Parallel Modelling of Diffraction Gratings CMPT 851 Final Report

Over the last two hundred years, diffraction grating spectroscopy has unlocked fundamental discoveries in physics, astronomy, chemistry, and biology. Recently, synchrotron light sources have extended grating spectroscopy to the soft X-ray range, where it has provided powerful techniques for material science research. However, it is inherently challenging to produce diffraction gratings with good efficiency in this wavelength range. Given that the efficiency is critical to the speed and feasibility of experiments, there is a strong motivation for improving it. Due to the high cost and long times associated with grating manufacturing, this optimization cannot be done by trial-and-error. Therefore, the long-term goal of this project is to produce software that can quickly predict and optimize the grating efficiency. In general, there is no analytic solution for calculating the grating efficiency. A variety of numerical methods have been proposed [12][5][1][6][7][13][10][8]; almost all of these seek to find a numerical vector solution to the Maxwell Equations in the presence of the incident light and the periodic boundary conditions imposed by the grating. The differential method of Neviere et al. [10] has been found to be the most accurate in the soft X-ray regime. A commercial implementation of the method is available, but it requires between 30 seconds and 3 minutes to compute the efficiency for a single grating at a single wavelength on