Focusing Efficiency for Large Intelligent Surfaces

I. INTRODUCTION

• In large-scale LIS deployments, many devices are in the near field, where focusing can provide substantially higher transfer efficiency than conventional far-field WPT.WPT is presented as an application that can reduce battery dependence for low-power IoT devices.Source: §I · p. 1
• Prior work derived optimal aperture excitations and efficiency bounds, while later simulations and experiments reported efficiency improvements for near-field WPT.Reported examples include a 30% improvement in implantable WPT and 72% beam collection efficiency with a 256-element prototype.Source: §I · p. 1
• The paper derives optimal LIS currents under a total-power constraint for arbitrary receiving antenna patterns and examines antenna pattern, orientation, and transmission distance.The theoretical results are validated with full-wave FEKO simulations.Source: §I · p. 1
• The framework is intended to provide a general basis for efficient single-user LIS-enabled WPT design.Source: §I · p. 1

II. MODELLING AND ERROR FORMULATION

• Because the receiver is much smaller than its separation from the LIS, its incident field is locally approximated as far-field excitation while the LIS remains a continuous radiating aperture.The formulation accommodates arbitrary receiver patterns; only electric surface current is considered on the LIS.Source: §II · p. 1
• As conductor loss increases, rapidly varying, spatially irregular optimal currents are suppressed, making the distributions smoother and more practical to implement.The lossless or weakly lossy solution is an upper-bound reference; with increasing loss, the optimum approaches time-reversal excitation, while direct optimization can be more efficient under low-loss conditions but harder to realize.Source: §II · p. 2
• The optimization maximizes received power under a total-power constraint, and focusing efficiency is received RF power before rectification divided by total LIS radiated power.Source: §II · pp. 1–2

IHZ I

• The framework maximizes WPT efficiency under a total-power constraint and solves the current problem using MoM with RWG basis functions.The implementation uses at least 10 elements per wavelength and accounts for bidirectional LIS radiation by multiplying the calculated efficiency by 2.Source: IHZ I · p. 3
• ηfocus decreases monotonically with distance, and FEKO results for a λ/2 dipole agree well with the theoretical curves.The agreement is reported for a 4λ × 4λ planar LIS aperture.Source: IHZ I · p. 3
• For a λ/2 dipole, ηfocus is about 3.5% at an aperture-to-distance ratio of 0.5 and about 1% at 0.25.At very large ratios, the LIS approaches half-space coverage and can collect up to half the dipole's radiated power, consistent with reciprocity.Source: IHZ I · pp. 3–4
• The patch has the highest ηfocus throughout the investigated distances, while the PIFA, dipole, and monopole are lower and relatively similar at larger distances.The comparison covers a probe-fed patch, PIFA, meander dipole, and folded L-shaped monopole, with antenna normals directed toward the LIS.Source: IHZ I · p. 4
• The patch has the highest peak ηfocus at 0°, but is most orientation-sensitive, falling below 1% at certain polar angles before recovering at larger angles; the monopole varies more moderately than the dipole.The PIFA shows high efficiency at small angles, pronounced degradation at intermediate angles, and subsequent recovery.Source: IHZ I · p. 4
• Spherical-wave expansion coefficients reconstruct the antenna field at arbitrary observation points, and a coordinate transformation evaluates rotated fields without additional full-wave simulations.The rotation matrix maps the antenna body coordinates to global coordinates; the same expansion coefficients can be reused for different orientations.Source: IHZ I · p. 4
• Uniformly sampled orientations yield approximately 2% average ηfocus for all four antennas, with the far-field estimate of 0.0199 close to that result.After directional averaging, the remaining contribution depends on the solid angle subtended by the receiving surface; the estimate uses A = 16λ² and η ≈ A/(4πd²).Source: IHZ I · p. 5

• The framework finds the LIS current distribution that maximizes received power under a total-power constraint for an arbitrary receiving antenna pattern.Source: §III · p. 5
• The resulting power-transfer efficiency is characterized across different receiver configurations.Source: §III · p. 5
• Numerical results and full-wave FEKO simulations confirm the theoretical predictions and demonstrate effects of receiver type, orientation, and transmission distance on focusing efficiency.Source: §III · p. 5