Propagation of electromagnetic waves in spatially modulated Josephson junctions

The propagation of small amplitude (linear) electromagnetic waves in periodically spatially modulated finite Josephson junctions is studied using the transfer matrix approach. The transmittance of a finite length Josephson junction with thick, identical, periodic defects is presented. The linear wave spectrum consists of pass- and stop-bands, whose width may vary with the geometrical and/or the physical parameters of the junction. The band boundaries as a function of several junction parameters are also presented, and the possibility of creating mid-gap states of finite transmittance within the gaps by slightly disturbing the periodicity is demonstrated. The dependence of the plasma frequency on the parameters of the junction is also calculated using, several simple approaches. The possibility of applying this approach to phi-junctions is briefly discussed. The knowledge of the mode spectrum may be useful in constructing elements of nonlinear systems for development of tunable superconducting resonators. It can also be useful in calculating the resonance voltages appearing in the current-voltage characteristics of a long periodically defected Josephson junction in a magnetic field, as proposed by Fistul et al.