Enhanced scattering from a thin film with one-dimensional disorder

Abstract

This paper deals with a TE plane wave scattering from a thin film with one-dimensional disorder by means of the stochastic functional approach. The thin film is one-dimensionally inhomogeneous in the horizontal direction with infinite extent, and is homogeneous in the vertical direction with finite thickness. Based on an approximate wavefield representation in terms of a Wiener–Hermite expansion in a preceding paper (Tamura et al., 2004, Waves in Random Media, 14, 435–465), the first- and second-order incoherent scattering cross-sections are presented in explicit forms and scattering properties are discussed. The scattering properties vary entirely with the film thickness. In a case where the thickness is smaller than a few wavelengths in the thin film, enhanced scattering and associated enhanced scattering may appear as sharp peaks or dips on the second-order incoherent scattering distribution if the thin film has guided wave modes. When the thickness becomes sufficiently larger than the wavelength inside the film, a new enhanced scattering phenomenon appears as gentle peaks on the second-order incoherent scattering distribution in four special directions. Such four directions are the directions of forward scattering, specular reflection, backscattering, and the symmetrical direction of forward scattering with respect to the normal of the film surface.The first-order incoherent scattering occurs distinctly in four such directions. Such enhanced scattering is independent of the existence of the guided wave modes inside the thin film, and deeply relates to the structure of the thin film with one-dimensional disorder that has infinite correlation in the vertical direction. For SiC and glass thin films having one-dimensional disorder with a Gaussian correlation and three types of exponential correlation, the first- and second-order incoherent scattering cross-sections are illustrated in figures. The narrow enhanced scattering peaks appear for the glass film in a thin case. The gentle enhanced peaks turn up for both the SiC and glass films in a thick case. Furthermore, the optical theorem is calculated for several cases. It is then found that the error of the optical theorem decreases and the performance of the wavefield is improved by taking into account the second-order incoherent scattering.