Frequency analysis of the dielectric constant of YBa2Cu3O7 Josephson junctions fabricated on bicrystalline substrates

We have studied the electromagnetic parameters of $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ Josephson junctions fabricated on bicrystalline substrates with different angles tilted around the [100] and [001] axis. Changing a technological parameter such as the junction width permits change to the resonant frequency of the barrier cavity. This change in the resonance frequency allows one to determine a frequency dependent dispersion relation of the dielectric constant $\ensuremath{\epsilon}(\ensuremath{\omega})$. We have explored the proximity to a resonance in the dielectric response and analyzed its resonance frequency and damping constant. In terms of a $RLC$ circuital equivalence additional information on the inductive response is presented as a comparative study of junctions fabricated on substrates with different bicrystalline misorientations.