Energy considerations in open and closed waveguides

Energy relations derived for a lossless, closed uniform and periodic structure show that the total complex Poynting vector integrated over the cross section is identically zero for the case of an arbitrary complex wave. These results are also applicable to open structures provided certain conditions are satisfied. The application of these results in the field of leaky wave antennas is discussed. Two illustrative examples, those of the sinusoidally modulated reactance surface and the sheath helix, are worked out. It is shown that although the slope of the curve can no longer be associated with the direction of net power flows the knowledge of the slope may still be helpful in selecting certain modes for representing a given source.