Research of orbital angular momentum of superpositions of diffraction-free Bessel beams with a complex shift

We derive an analytical relationship for calculating the normalized orbital angular momentum (OAM) of the superposition of off-axis Bessel beams characterized by the same topological charge. This relationship enables generating nondiffractive beams with different intensity distributions but identical OAM. As a result of a complex shift of the Bessel beam, the transverse intensity distribution and OAM of the beam are also shown to change. We show that in the superposition of two or more complex-shifted Bessel beams, the OAM may remain unchanged, while the intensity distribution is changed. Numerical simulation is in good agreement with theory.