Abstract :
The conventional treatment of propagation coefficients in lossy periodic waveguides suffers from certain major defects. It gives no information about the effects of the losses on the phase-change coefficient, it breaks down when the frequency approaches the edge of a pass-band from within and it does not work at all in a stop-band. A new treatment is described which removes all these defects. It is based on the following result: the propagation coefficient of a mode in a lossy guide at the frequency ¿ is equal to the propagation coefficient of the corresponding mode in the lossless guide at the frequency ¿(1 ¿ j/2Qc). Here, Qc is the ¿complex Q-factor¿ of the mode at the frequency ¿. It is given by an explicit formula which holds good at all frequencies when the losses are small. When ¿ lies within a pass-band Qc is equal to ¿ times the mean energy stored in a period of the guide divided by the complex power dissipated in the same period. When ¿ lies in a stop-band Qc is equal to the analytic continuation of its values in the pass-bands.
