Electromagnetic Transverse Modes in Periodic Structures: Mathematical Analysis and Engineering Applications

Abstract

This study explores the electromagnetic transverse modes in periodic structures, combining mathematical analysis with practical engineering applications. We showcase how the deliberate arrangement of materials, using Maxwell's equations and Bloch's theorem, may control and guide electromagnetic waves for novel applications in devices. We emphasize the progress made in photonic crystals and metamaterials, which have resulted in significant developments in fields such as optical computing and stealth technologies. The debate encompasses the potential of computational methods to further improve the functions of materials and devices. This paper highlights the important interaction between theoretical physics and applied engineering, which lays the foundation for future technical advancements in wave manipulation.