Paraxial shifted elliptic beams, conserving their shape on free space propagation

In optical data transmission, among the information carriers of special interest are laser beams, whose shape does not change on propagation in free space and in a homogeneous medium. In this work, we study a continuous superposition of paraxial propagation-invariant off-axis Gaussian beams. We obtain conditions when this superposition yields an offaxis elliptic beam with a given geometric parameters (center displacement, waist radii, tilt angle), which conserves its shape on propagation and rotates around the optical axis. Properties are derived of the normalized-to-power orbital angular momentum of such beams.