Measurement of the Far Infrared Magneto-Conductivity Tensor of Superconducting YBa$_2$Cu$_3$O$_{7-δ}$ Thin Films

We report measurements of the far infrared transmission of superconducting YBa$_2$Cu$_3$O$_{7-\delta }$ thin films from 5 cm$^{-1}$ to 200 cm$^{-1}$ in fields up to 14$T$. A Kramers-Kronig analysis of the magneto-transmission spectrum yields the magneto-conductivity tensor. The result shows that the magneto-conductivity of YBa$_2$Cu$_3$O$_{7-\delta }$ is dominated by three terms: a London term, a low frequency Lorentzian ($\omega _1\approx $ 3 cm$% ^{-1}$) of width $\Gamma _1=$ 10 cm$^{-1}$ and a finite frequency Lorentzian of width $\Gamma _2=$ 17 cm$^{-1}$ at $\omega _2=$ 24 cm$^{-1}$ in the hole cyclotron resonance active mode of circular polarization.\\