In the search for improved computational capabilities, conventional microelectronic computers are facing various problems arising from the miniaturization and concentration of active electronics. Therefore, researchers have explored wave systems, such as photonic or quantum devices, for solving mathematical problems at higher speeds and larger capacities. However, previous devices have not fully exploited the linearity of the wave equation, which as we show here, allows for the simultaneous parallel solution of several independent mathematical problems within the same device. Here we demonstrate that a transmissive cavity filled with a judiciously tailored dielectric distribution and embedded in a multi-frequency feedback loop can calculate the solutions of a number of mathematical problems simultaneously. We design, build, and test a computing structure at microwave frequencies that solves two independent integral equations with any two arbitrary inputs and also provide numerical results for the calculation of the inverse of four 5 x 5 matrices.

The process of diffusion is central to the ever increasing entropic state of the universe and is fundamental in many branches of science and engineering. Although non-reciprocal metamaterials are well developed for wave systems, the studies of diffusive metamaterials have been limited by their characteristic spatial inversion symmetry and time inversion antisymmetry. Here, we achieve large spatial asymmetric diffusion characteristics inside a metamaterial whose material parameters are space- and time-modulated. Inside such a spatiotemporal metamaterial, diffusion occurs as if the material had an intrinsic flow velocity, whose direction is dictated by the relative phase between the modulations of the conductivity and capacity. This creates dramatic out-of-equilibrium concentrations and depletions, which we demonstrate experimentally for the diffusion of electric charges in a one-dimensional electrical system composed of an array of space-time-modulated variable capacitors and switches. These results may offer exciting possibilities in various fields, including electronics, thermal management, chemical mixing, etc.

In this Letter, we explore the dispersion of spoof surface plasmons supported by a single-layer glide-symmetric structure. This structure consists of an infinitely long double-notched slot perforated in a metal layer. The presence of a degeneracy of the two lowest-order modes at the Brillouin zone boundary, which have non-zero group velocity is explained and experimentally demonstrated. Further, the dependence of the band structure when glide-symmetric configuration is broken is also explored.

Geodesic lenses are a compelling alternative to traditional planar dielectric lens antennas, as they are low loss and can be manufactured with a simple mechanical design. However, a general approach for the design and analysis of more advanced geodesic lens antennas has been elusive, limiting the available tools to rotationally symmetric surfaces. In this paper, we present a fast and efficient implementation built on geometrical optics and scalar diffraction theory. A numerical calculation of the shortest ray path (geodesic) using an open-source library helps quantify the phase of the electric field in the lens aperture, while the amplitude is evaluated applying ray-tube power conservation theory. The Kirchhoff-Fresnel diffraction formula is then employed to compute the far-field of the lens antenna. This approach is validated by comparing the radiation patterns of a transversely compressed geodesic Luneburg lens (elliptical base instead of circular) with the ones computed using commercial full-wave simulators, demonstrating a substantial reduction in computational resources. The proposed method is then used in combination with an optimization procedure to study possible compact alternatives of the geodesic Luneburg lens with size reduction in both the transverse and vertical directions.

In this letter, we demonstrate that the dispersion properties associated with glide symmetry can be achieved in systems that only possess reflection symmetry by balancing the influence of two sublattices. We apply this approach to a pair of coupled slots cut into an infinite perfectly conducting plane. Each slot is notched on either edge, with the complete two-slot system having only mirror symmetry. By modifying the relative size of the notches on either side of the slots, we show that a linear dispersion relation with a degeneracy with non-zero group velocity at the Brillouin zone boundary can be achieved. These properties, until now, only found in systems with glide symmetry are numerically and experimentally validated. We also show that these results can be used for the design of ultra-wideband one-dimensional leaky wave antennas in coplanar waveguide technology.

The authors present a computationally efficient technique for the analysis of extraordinary transmission through both infinite and truncated periodic arrays of slots in perfect conductor screens of negligible thickness. An integral equation is obtained for the tangential electric field in the slots both in the infinite case and in the truncated case. The unknown functions are expressed as linear combinations of known basis functions, and the unknown weight coefficients are determined by means of Galerkin's method. The coefficients of Galerkin's matrix are obtained in the spatial domain in terms of double finite integrals containing the Green's functions (which, in the infinite case, is efficiently computed by means of Ewald's method) times cross-correlations between both the basis functions and their divergences. The computation in the spatial domain is an efficient alternative to the direct computation in the spectral domain since this latter approach involves the determination of either slowly convergent double infinite summations (infinite case) or slowly convergent double infinite integrals (truncated case). The results obtained are validated by means of commercial software, and it is found that the integral equation technique presented in this paper is at least two orders of magnitude faster than commercial software for a similar accuracy. It is also shown that the phenomena related to periodicity such as extraordinary transmission and Wood's anomaly start to appear in the truncated case for arrays with more than 100 $(10\times 10)$ slots.