Harmonic engineering of antennas with time-periodic substrate permittivity

Microstrip patch antennas are one of the most widely used antennas in communication systems due to their compact size, conformability, ease of implementation, and low cost. The cavity model, which assumes that a microstrip patch antenna is surrounded by four perfect magnetic conducting (PMC) walls on its periphery and perfect electric conducting (PEC) boundaries on the top (patch) and bottom (ground plane), is a well-established analytical method to evaluate its radiated fields and input impedance. In this paper, we extend the traditional cavity model approach to include the response of a microstrip patch antenna with a time-periodic substrate permittivity ${\ensuremath{\epsilon}}_{r}(t)={\ensuremath{\epsilon}}_{r}(t+T)$. We show that this time-periodic permittivity modulation provides an unprecedented ability to tailor the harmonic response of the antenna. Importantly, we achieve a remarkable 40% fractional bandwidth through such a customized time-periodic permittivity modulation, which is substantially higher than the typical 1--2% fractional bandwidth of conventional microstrip patch antennas.