Energy-Viewpoint-Based Electromagnetic Modal Analysis

This is the authors' abstract. We don't add key points for this paper.

In computational physics and mathematical physics, modal analysis method has been one of important study topics. The central purposes of this Post-Doctoral Concluding Report are (1) to reveal the core position of energy viewpoint in the realm of electromagnetic modal analysis; (2) to show how to do energy-viewpoint-based modal analysis for various electromagnetic structures. The major conclusions of this report are that: energy conservation law governs the energy utilization processes of various electromagnetic structures, and its energy source term sustains the steady energy utilization processes; the whole modal space of an electromagnetic structure is spanned by a series of energy-decoupled modes (DMs), which don't have net energy exchange in any integral period; the DMs can be effectively constructed by orthogonalizing energy source operator, which is just the operator form of the energy source term. Specifically speaking: in classical electromagnetism, energy conservation law has five different manifestation forms, that are power transport theorem (PTT), partial-structure-oriented work-energy theorem (PS-WET), entire-structure-oriented work-energy theorem (ES-WET), Poynting's theorem (PtT), and Lorentz's reciprocity theorem (LRT) forms; the energy source terms in the first four forms are formulated as input power operator (IPO), partial-structure-oriented driving power operator (PS-DPO), entire-structure-oriented driving power operator (ES-DPO), and Poynting's flux operator (PtFO); the DMs of wave-port-fed, lumped-port-driven, externally-incident-field-driven, and energy-dissipating/self-oscillating electromagnetic structures can be constructed by orthogonalizing IPO, PS-DPO, ES-DPO, and PtFO; LRT guarantees that the obtained DMs satisfy some useful Em-Hn orthogonality relations, where the Em and Hn represent the electric field of the m-th DM and the magnetic field of the n-th DM.