To See a World in a Grain of Sand: From WET-CMT to ETT-DMT to MTT-DMT to AMTT-DMT

Some commonly used electromagnetic (EM) modal analysis theories are simply reviewed. The theories include the classical Sturm–Liouville eigen-mode theory (SL-EMT), the scattering matrix (SM)-based and integral equation (IE)-based characteristic mode theories (CMTs) for scatterers, the work-energy theorem (WET)-based CMTs for scatterers and lumped-port-driven structures, and the energy transport theorem (ETT)-based decoupling mode theory (DMT) for wave-port-fed structures. The applicable scopes and evolution progress of the theories are emphasized, and the core physical principles and mathematical formulas related to the ETT-based DMT (ETT-DMT) for wave-port-fed metallic transmitting antennas are given. Inspired by the evolution progress from the WET-based CMT (WET-CMT) to ETT-DMT and the principles and formulas of ETT-DMT, this paper focuses on proposing two novel modal analysis theories: the momentum transport theorem (MTT)-based and angular-momentum transport theorem (AMTT)-based DMTs for wave-port-fed metallic transmitting antennas. The engineering applications for the MTT-based DMT (MTT-DMT) and the AMTT-based DMT (AMTT-DMT) will be provided in our future papers. By outlining the evolution progress from WET-CMT to ETT-DMT to MTT-DMT to AMTT-DMT, this paper displays how to see a world in a grain of sand.