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Abstract
We have investigated the spectrum of localized modes in both finite and phase inhomogeneous long one-dimensional Josephson junctions in the presence of an external magnetic field. For finite junctions these excitations correspond to evanescent waves localized near the edges. Both the frequency and the characteristic decay lengths depend on the magnetic field. In particular, a different behavior is expected for the Meissner state and the mixed state in which wholesale penetration of Josephson vortices occurs. The related problem of the spectrum of modes localized near phase inhomogeneities occurring well inside a long junction has been also tackled. This problem is relevant to the case in which Abrikosov vortices penetrate the electrodes and become pinned near the junction plane.
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