Coherent and Incoherent Nonparaxial Self-Accelerating Weber Beams

We investigate coherent and incoherent nonparaxial Weber beams both theoretically and numerically. We clarify the understanding of coherence properties of Weber beams. We show that the superposition of coherent self-accelerating Weber beams with transverse displacement cannot display the nonparaxial accelerating Talbot effect because their lobes do not accelerate in unison, which is the requirement for the appearance of the effect. The incoherent Weber beams also cannot display the accelerating Talbot effect but can exhibit nonparaxial accelerating properties, although the transverse coherence length is smaller than the beam width, based on the second-order coherence theory. Our research method applies to the nonparaxial Mathieu beams as well, and one obtains similar conclusions as for the Weber beams, although this is not discussed in the paper.