Propagation characteristics of the space-time complex variables Airy-Laguerre-Gaussian wave packets

Abstract

The space-time complex variables Airy-Laguerre-Gaussian wave packets are the Laguerre-Gaussian wave packets, which is their intensity distribution at the cross section showing as the complex variables Laguerre-Gaussian functions in the space domain, are modulated by the Airy pulses in the time domain. The method of separating variables is a mathematical method to obtain this solution. According to solving the (1+3)D Pxi-axis equations, the analytical solution of the space-time complex variables Airy-Laguerre-Gaussian wave packets in free space has been accessed. When the initial incident power of the space-time complex variables Airy-Laguerre-Gaussian wave packets is not equal to the critical power, the wave packets’ width will fluctuate periodically. Poynting vector reveals the essence of this phenomenon.