Properties of Near Field Focusing for Three-Dimensional Large Intelligent Surface

This work investigates near-field focusing using a three-dimensional (3D) large intelligent surface (LIS) across frequencies and polarizations. Specifically, the LIS elements are distributed in 3D space within a long corridor, rather than being confined to a single planar aperture, and the focal point is located at a prescribed position in the radiating near field. By formulating optimization problems under both local and global power constraints, we obtain the corresponding optima. For continuous apertures, the optimal current magnitude distribution matches time-reversal (TR) solution under the global constraint and conjugate-phase (CP) solution when the local constraint dominates. When both constraints are active, the solution assigns larger excitation magnitudes to elements closer to the illumination field. This behavior remains invariant with respect to frequency and polarization for a fixed-size LIS. These findings are consistent to the more practical case of using discretized apertures in the form of Hertzian dipole arrays, studied using both analytical results and full-wave simulation. In addition, with the CP method, specific polarizations lead to identical transverse and longitudinal resolution, in contrast, under the TR method, these quantities can differ across polarizations.