Scattering of light from an amplifying medium bounded by a randomly rough surface

We study theoretically the scattering of s-polarized light from the one-dim ensional, randomly rough surface of a homogeneous amplifying dielectric med ium deposited as a film on the planar surface of a semi-infinite perfectly conducting substrate. The reflectivity of the rough him is found to be grea ter than that of the corresponding planar film if only true guided waves su pported 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 le aky guided wave also exists at the frequency of the incident Light. Althoug h the reflectivity of an amplifying film with a planar surface is greater t han unity for all angles of incidence, that of an amplifying Aim with a ran dom surface tan be smaller than unity in a certain range of angles of incid ence as a consequence of the existence of a leaky guided wave. The contribu tion to the mean differential reflection coefficient from the incoherent co mponent of the scattered light displays an enhanced backscattering peak and satellite peaks (the latter if the scattering structure supports two or mo re 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 imag inary part of its dielectric constant, but of opposite sign, irrespective o f 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 ar e nonmonotonic functions of the magnitude of the imaginary part of the diel ectric constant of the aim, when a leaky wave is present, but depend monoto nically on it when no leaky wave is present. In the case of an absorbing fi lm these functions depend monotonically on the imaginary part of the dielec tric constant. [S0163-1829(99)02242-0].