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Transformation of decelerating laser beams into accelerating ones

We propose a method for obtaining paraxial accelerating two-dimensional laser beams on a finite section of their path in which the complex amplitudes of familiar decelerating light beams are complex-conjugated and shifted along the optical axis. With this method, Fresnel and Laplace beams accelerating along a square-root-parabola path and a paraxial ‘half-Bessel’ beam are generated. As distinct from the familiar diffraction-free accelerating Airy beams, the beams under analysis are found to be converging on the final section of the accelerating path.