Spatial Green Function of a Constant Medium Overlying a Duct With Linear-Square Refractive Index Profile

For a two-dimensional problem, this paper presents the evaluation of the spatial Green function of environments made up of a constant medium overlying a duct having a linear-square refractive index profile. This function must be determined to deal with the more general problem of scattering from a rough sea surface in the presence of a duct. Indeed, knowing the spatial Green function, the sea surface roughness effect can be taken into account rigorously in the calculation of the scattered field by solving the integral equations on the rough surface. Assuming a slowly-varying refractive index profile, by using the method of steepest descents, closed-form expressions of the spatial Green function in different regions (illuminated and shadowed) are derived. In addition, they are compared with that obtained from the parabolic wave equation.