The scattering of electromagnetic radiation by a layered periodic diffraction grating is a central model in engineering and the sciences. The numerical simulation of this experiment has been widely explored in the literature and we advocate for a novel interfacial method which is perturbative in nature. This repository contains a High–Order Perturbation of Surfaces/Asymptotic Waveform Evaluation (HOPS/AWE) algorithm which is well–suited for PDEs posed on piecewise homogeneous domains. The algorithm was built and designed by Matthew Kehoe ([email protected]) and David Nicholls at the University of Illinois at Chicago.
Download the Matlab code in the src directory. The three main files are
refl_map.m: Calculates the Reflectivity Map, R, which measures the response (reflected energy) of a periodically corrugated grating structure as a function of illumination frequency, ω, and corrugation amplitude, h.mms_error.m: Validates the accuracy of the algorithm through the Method of Manufactured Solutions (MMS).test_mms_error.m: Rigorously validates all of the important Matlab code.
Example 1: The Reflectivity Map and Energy Defect (D) for vacuum over a dielectric.
Example 2: The Reflectivity Map for vacuum over silver and gold.
More examples (with instructions on how to run the code) can be found in the plots directory.
- Alongside the Matlab implementation, a Julia implementation is currently under development. The ongoing work resides in the
src_juliadirectory, where the filerefl_map.jloffers functionality comparable to its Matlab counterpart. - At present, the implementation accommodates two layers. Work is underway to extend support to three or more layers, with ongoing development taking place in the
src_three_layersdirectory.
[1] M. Kehoe and D. P. Nicholls, Joint Geometry/Frequency Analyticity of Fields Scattered by Periodic Layered Media, SIAM Journal on Mathematical Analysis, Volume 55, Issue 3, 1737-1765 (2023). https://doi.org/10.1137/22M1477568
[2] M. Kehoe and D. P. Nicholls, A stable high-order perturbation of surfaces/asymptotic waveform evaluation method for the numerical solution of grating scattering problems, Journal of Scientific Computing, 100(1) (2024). https://doi.org/10.1007/s10915-024-02566-6
[3] M. Kehoe, Joint Analyticity of the Transformed Field and Dirichlet–Neumann Operator in Periodic Media, PhD Thesis, University of Illinois at Chicago (2022).
All code within this repository is freely available for use under the terms of the MIT license. However, if you intend to utilize or are currently using the code, especially for academic or research purposes, we kindly request that you send an email to Matthew Kehoe ([email protected]) with your name, institution, and a brief description of your interest in this work. If you use the HOPS/AWE algorithm in any work resulting in a scientific or academic publication, we would greatly appreciate it if you could cite the HOPS/AWE algorithm in your manuscript as follows:
M. Kehoe and D. P. Nicholls, A stable high-order perturbation of surfaces/asymptotic waveform evaluation method for the numerical solution of grating scattering problems, Journal of Scientific Computing, 100(1) (2024). https://doi.org/10.1007/s10915-024-02566-6