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Orbital angular momentum and paraxial propagation characteristics of non-coaxial Laguerre-Gaussian beams.

The orbital angular momentum (OAM) and paraxial propagation characteristics of non-coaxial Laguerre-Gaussian (LG) beams are discussed. In the initial plane, the amplitudes of non-coaxial LG modes are the product of a Laguerre polynomial, a vortex phase factor, and a non-coaxial Gaussian window function. Because of displacement between the centroid and vortex center of the beams, the non-coaxial LG beams demonstrate a non-zero extrinsic OAM, which causes the propagation of beam centroid to have a small tilt angle relative to the z axis. Through separating the extrinsic OAM from the total OAM carried by the non-coaxial LG beams, the tilt angle and trajectory of the beam centroid are derived. Furthermore, the paraxial propagating characteristics of these beams are also discussed analytically. The results show the vortex center initially at origin demonstrates a linear lateral shift with propagation and the peak of transverse intensity has a trajectory of a straight line, although the intensity profile rotates itself with propagation.