Perfectly Matched Metamaterials

TL;DR

The paper introduces Perfectly Matched Metamaterials (PMMs), a class of passive, inhomogeneous media that perform purely refractive, reflectionless field transformations using anisotropic unit cells without coordinate mappings. By enforcing all-angle impedance matching, PMMs achieve broadband, true-time-delay–like field control, with analytic parameterizations that reduce design to a few degrees of freedom in reciprocal media. The authors derive simple, closed-form relationships for unit-cell parameters, and validate the approach with broadband beam-collimator designs operating from $5$ to $30$ GHz that maintain high efficiency and tolerate source shifts. PMMs are contrasted with Transformation Optics and Perfectly Matched Layers, highlighting their discrete, inverse-design–friendly, lossless nature and potential for broadband beamforming and analog computing applications.

Abstract

Fully harnessing the vast design space enabled by metamaterials to control electromagnetic (EM) fields remains an open problem for researchers. Inverse-design techniques have shown to best exploit the degrees of freedom available in design, resulting in high-performing systems for wireless communications, sensing and analog signal processing. Nonetheless, fundamental yet powerful properties of metamaterials are still to be revealed. In this paper, we introduce the concept of Perfectly Matched Metamaterials (PMMs). PMMs are passive, inhomogeneous media that perform purely refractive field transformations under different excitations. Their advantage lies in their simplicity, reflectionless behavior and suitability for both analytical and numerical design methods. Unlike Transformation Optics, PMM-based designs are devoid of coordinate transformations. Anisotropic unit cells are configured to control EM fields in a true-time delay manner. Simple analytical designs are reported which demonstrate the broadband capability of PMM devices. Proposed PMMs may find application in wideband beamforming and analog computing, realizing functionalities such as spatial filtering and signal pre-processing.

Figures (9)

• Figure 1: Representation of reflectionless field transformation (beam-collimator) using Perfectly Matched Metamaterials (PMMs). Blue lines symbolize the purely-refractive field progression, which combines with the independent control of Poynting vector $\boldsymbol{S}$ (power) and wavevector $\boldsymbol{k}$ (phase). The transformation region is formed from anisotropic unit cells with the material parameters given in \ref{['eq:pm_media_genEpsMu']}. Unit cells have a size $d \ll \lambda$, where $\lambda$ is the free-space wavelength.
• Figure 2: Time snapshot of $E_z$ for a plane wave propagating across multiple perfectly matched media. The material parameters for each medium are provided in Table \ref{['table:mu_eps_multilayer']}. Note that each medium is reciprocal, i.e., $\mu_{xy}=\mu_{yx}$.
• Figure 3: Representation of fields, wavevector $\boldsymbol{k}$ and Poynting vector $\boldsymbol{S}$ in a magnetically, anisotropic unit cell. Since the permeability is a tensor, the magnetic flux density $\boldsymbol{B}$ and magnetic field intensity $\boldsymbol{H}$ may not be parallel.
• Figure 4: Representation of design procedure and beam-collimator performance. (a) The input and output power density profiles are discretized into the same number of power points. These points are connected through straight lines, whose direction dictates $\kappa$ in each unit cell. In the inset, the black line represents the closest line to the unit cell's center, while the gray lines represent other lines passing through the cell (see the Supplemental Material Ruiz:2024_PMM_SupplMaterial). (b) The local phase progression follows a linear evolution from input to output along each $x$-directed row of cells. The inset shows the wavenumbers at the boundaries of each unit cell, whose average provides $k_x$ and $k_y$ (see the Supplemental Material Ruiz:2024_PMM_SupplMaterial).
• Figure 5: Desired and simulated power density and phase profiles at input and output interfaces of the transformation region at 10 GHz.