Wave Propagation in Lossy and Superconducting Circular Waveguides

We present an accurate approach to compute the attenuation of waves, propagating in circular wave-guides with lossy and superconducting walls. A set of transcendental equation is developed by matching the fields at the surface of the wall with the electrical properties of the wall material. The propagation constant k(z) is found by numerically solving for the root of the equation. The complex conductivity of the superconductor is obtained from the Mattis-Bardeen equations. We have compared the loss of TE11 mode computed using our technique with that using the perturbation and Stratton's methods. The results from the three methods agree very well at a reasonable range of frequencies above the cutoff. The curves, however, deviate below cutoff and at millimeter wave frequencies. We attribute the discrepancies to the dispersive effect and the presence of the longitudinal fields in a lossy waveguide. At frequencies below the gap, the superconducting waveguide exhibits lossless transmission behavior. Above the gap frequency, Cooper-pair breaking becomes dominant and the loss increases significantly.