Theory and experiment on electromagnetic-wave-propagation velocities in stacked superconducting tunnel structures

Characteristic velocities of the electromagnetic waves propagating in vertically stacked Josephson transmission are theoretically discussed. An equation for solving n velocities of the waves in an n Josephson-junction stack is derived. The solutions of two- and threefold stacks are especially focused on. Furthermore, under the assumption that all parameters of the layers are equal, analytic solutions for a generic N-fold stack are presented. The velocities of the waves in two- and three-junction stacks by Nb-Al-${\mathrm{AlO}}_{\mathit{x}}$-Nb systems are experimentally obtained by measuring the cavity resonance (Fiske step) modes. Comparison of the theory with the experimental data reveals good quantitative agreement.