  We experimentally and theoretically investigate electromagnetic cavity modes
in ultra-narrow Al-AlO$_x$-Al and Nb-AlO$_x$-Nb long Josephson junctions.
Experiments show that the voltage spacing between the Fiske steps on the
current-voltage characteristics of sub-$\mu$m wide and several hundred $\mu$m
long Al-AlO$_x$-Al and Nb-AlO$_x$-Nb Josephson junctions increases when
decreasing the width of a junction. 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
good 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 vortex size to the experimentally measured critical
magnetic field of the junction.
