The phase-only generation of self-accelerating Weber beams

A non-diffracting beam maintains its lateral intensity profile as it propagates. Because a Weber beam is the solution of the Helmholtz equation with parabolic coordinates, it is a non-diffracting beam. Its transverse profile follows a parabolic trajectory, giving it applications in many fields. We propose a single-beam, phase-only method to directly generate self-accelerating Weber beams, which significantly simplifies Weber-beam generation. To remove the need for computationally intensive calculations or programming of Weber functions, we derived a simplified approximation of the Weber beam's initial phase profile from the asymptotic form of the Weber equation solution, verified its validity through numerical simulation, and demonstrated the intensity distribution of the beam via Schlieren imaging. Finally, we reveal the unique physical properties of Weber beams and generalize their phase profile to achieve adaptable emission angles, significantly enhancing their practical versatility.