Topological charge of optical vortices devoid of radial symmetry

Here we theoretically obtain values of the topological charge (TC) for vortex laser beams devoid of radial symmetry: asymmetric Laguerre-Gaussian (LG) beams, Bessel-Gaussian (BG) beams, Kummer beams, and vortex Hermite-Gaussian (HG) beams. All these beams consist of conventional modes, namely, LG, BG, or HG modes, respectively. However, all these modes have the same TC equal to that of a single constituent mode $n$. Orbital angular momenta (OAM) of all these beams, normalized to the beam power, are different and changing differently with varying beam asymmetry. However, for arbitrary beam asymmetry, TC remains unchanged and equals $n$. Superposition of just two HG modes with the adjacent numbers $(n, n+1)$ and with the phase retardation of $(pi)/2$ yields a modal beam with the TC equal to – $(2n+1)$. Numerical simulation confirms the theoretical predictions.