We study theoretically the scattering of s-polarized light from the one-dimensional, randomly rough surface of a homogeneous amplifying dielectric medium deposited as a film on the planar surface of a semi-infinite perfectly conducting substrate. The reflectivity of the rough film is found to be greater than that of the corresponding planar film if only true guided waves supported by the scattering structure exist at the frequency of the incident light; it can be smaller than that of the corresponding planar film if a leaky guided wave also exists at the frequency of the incident light. Although the reflectivity of an amplifying film with a planar surface is greater than unity for all angles of incidence, that of an amplifying film with a random surface can be smaller than unity in a certain range of angles of incidence as a consequence of the existence of a leaky guided wave. The contribution to the mean differential reflection coefficient from the incoherent component of the scattered light displays an enhanced backscattering peak and satellite peaks (the latter if the scattering structure supports two or more guided waves). The overall intensity of the light scattered incoherently from the surface of a rough amplifying film is always greater than that of the light scattered from the same film with the same magnitude of the imaginary part of its dielectric constant, but of opposite sign, irrespective of the presence or absence of a leaky wave at the frequency of the incident light. However, the height and width of the enhanced backscattering peak are nonmonotonic functions of the magnitude of the imaginary part of the dielectric constant of the film, when a leaky wave is present, but depend monotonically on it when no leaky wave is present. In the case of an absorbing film these functions depend monotonically on the imaginary part of the dielectric constant.

• Received 5 May 1999

DOI:https://doi.org/10.1103/PhysRevB.60.12692