Generalized modal expansion and reduced modal representation of 3-D electromagnetic fields

A generalized modal expansion theory for investigating arbitrary 3-D bounded and unbounded electromagnetic fields is presented. When an inhomogeneity is enclosed with impenetrable boundaries, the field excited by arbitrary sources is expanded with a complete set of eigenmodes, which are classified into trapped modes and radiation modes. As the boundaries tend to infinity, trapped modes remain unchanged, while radiation modes form a continuum. To illustrate the theory, several real-life structures are investigated with a conformal finite-difference technique in the frequency domain. Perfectly matched layers (PMLs) are imposed at finite extent to emulate the unbounded problems. Numerical examples show that, only a few system modes are prominent in expanding an excited field, leading to a reduced modal picture which provides a quick guidance as well as useful physical insight for engineering design and optimization of electromagnetic devices and components.