Controllable Bessel-like beams self-reconstruct

Abstract

We tested the self-reconstructing property of Bessel-like beams (BLBs) with phases ψ_f = 2πα(1 - (x² + y²)^1/2/r₀) + 2πf(x+y) and ψ_n = 2πα(1 - ((x-ax²)² + y²)^1/2/r₀) , where f and  are the carrier frequency and nonlinear factor, respectively. We observed that these BLBs self-reconstruct due to their transverse energy flow. We quantified these reconstructions in reference to unobstructed beam via normalized mean square error (NMSE). It was shown that by 1) placing an opaque obstacle with varying sizes σ on the beams' path , the minimum distance of reconstruction  takes longer as  increases, and 2) the τ is independent on the beams' f and a values but dependent on σ. Determining τ will help find applications for these beams.