FISKE MODES IN ONE-DIMENSIONAL PARALLEL JOSEPHSON-JUNCTION ARRAYS

We have performed measurements on one-dimensional (1D) arrays of under damped Josephson junctions connected in parallel by superconducting wi res which in a magnetic field show resonances in the current-voltage c haracteristics. From analytical calculations, we find that the positio n of the steps is determined by the dispersion relation omega(k) of a ID discrete, linear transmission line, where the Josephson junction ha s been replaced by the capacitor and the resistance of the junction. W hen nearest-neighbor inductances are accounted for, the model agrees w ell with the measured positions of the steps. Numerical calculations o f the full dynamics with inclusion of inductances between all cells su pport our model. As an example of a system with a more complicated dis persion, we have measured 1D arrays with two different junctions per p rimitive cell. The measured dispersion relation shows an acoustic and an optical branch in agreement with numerical simulations of the full dynamics.