Power transport theorem (PTT) governing the transport process of the power-flow passing through waveguide is derived. The input power as the source term in PTT is found to be the one for sustaining a stationary power transport, and the corresponding input power operator (IPO) is formulated. The travelling-wave condition satisfied by the travelling-wave modes one-directionally propagating along the waveguide is introduced as a counterpart of the famous Sommerfeldâ€™s radiation condition satisfied by the radiative fields distributing in far zone. Employing the travelling-wave condition and some other necessary conditions, the dependent currents in IPO are effectively eliminated. Under PTT framework, the recently developed decoupling mode theory (DMT) for 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 orthogonalizing the IPO with only independent current, and any two different DMs donâ€™t have net energy exchange in an integral period. The PTT-DMT is an effective alternative for classical eigen-mode theory. The alternative realizes an effective unification for waveguide-oriented modal analysis theory and antenna-oriented modal analysis theory, such that the theories can be easily integrated into a single theory for whole waveguide-antenna combined system in the future.