Antireflection temporal coatings

It is known that complete transmission of waves through the interface between two different media can be achieved by proper impedance matching between them. One of the most common techniques for such reflectionless propagation is the quarter-wave impedance transformer, where an additional slab of material with proper material parameters and carefully engineered dimensions is added between the two media, minimizing reflections. Metamaterials, with properly designed spatial inhomogeneity, have exhibited unprecedented ability to tailor and manipulate waves, and recently temporal metamaterials have also gained much attention, enabling spatiotemporal control of wave propagation. Here a temporal analogue of the quarter-wave impedance transformer technique, which we name “antireflection temporal coating,” is proposed using time-dependent materials. The proposed technique is demonstrated, analytically and numerically, using metamaterials with a time-dependent permittivity. Comparison with the conventional (spatial) impedance-matching technique is shown, demonstrating that both impedance matching and frequency conversion are achieved with our proposed temporal version. As an illustrative example, the present technique is also applied to match two waveguides with different cross sections, demonstrating an example of scenarios where it may be applied.