Electromagnetic-Power-based Modal Classification, Modal Expansion, and Modal Decomposition for Perfect Electric Conductors

Traditionally, all working modes of a perfect electric conductor are classified into capacitive modes, resonant modes, and inductive modes, and the resonant modes are further classified into internal resonant modes and external resonant modes. In this paper, the capacitive modes are further classified into intrinsically capacitive modes and non-intrinsically capacitive modes; the resonant modes are alternatively classified into intrinsically resonant modes and non-intrinsically resonant modes, and the intrinsically resonant modes are further classified into non-radiative intrinsically resonant modes and radiative intrinsically resonant modes; the inductive modes are further classified into intrinsically inductive modes and non-intrinsically inductive modes. Based on the modal expansion corresponding to these new modal classifications, an alternative modal decomposition method is proposed. In addition, it is also proved that: all intrinsically resonant modes and all non-radiative intrinsically resonant modes constitute linear spaces respectively, but other kinds of resonant modes cannot constitute linear spaces; by including the mode 0 into the intrinsically capacitive mode set and the intrinsically inductive mode set, these two modal sets become linear spaces respectively, but other kinds of capacitive modes and inductive modes cannot constitute linear spaces.