Abstract
Generalization of a Friis transmission equation for orbital angular momentum (OAM) radios is rigorously formulated using the Lorentz reciprocity theorem and a near-and-far-field convolution integral (NFCI). Based on the discretization of NFCIs, we computed the generalized Friis transmission equation to obtain the power-receiving behaviors of practical helicoidal parabolic reflector antennas (HPRAs) with continuously deformed surfaces. A simplified Friis equation is also used for computing the link budget and approximate Rayleigh length of discrete uniform circular arrays (UCAs) composed of $2\times 2$ dipole antennas. The transmission coefficients for the given OAM modes, represented by our equations for the HPRA and UCA, agree very well with commercial numerical simulators. In addition, an $m$ th-order NFCI, which is an orthogonal convolution integral for the $m$ th OAM mode, is proposed to define a figure of merit for the OAM mode purity of transmitting and receiving antennas.
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