Cylindrical Vector Beams for Wireless Power Transfer

Abstract

This article investigates wireless power transfer in the Fresnel zone using cylindrical vector beams. First, a generalized coupling coefficient between two circular apertures in the Fresnel zone is derived. From the generalized coupling coefficient, explicit coupling coefficients between two circular (focused or unfocused) apertures supporting Gaussian, Bessel-Gaussian, and Laguerre-Gaussian beams are found in closed form. The analytically derived coupling coefficients and corresponding efficiencies are compared with those obtained through numerical integration of the reaction integral, as well as the results of a commercial electromagnetic solver. Then, it is demonstrated that a finite aperture, which supports a cylindrically apodized Bessel beam, is close to the optimal illumination. Also, it is shown that Bessel beams have a higher coupling coefficient than conventional Gaussian beams. Finally, the optimal aperture illumination is found numerically by constructing an aperture field from a summation of Bessel beams with different axicon angles. That is, the complex amplitude of each Bessel beam is found that maximizes coupling between the two apertures. The optimal illumination radiates a magnetic field equal to the complex conjugate of the receiver aperture's electric field. This observation agrees with those for optimal illumination in the context of a confocal optical resonator.