Generalized Eigenvalue Problem for Spatially Discrete Traveling-Wave-Modulated Circuit Networks

Space-time-modulated electromagnetic structures have become a topic of significant research interest due to their frequency-converting, amplifying, and nonreciprocal properties. In particular, traveling-wave modulation (TWM) is of interest due to its simplicity. Often, TWM is realized by applying staggered time-modulation signals to a discrete array of unit cells. This modulation is referred to as spatially discrete TWM (SDTWM), and the constituent unit cells are called stixels: space-time pixels. Recently, a boundary condition referred to as the interpath relation was derived that relates the field in neighboring stixels. In this article, the interpath relation is applied to SDTWM electrical networks to obtain a generalized eigenvalue problem that can be used to efficiently simulate a cascade of SDTWM stixels. The proposed eigenmode analysis technique is used to simulate three representative SDTWM structures designed to support frequency conversion, parametric amplification, and nonreciprocal propagation. While currently available techniques would require an entire spatial period (or even the whole cascade) to be simulated simultaneously, the presented technique relies only on a single stixel.