Topological Charge of a Coaxial Superposition of the Bessel-Gaussian Laser Beams

Abstract

Here, we study a superposition of Bessel-Gaussian beams with topological charges (TC) m and n. We prove theoretically that continuous varying the amplitudes of the constituent beams allows controlling the TC of the entire superposition. We obtain the conditions, when the TC is equal to n or m. In the cross-section of such a superposition, there is an m-order optical vortex (if m<n) and n-m unitary-charge vortices residing in the beam periphery. If the amplitudes of both constituent beams become equal, we show that peripheral optical vortices move away to infinity and that TC becomes half-integer. In addition, this TC is conserved on free space propagation. Fractional part of this TC is, however, hidden in infinity.