Abstract
We have analytically and numerically investigated the propagation of three-dimensional self-decelerating Airy-Elegant-Laguerre-Gaussian (AiELG) wave packets by solving the (3+1)D free-space Schrödinger equation. We found that their intensity profiles are determined by three parameters: the azimuthal mode number, the radial mode number and the modulation depth. The modulation depth has effect on the azimuthal mode number. If the modulation depth equals to 1, the azimuthal mode number cannot take affect. The beam dose not split along the angular orientation. The self-decelerating AiELG wave packet shows ring. Otherwise, the modulation depth equals to 0, azimuthal mode number will take affect, and the self-decelerating AiELG wave packet shows necklace. It is worth mentioning that the radial mode number of self-decelerating AiELG wave packet will change in propagation. The reason is that the direction of the energy flow is always kept away from the centre during propagation.
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