Theory of Periodic Sequence: A Generalized Formalism of Maxwell's Equations in Discrete Transform Domain

Abstract

Time-periodic form or expression is commonly observed in both natural and man-made phenomena across a wide range of scientific and engineering disciplines. In this article, we propose the theory of periodic sequence (TPS), marking the first effort to mathematically formalize Maxwell's equations in the discrete transform domain (corresponding to time domain) and to legitimize the application of the discrete Fourier transform to the temporal aspect of Maxwell's equation. TPS is intended to serve as a comprehensive theory to depict the physical behavior of electromagnetic (EM) periodic sequential fields and waves. Within the TPS framework, periodic-sequential Maxwell's curl equations are decomposed and decoupled to independent and paralleled instances via designated mappings. The fundamental solutions of EM periodic sequential excitation are elucidated and corroborated by radio-frequency (RF)/microwave measurements. This involves potential applications in the analysis of broadband RF transmission and the design of high-speed RF devices.