Propagation behaviors of two-dimensional chirped finite-energy Pearcey beams in free space

We introduce two-dimensional chirped finite energy Pearcey beams (FEPBs) for the first time and investigate the propagation dynamics. First, we applied the Huygens–Fresnel integral to derive an explicit analytical expression which is suitable for describing FEPB propagation in free space. It is interesting to find that FEPBs will experience three typical propagation patterns, i.e. the single-autofocusing case, dual-autofocusing case and non-autofocusing diffraction case, only depending on the value of the input asymmetric chirp. We further arrive at the critical condition of these three patterns analytically. However, by changing the sign, another input symmetric chirp acts to strengthen or weaken the autofocusing intensity but does not affect the focal distance. Our findings suggest that two-dimensional chirped FEPBs have more potential in controlling linear self-focusing and optical particle manipulation, when compared with the corresponding Airy field or conventional Gaussian field.