Energy Functionals and Variational Principle in Electromagnetic Modal Analysis-Part I: Diagonalizing Input Power Operator Method Revisited

The energy transport theorem (ETT)-based decoupling mode theory (DMT) uses diagonalizing input power operator (IPO) method to calculate the energy-decoupled modes (DMs) of wave-port-fed transmitting antennas. This paper focuses on examining the rationality of the method. To examine the rationality, a set of energy functionals involved in the wave-port-fed energy-transmitting problem are proposed. It is proved that: 1) the physical laws-Maxwell equations and boundary conditions-used to govern classical electrodynamics can be derived from the energy functionals by using variational principle; 2) the energy functionals are equivalent to the input power (or its complex conjugation) in physical essence; 3) the DMs derived from the diagonalizing IPO method can diagonalize both the input power and energy functionals simultaneously. The above conclusions clearly reveal the rationality of using diagonalizing IPO method to calculate DMs.