Nonlinear microwave impedance of short and long Josephson junctions

The nonlinear dependence on applied ac field (bv) or current (iv) of the microwave ~ac! impedance Rv 1iXv of both short and long Josephson junctions is calculated under a variety of excitation conditions. The dependence on the junction width is studied, for both field symmetric ~current antisymmetric! and field antisymmetric ~current symmetric! excitation configurations. The resistance shows steplike features every time a fluxon ~soliton! enters the junction, with a corresponding phase slip seen in the reactance. For finite widths the interference of fluxons leads to some interesting effects which are described. Many of these calculated results are observed in microwave impedance measurements on intrinsic and fabricated Josephson junctions in the high temperature superconductors. When a dc field (bdc) or current (idc) is applied, interesting phase locking effects are observed in the ac impedance Zv . In particular an almost periodic dependence on the dc bias is seen similar to that observed in microwave experiments at very low dc field bias. These results are generic to all systems with a cos(f) potential in the overdamped limit and subjected to an ac drive. @S0163-1829~99!00610-4#