Propagation characteristics of space-time Airy-Ince-Gaussian beams in highly nonlocal nonlinear media

The space-time Airy-Ince-Gaussian Beams are the Ince-Gaussian beams, which is their intensity distribution at the cross-section showing as the Ince functions in the space domain, are modulated by the Airy pulses with initial velocity in the time domain. The solutions of the space-time Airy-Ince-Gaussian functions basing on the initial velocity, the power ratio about the critical power and the input power, and the ellipticity have been accessed according to solving the cylindric coordinates’ (1+3)D Schrödinger equations in Highly Nonlocal Nonlinear Media. Their propagation characteristics are studied in the paper. According to the incident power of the beam is not equal to the critical power, the beam width changes periodically when the beam is propagating. The Poynting vector of the propagating beams at cross section reveals the essence of physics.