Attenuation in Superconducting Rectangular Waveguides

We present an accurate analysis on the attenuation of waves, propagating in rectangular waveguides with superconducting walls. The wavenumbers k_x and k_y in the x and y directions, respectively, are first obtained as roots of a set of transcendental equations developed by matching the tangential fields at the surface of the wall with the electrical properties of the wall material. The complex conductivity of the superconducting waveguide is obtained from the extended Mattis-Bardeen theory. The propagation constant k_z is found by substituting the values of k_x and k_y into the dispersion relation. We have computed and compared the loss in the waveguides below and above the critical temperature. At frequencies above the cutoff frequency f_c but below the gap frequency f_g, the loss in the superconducting waveguide is significantly lower than that in a normal conducting waveguide. Above the gap frequency, however, the result indicates that the attenuation in the waveguide below the critical temperature is higher than that at room temperature. We attribute the higher loss as due to the higher surface resistance and field penetration for superconducting waveguides operating above the gap frequency.