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Various tools have been employed in studying and computing beam or field propagation in a medium with variation of small refractive index Feit and (Fleck,et al,1976)(Fleck,1978)( Ugwu et al,2007) some researchers had employed beam propagation method based on diagonalization of the Hermitian operator that generates the solution of the Helmholtz equation in media with real refractive indices (Thylen and Lee,1992), while some had used 2x2 propagation matrix formalism for finding the obliquely propagated electromagnetic fields in layered inhomogeneous un-axial structure (Ong,1993) Recently, we have looked at the propagation of electromagnetic field through a conducting surface (Ugwu, 2005) and we observed the behaviour of such a material. The effect of variation of refractive index of FeS2 had also been carried out (Ugwu, 2005) The parameters of the film that were paramount in this work are dielectric constants and the thickness of the thin film. The dielectric constants were obtained from a computation using pseudo-dielectric function in conjunction with experimentally measured extinction co-efficient and the refractive indices of the film and the thickness of the film which was assumed to range from 0.1μm to 0.7μm [100nm to 700nm] based on the experimentally measured value, at the wavelength, 450μm (Cox, 1978)( Lee and Brook,1978) This work is based on a method that involves propagating an input field over a small distance through the thin film medium and then iterating the computation over and over through the propagation distance using Lippmann-Schwinger equation and its counterpart, Dyson’s equation (Economou, 1979) here, we first derived Lippmann-Schwinger equation using a specific Hamiltonian from where the field function ┰k (z) was obtained. From this, it was observed that to ease out the solution of the Lippmann-Schwinger equation, it was discretized. After this, Born approximation was applied in order to obtain the solution. The formalism is logically built up step-by-step, which allowed point-to-point observation of the behaviour of the field propagating through the film inorder to analyze the influence of the field behavior as it propagates through small thin film thickness with consideration given to solid state properties such as dielectric function/refractive index, determine the absorption characteristics within the wavelength regions of electromagnetic wave spectrum and then to have a view of the influence of the dielectric function on the amplitude of the propagated field from the theoretical solution of the scalar wave equation considered within the ultra

Wave Propagation in Dielectric Medium Thin Film Medium