Formation of Angular Harmonics Spectrum upon Focusing Vortex Beam with Elliptic Polarization

By employing the Richards–Wolf formalism, analytical expressions for the orbital angular momentum spectrum (OAM-spectrum) in the focus of an elliptically polarized optical vortex are derived. It is found that the OAM-spectrum remains independent of the phase of the focused light beam. Polarization of the incident field influences solely the asymmetry of the spectrum, leaving unchanged the energy partitioning into the side and main components. In contrast, the radial amplitude of the focused light beam does not alter the spectral asymmetry. However, it governs the energy fractions carried by the side and the main spectral components. Quadratic inequalities are obtained, which enable one to assess the feasibility of generating a prescribed OAM-spectrum when the incident beam is confined by a ring diaphragm.