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The energetic characteristics of cylindrical medium-free time-domain waveguide fields are solved within the framework of the evolutionary approach to electromagnetics. Solving the boundary-eigenvalue problem for transverse Laplacian yields a configurational basis in the waveguide cross section. Elements of the basis depend on transverse coordinates, whereas the modal amplitudes depend on the longitudinal coordinate, z, and time, t . Solving the resulted Klein–Gordon equation yields a basis for analysis of the modal amplitudes. Exact solutions for the amplitudes of TE-modes are obtained, and the energetic field characteristics are derived in accordance with the causality principle.

Study of the energetic field characteristics of the TE-modalwaves in waveguides