Controlling the orbital angular momentum of Gaussian vortices by shifting the point of phase singularity

A simple formula is obtained to describe the normalized orbital angular momentum (OAM) of a Gaussian beam after passing through a shifter spiral phase plate (SPP). The formula shows that while being equal to the topological charge at the zero off-axis shift, the OAM becomes fractional with increasing shift and it is tending to zero exponentially. Analytic expressions of the complex amplitude of the Gaussian beam having passed through the off-axis SPP show that as the beam propagates, the isolated intensity null moves from the initial point defined by the vector of the SPP's center shift along a straight line perpendicular to the said vector. Using a liquid crystal light modulator, crescent-shaped beams are experimentally generated.