Diffraction-free asymmetric elegant Bessel beams with fractional orbital angular momentum

This paper introduces a new family of diffraction-free asymmetric elegant Bessel beams (EB-beams) with fractional orbital angular momentum (OAM). EB-beams are modes of free space and described by the $n$-th order Bessel function of the first kind with a complex argument. Functions of complex amplitudes of EB-beams are orthogonal by continuous scaling parameter and not orthogonal on a discrete parameter (topological charge). The intensity distribution of EB-beams has a countable number of isolated zeros of intensity, located on the horizontal axis. These zeros are centers of optical vortices with unit topological charge and opposite signs on different sides of the origin. Isolated intensity zero on the optical axis generates an optical vortex with topological charge of $n$. OAM of the EB-beams is $(n + 0,69777)\hbar$ per photon, where $\hbar$ is the Planck's constant.