Gain and One-Way Propagation in Synthetically Moving non-Foster Gratings

In this paper, we analyze the electromagnetic properties of space-time grooved metal surfaces governed by uniform-velocity modulations. We begin by deriving the electromagnetic fields of a uniform-velocity-modulated parallel-plate waveguide (PPW) using Lorentz transformations, establishing it as the fundamental building block of a more complex space-time structures. We then analyze the dispersion and scattering characteristics of a space-time grooved surface and later extend the study to the interaction between two facing surfaces. Our findings show that these systems can indeed amplify electromagnetic waves and exhibit non-reciprocal as well as non-Foster behavior. Moreover, under specific conditions, they enable the formation of unidirectional propagation channels, effectively constraining light to be guided along a single direction. These results unveil new opportunities for the design of advanced electromagnetic and photonic devices.