Electromagnetic Energy Theorems and the Energy-Viewpoint-Based Modal Analysis Theories

The energy conservation law (ECL) is one of the most fundamental physical laws in the nature. The ECL has some different manifestation forms. The various manifestation forms can be mathematically expressed in terms of the corresponding energy theorems. The various energy theorems govern the energy utilization mechanisms of the corresponding physical phenomena. This paper simply reviews some important electromagnetic energy theorems, such as the entire-structure-oriented work-energy theorem (ES-WET), the partial-structure-oriented work-energy theorem (PS-WET), the energy transport theorem (ETT), the Poynting theorem, the Rayleigh-Carson reciprocity theorem (RT), the Rumsey RT, the Lorentz RT, and the Parseval theorem. The ES-WET governs the energy-scattering phenomenon; the PS-WET governs the lumped-port-driven energy-transmitting phenomenon; the ETT governs the wave-port-fed energy-transmitting phenomenon; the Poynting theorem governs the energy-absorbing phenomenon; the RTs govern the energy-coupling phenomenon; the Parseval theorem guarantees the energy invariance in the time domain, frequency domain, and spectrum domain. This paper simply summarizes some valuable energy-viewpoint-based modal analysis theories, such as the ES-WET-based characteristic mode theory (CMT) for energy-scattering phenomenon, the PS-WET-based CMT for lumped-port-driven energy-transmitting phenomenon, the ETT-based decoupling mode theory (DMT) for wave-port-fed energy-transmitting phenomenon, and the Poynting-theorem-based DMT for energy-absorbing phenomenon.