Toroidal metasurface resonances in microwave waveguides

We theoretically investigate the possibility to load microwave waveguides with dielectric particle arrays that emulate the properties of infinite, two-dimensional, all-dielectric metasurfaces. First, we study the scattering properties and the electric and magnetic multipole modes of dielectric cuboids and identify the conditions for the excitation of the so-called anapole state. Based on the obtained results, we design metasurfaces composed of a square lattice of dielectric cuboids, which exhibit strong toroidal resonances. Then, three standard microwave waveguide types, namely parallel-plate waveguides, rectangular waveguides, and microstrip lines, loaded with dielectric cuboids are designed, in such a way that they exhibit the same resonant features as the equivalent dielectric metasurface. The analysis shows that parallel-plate and rectangular waveguides can almost perfectly reproduce the metasurface properties at the resonant frequency. The main attributes of such resonances are also observed in the case of a standard impedance-matched microstrip line, which is loaded with only a small number of dielectric particles. The results demonstrate the potential for a novel paradigm in the design of "metasurface-loaded" microwave waveguides, either as functional elements in microwave circuitry, or as a platform for the experimental study of the properties of dielectric metasurfaces.