In this paper, we present the design procedure of modulated metasurface leaky-wave antennas (MMLWAs) to generate coaxial superposition of vortex beams with several orbital angular momentum (OAM) states. Based on the Flat Optics (FO) technique and aperture field estimation (AFE) method, an analytical framework is proposed to facilitate the implementation of MMLWAs generating multiple topological charges in the OAM regimen. Furthermore, using the spectral analysis which has been derived from the proposed model, we have shown that the symmetry of aperture shape can affect the purity of the mode. Also the perfectly symmetric circular shape is introduced as an ideal choice for high-purity vortex generation. This single aperture antenna with embedded monopole feed can be an appropriate alternative to more complex vortex beam generators such as spiral phase plates and circular antenna arrays.
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