  Interaction of a fluxon in the two-dimensional large Josephson junction with
the finite area inhomogeneity is studied within the sine-Gordon theory. The
spectral density of the emitted plane waves is computed exactly for the
rectangular and rhombic inhomogeneities. Total emitted energy as a function of
the fluxon velocity exhibits at least one local maximum. Connection to the
previously studied limiting cases including the point impurity and the
one-dimensional limit has been performed. An important feature o f the emitted
energy as a function of the fluxon velocity is a clear maximum (or maxima). The
dependence of these maxima on the geometric properties of the impurity has been
studied in detail.
