scorer beam. Through theoretical analysis and numerical simulation, we explore several characteristics of both infinite- and finite-energy Scorer beams, particularly focusing on their non-diffractive and self-accelerating properties. Additionally, we compare the Scorer beam with – and distinguish from – the related Airy beam. This investigation provides both theoretical and numerical insights that may guide the experimental realization of Scorer beams.
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