‘Anomalous’ dissipation of a paraxial wave beam propagating along an absorbing plane

We present solutions of the Leontovich–Fock parabolic equation which describe the structure of a paraxial quasi-optical wave beam in a medium with strong spatial inhomogeneity of the absorption coefficient transverse to the direction of beam propagation. Using as an example the simplest reference problem of a beam propagating along an infinitely narrow plane absorbing layer, it is shown that, in this case, the energy dissipation and refraction of the beam affect each other, so that they should be considered simultaneously, while the application of the perturbation theory can lead to qualitatively incorrect results.