Power Transport Theorem (PTT)-Based Decoupling Mode Theory (DMT) for Wave-Guiding Structures

Abstract

Power transport theorem (PTT) governing the transport process of the power-flow passing through waveguide is derived. Input power as the source term in PTT is found to be the one for sustaining the steady power transport, and the corresponding input power operator (IPO) is formulated. Travelling-wave condition satisfied by the travelling-wave modes one-directionally propagating along the waveguide is introduced as a counterpart of the famous Sommerfeld’s radiation condition satisfied by the radiative fields distributing in the far zone. Using the travelling-wave condition and some other necessary conditions, the dependent currents in IPO are effectively eliminated. Under the PTT framework, the recently developed decoupling mode theory (DMT) for the wave-port-fed antennas is further generalized to waveguides. The PTT-based DMT (PTT-DMT) focuses on constructing a set of energy-decoupled modes (DMs) for any pre-selected objective waveguide by diagonalizing the IPO with only independent current, and any two different DMs do not have net energy exchange in an integral period. The PTT-DMT is an effective alternative for the classical eigen-mode theory. The alternative realizes an effective unification for the waveguide-oriented modal analysis theory and the antenna-oriented modal analysis theory, such that the theories can be easily integrated into a single theory for the whole waveguide-antenna combined system in the future.