Nonlinear science at the dawn of the 21th century: Josephson Flux-Flow Oscillators in Microwave Fields

In this chapter we investigate, both analytically and numerically, the flux-flow resonance of long Josephson junctions in the presence of microwave fields. We consider the microwaves to be coupled to the junction both uniformly in space and trough boundary conditions. Using a perturbation analysis around the rotating background we derive analytical expressions for the current-voltage characteristics. The dependence of the flux-flow step on the amplitude of the rf-field and the appearance of satellite steps is explained. As a result we find that for uniform microwave fields the satellite steps are spaced around the main flux-flow resonance by both odd and even harmonics of the rf-frequency, while for non uniform fields only the even harmonic satellites are present. These results are found in good agreement with direct numerical integration of the system.