Keywords

Greene's, function, optics, reflectance, roughness, XUV, impedance

Abstract

A Fortran program is set up to solve for the reflectance of XUV light from a rough two dimensional surface, resembling experimental mirrors used to reflect XUV light. Because the roughness of the surface is on the order of magnitude of the wavelength of XUV light, our approach requires a Greene's Function instead of using traditional geometrical optics or physical optics. Our Fortran program calculates the impedance (Z) matrix which requires integration over Greene's Function at non-singular points. The Z matrix helps solve for the induced surface current J(x') at non-singular points. At singular points, the program implements a series of transformations, including the Duffy transformation, in order to eliminate the singularities. This allows for integration of the Greene's Function over the rough surface using numerical Gaussian quadrature rules. The transformations lead to solving for weights specific to each singularity that aid in the calculation of J(x') at singular points. After an incident electric field is generated in the program, the scattered electric field can be solved for directly.

Description

This paper was completed during the 2017 Research Experiences for Undergraduates in Physics (REU) program. More information about this program can be found here.