Leaky-Wave Antenna Analysis using Multi-Modal Network Theory with Open Periodic Boundaries

This paper introduces two methods for analyzing periodic leaky-wave antennas (LWAs) within a new framework denoted as multi-modal network theory (MNT) with open periodic boundaries (OPBs). The approach is hybrid, combining analytical techniques with a commercial full-wave solver. The first method computes the dispersion diagram of periodic LWAs. It is iterative and relies on the full-wave simulation of a single unit-cell of a LWA, coupled with the analytical solution of an eigenvalue problem. This method effectively captures both the phase and attenuation constants of periodic LWAs while using fewer modes than previous methods with commercial frequency-domain solvers. The method is validated by computing the dispersion of classic LWA unit-cells and comparing them to those obtained through full-wave simulations of the full-length antenna and other state-of-the-art methods. The second, also based on OPB-MNT, focuses on LWA analysis in reception. Specifically, it determines the response of a unit-cell to an incident plane wave. To validate this method, we compute the response of LWA with different unit-cell designs. By comparing these results with the corresponding dispersion analysis, we show that the receiving case and the eigenvalue problem are related but not simply time-reversed versions of each other.