The virtual source for generation of rotational symmetric Lorentz-Gaussian （RLG） wave whose propagating dynamics present the rotational symmetry is identified. Closed-form expressions, including integral and differential representations, are derived for this kind of Lorentz-Gaussian （LG） wave, thereby yielding paraxial approximation of the RLG beam in the appropriate regime. From the spectral representation of this wave, the first three order corrections of nonparaxial approximations are determined for a corresponding paraxial RLG beam. Moreover, the relationship between the RLG beam and the Hermite-Gaussian beam is revealed.
A generalized type of spiral Bessel beam has been demonstrated by using a spatially displaced helical axicon （HA）. The topological charge of the spiraling Bessel beams is determined by the order of the input Laguerre Gaussian （LG） beam and the topological charge of the HA. The obtained spiraling Bessel beams have an LG type of modulation along their propagation direction and exhibit annihilation-reconstruction properties. Theoretical analysis is presented, including that of the stability, propagation distance, topological charge, and spiraling dynamic characteristics. The mathematical and numerical results show that the propagation distance and helical revolution of the spiraling Bessel beams can be controlled through choosing appropriate radius of the HA.
