We experimentally and theoretically investigate electromagnetic cavity modes in ultranarrow $\mathrm{Al}\text{−}{\mathrm{AlO}}_x\text{−}\mathrm{Al}$ and $\mathrm{Nb}\text{−}{\mathrm{AlO}}_x\text{−}\mathrm{Nb}$ long Josephson junctions. Experiments show that the voltage spacing between the Fiske steps on the current-voltage characteristics of sub-$\mathrm{\mu }\mathrm{m}$-wide and several hundred $\mathrm{\mu }\mathrm{m}$-long $\mathrm{Al}\text{−}{\mathrm{AlO}}_x\text{−}\mathrm{Al}$ and $\mathrm{Nb}\text{−}{\mathrm{AlO}}_x\text{−}\mathrm{Nb}$ Josephson junctions increases when decreasing the junction width. This effect is explained by stray magnetic fields, which become important for narrow junctions. Theoretical estimates of the Fiske step voltage based on a nonlocal wave propagation equation are in agreement with our experimental data. Using the nonlocal model, we determine the size and mass of a Josephson vortex by means of a variational approach, and relate the vortex size to the experimentally measured critical magnetic field of the junction.

• Received 12 July 2006

DOI:https://doi.org/10.1103/PhysRevB.74.134515