Shifted nondiffractive Bessel beams

Nondiffractive Bessel beams are well known to have infinite energy and infinite orbital angular momentum (OAM). However, when normalized to unity of energy, their OAM is finite. In this work, we derive an analytical relationship for calculating the normalized OAM of the superposition of off-axis Bessel beams characterized by the same topological charge. We show that if the constituent beams of the superposition have real-valued weight coefficients, the total OAM of the superposition of the Bessel beams equals that of an individual nonshifted Bessel beam. This property enables generating nondiffractive beams with different intensity distributions but identical OAM. The superposition of a set of identical Bessel beams centered on an arbitrary-radius circle is shown to be equivalent to an individual constituent Bessel beam put in the circle center. 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.