Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space

We demonstrate three-dimensional (3D) Airy-Laguerre-Gaussian localized wave packets in free space. An exact solution of the (3 + 1)D potential-free Schrödinger equation is obtained by using the method of separation of variables. Linear compressed wave pulses are constructed with the help of a superposition of two counter-accelerating finite energy Airy wave functions and the generalized Laguerre-Gaussian polynomials in cylindrical coordinates. Such wave packets do not accelerate and can retain their structure over several Rayleigh lengths during propagation. The generation, control, and manipulation of the linear but localized wave packets described here is affected by four parameters: the decay factor, the radial mode number, the azimuthal mode number and the modulation depth.