Nonparaxial propagation of a (1+1)-dimensional Pearcey beam

We introduce a virtual source that generates a family of a Pearcey wave. We derive a closed-form expression for the (1+1)-dimensional Pearcey wave that in the appropriate limit yields the paraxial accelerating and non-diffracting Pearcey beam (PB). From the perturbative series representation of a complex-source-point spherical wave, we derive an infinite series nonparaxial correction expression for PB. The infinite series expression of a PB can provide accuracy up to any order of diffraction angle. From the integral representation of the Pearcey wave, the first three orders of nonparaxial corrections to the paraxial Pearcey beam are derived.