R.F. self-field depression of microwave induced currents steps in Josephson tunnel junction

This paper reports that experimentally observed amplitudes of microwave induced steps in Josephson tunnel junctions are significantly reduced respect to the predictions of a simple model developed for a junction that is small respect to the Josephson penetration depth and radiation wavelength. In this approximation the amplitude of the n-th step in the critical current units (the reduced units will be used throughout the paper) is: ln = Jn(γb); γb = nvrf/Vn; Vn = (h/4πe)ωrn, where Jn (γ) is the Bessel function of the order n, ωrf radiation frequency and Vrf that amplitude of the r.f. signal. We will refer to this as the Bessel model. In resonant junctions the spatial variations of the microwave voltage in the barrier cannot be neglected. Pech and Sain-Michel considered the resonant junction irradiated at the frequency at which the half wavelength of the incident radiation matches the junction length (L = λ /2). Recently Costabile at al have solved the perturbed Sine-Gordon equation in the single mode approximation obtaining for the step height at the finite value of the standing wave ratio (SWR) and the intermediate junction length we will referred to this approximation as the SWR model