Microwave transmission through films of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$

We report measurements of the magnitude and phase of microwave transmission through thin films (1 μm) of the 90-K superconductor $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ on ${\mathrm{Al}}_2$${\mathrm{O}}_3$, MgO, and Zr${\mathrm{O}}_2$ substrates. Real and imaginary parts of the conductivity, ${\sigma }_1$ and ${\sigma }_2$, were evaluated from the measurements by comparing with a calculation of the transmission for our experimental configuration. Both parts of the conductivity show qualitative agreement with Bardeen-Cooper-Schrieffer type conductivities. From ${\sigma }_1$ we find a range of gap values $\frac{2\Delta }{k_B{T}_c}=1.3\mathrm{} \mathrm{to} 6.5$. From the measured ${\sigma }_1$ the magnetic penetration depth can be evaluated.