Nonlinear Self-Coupling of Josephson Radiation in Superconducting Tunnel Junctions

A study is made of the nonlinear feedback of the ac tunnelling current (first pointed out by Josephson) in a superconducting tunnel junction via the electromagnetic fields radiated by the current into the resonantmode structure of the junction. The junction operating point is investigated, and a calculation is made of the dc current drawn by a strongly self-coupled fundamental mode together with weakly self-coupled harmonic modes. Attention is directed to the frequency dependence of the tunneling-current amplitudes reported briefly by Riedel, as tentative explanation of the bumps in current-voltage characteristics which have been observed at $eV=\frac{2\Delta }{\left(\mathrm{integer}\right)}$, where $2\Delta$ is the energy gap.