Propagation dynamics of (3+1)-dimensional self-accelerating sinh-Gaussian and cosh-Gaussian wave packets in a harmonic potential

Abstract

In a harmonic potential, the propagation properties of self-accelerating sinh-Gaussian and cosh-Gaussian wave packets are investigated. Analytical results from a (3+1)-dimensional evolution equation are derived. Changing the distribution factor allows these wave packets to present different forms, including dipoles, elliptic vortex, hollow rings, horizontal figure eight, and elliptic Gaussian. These spatiotemporal wave packets rotate periodically, and the period depends on the potential depth. Their shapes are strongly determined by the distribution factor and the cross-phase factor while propagating. Further, the wave packets with negative chirp parameters can reverse their self-accelerating direction. We also investigate these wave packets’ energy flow and angular moment density to explore their dynamic rotating features. The spatiotemporal self-accelerating sinh-Gaussian and cosh-Gaussian wave packets have distinctive characteristics, which may provide a novel platform for the realization of joint control of the optical field in the spatiotemporal domain.