Scaling quasi-self-imaging effect based on the one-dimensional Pearcey beam

We present a new type of self-imaging phenomenon named the scaling quasi-self-imaging effect, which is produced by adding shifted copies of the fundamental Pearcey beam. The recurrent solutions of two kinds of incident beams comprising one-dimensional ideal infinite Pearcey and apodized Gaussian Pearcey beams are found. The diffraction process is equivalent to that obtained where a disorder wave is transmitted through a “virtual” periodic grating at focusing plane; both the integer and fractional self-images of the intensity distribution on focusing plane can be induced at constant revival distance accompanied by a scaling, autofocusing, and inverse envelope propagation. The self-imaging image begins to invert after the focus plane, where the rate of scaling reaches a maximum value and a series of Gaussian-like bright spots is generated. Our theoretical predictions are numerically confirmed.