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

Abstract

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.

Figures (17)

• Figure 1: LIS application scenarios. The figure illustrates users moving within a long corridor. The corridor is surrounded by LIS, with each LIS panel represented by a region $\it{\Omega}$. The longitudinal polarization is along the corridor axis ($z$-directed), whereas the transverse polarization lies across the corridor ($x$- or $y$-directed), with respect to the coordinate system shown.
• Figure 2: Indoor LIS scenario of a long corridor as in Fig. \ref{['fig:LIS_scenario']}. The cross-sectional transformation replaces the original rectangular cross-section with an inscribed circle of radius $a_1$ and a circumscribed circle of radius $a_2$. In this model, the $z$-axis is aligned with the corridor's length.
• Figure 3: Decomposition of the surface current on a cylinder either electric or magnetic into its axial component $J_{\mathrm{z}}$ or $M_{\mathrm{z}}$ and its circumferential component $J_{\mathrm{\phi}}$ or $M_{\mathrm{\phi}}$.
• Figure 4: Amplitude distribution of $\mathbf w$ along the longitudinal direction of a cylindrical surface of radius 1 m and length 10 m when $\hat{\boldsymbol e} = \hat{\boldsymbol z}$. $P_0 = 1~{\mathrm{W}}$. The focal point optimized lies at $\boldsymbol r_\mathrm{f} = \boldsymbol0$ with $z$-polarization. $\mathrm{A1}$ denotes Algorithm 1.
• Figure 5: Normalized co-polarized electric field $E_{\mathrm{z}}$ optimization result for a cylindrical surface of radius 1 $\mathrm{m}$ and length 10 $\mathrm{m}$ as well as the normalized focusing field for point-source \ref{['kernel']} and Hertzian-dipole \ref{['kernel_vector']}, including the 1D normalized focal gain along the $z$-axis. The focal point lies at $\boldsymbol r_\mathrm{f}=\boldsymbol0$ with $z$-polarization. The 2D cut figure is along the $x$ axis and is symmetric with respect to both $x$ and $z$. "Point" follows \ref{['kernel']}, while "Dipole" follows \ref{['kernel_vector']} for $\vartheta = 90^\circ$. The 3-dB boundary (white ring) corresponds to the half-power region, equivalently, it is the $1/\sqrt{2}$-amplitude contour shown as the dashed line in the 2D cut.