Controllable plasma energy bands in a one-dimensional crystal of fractional Josephson vortices

We consider a one-dimensional chain of fractional vortices in a long Josephson junction with alternating ±κ phase discontinuities. Since each vortex has its own eigenfrequency, the intervortex coupling results in eigenmode splitting and in the formation of an oscillatory energy band for plasma waves. The band structure can be controlled at the design time by choosing the distance between vortices or during experiment by varying the topological charge of vortices or the bias current. Thus one can construct an artificial vortex crystal with controllable energy bands for plasmons.