Orbital angular momentum spectrum of a tightly focused elliptically polarized optical vortex

Using Richards-Wolf formulae, we derive analytical expressions for the orbital angular momentum spectrum (OAM-spectrum) in the focus of an elliptically polarized optical vortex. We find that the OAM-spectrum does not depend on the phase of the field being focused. Polarization affects only the asymmetry of the spectrum, but not the distribution into main and side components. On the contrary, radial amplitude of the focused field does not affect the spectrum asymmetry, but determines the portions of energy going into the main and into the side spectrum components. We derive quadratic inequalities that allow determining a possibility of generating specific OAM-spectrum by bounding the initial field by ring aperture.