Electromagnetic waves in a randomly inhomogeneous Josephson junction

Spectrum modification and damping of Josephson plasma waves induced by random inhomogeneities of the critical current through the superconductor contact and the averaged Green function of such excitations are analyzed. In the self-consistent approximation that makes it possible to take into account multiple wave scattering on the inhomogeneities, the frequency and damping of averaged waves, as well as position $\nu_m$ and peak width $\Delta\nu$ of the Fourier transform imaginary part of the averaged Green function, are determined as functions of wavevector $k$. The evolution of such functions with the variation of the correlation radius and the relative r.m.s. fluctuations of inhomogeneities is studied. The inhomogeneity-induced wave frequency decrease observed in the long wavelength spectral region qualitatively agrees with the $\nu$m behavior. It is established that in the case of “long-range” inhomogeneities, the linear dependence of damping on $k$ changes to the inversely proportional one, and damping tends to zero as $k\to$ 0, while $\Delta\nu$ at small $k$ attains its maximal values due to nonuniform broadening. In the presence of “short-range” inhomogeneities, the wave damping and $\Delta\nu$ are found to be similar functions of $k$. The results are compared to the numerical calculation data.