It is shown that a three-fluid model, which was successfully introduced to explain microwave characteristics of high-Tc superconductors phenomenologically, is suit also to explain those of low-Tc superconductors. In this model, the two contributions of a residual normal electron, in addition to a super and a normal electron in the two-fluid model, and of the temperature (T) dependence of momentum relaxation time τ for the two normal electrons are taken into account. Measured results of the T dependence of surface resistance Rs for a Nb film with critical temperature Tc9.2K agree very well with an Rs curve calculated using the present model, where a residual surface resistance at T0K, Rso, and the T dependence of τ were determined using the surface reactance at 0K Xso37.6mΩ calculated using the BCS theory to fit a calculated Rs curve with the measured values as a function of T. Furthermore, microwave characteristics predicted from the BCS theory cannot be explained phenomenologically using the conventional two-fluid model. This difficulty can be solved by using an improved two-fluid model, called the two-fluid (τ) model, where the T dependence of τ is taken into account. Finally the frequency dependence of Rs calculated for the Nb film is f1.9 for the BCS theory and f2.0 for the three-fluid (τ) model on the assumption of the frequency independence of τ.

In this paper, we applied the circuit synthesis theory of filters to the design of transmission-type metasurface cells and arbitrarily designed the amplitude and phase of the transmission and reflection by adjusting the resonant frequency and coupling coefficient. In addition, we successfully designed the phase of the unit cell by using the frequency conversion of filter theory. Moreover, we designed a refractive transmission-type metasurface plate with a novel cell structure that reacts to both polarizations. The prototype operated at the desired refraction angle, confirming the design theory.