Wave propagation in inhomogeneous media is studied by a new method, the ’’cutting‐out’’ Jessel’s method. Emphasis is on transition layers, where both the sound velocity and density variations are taken into account. Several classes of layers are studied and impedance matching by a smooth dioptre is described. By using the analogy between inhomogeneous media and waveguides, this property of impedance matching has been extended to connecting horns, thus leading to the definition of a new family : the aperiodic horns.