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Orbital angular momentum of a Gaussian beam without optical vortices produced by cylindrical lenses

An elliptical Gaussian beam does not contain optical vortices (phase dislocations) and its orbital angular momentum (OAM) equals zero. Here we study propagation of such beam in a paraxial ABCD system, including focusing by a cylindrical lens, placed in the waist plane and rotated by some angle. It is shown that this rotation leads to appearing of a non-zero OAM of such a beam, although typical laser beams with the OAM have optical vortices. Here, we obtain a simple expression for the normalized OAM. The OAM decreases with increasing focal length of the cylindrical lens. It also increases (in modulus) with increasing difference of squared waist radii. We study conditions, where this beam has large value of the OAM. The advantage of the proposed method is that laser beams with large values of OAM can be generated by using simple optical elements — cylindrical lenses. There is no need to use a spatial light modulator or a spiral phase plate or a fork hologram.