Analysis of orbital angular momentum of a misaligned optical beam

We report an analysis of the orbital angular momentum of an optical beam misaligned with respect to a reference axis. Both laterally displaced and angularly deflected Laguerre - Gaussian beams are represented in terms of the superposition of azimuthal harmonics with well-defined orbital angular momentum. Simultaneous parallel displacement and angular tilt cause the coupling between azimuthal harmonics and therefore change the projection of the orbital angular momentum on the reference axis. Rotation of beams around the reference axis was simulated by attributing corresponding rotational frequency shifts to the components.