2012/03/14 by Armin Lechleiter, Lechleiter, Armin, Dinh Liem Nguyen +1 · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Microwave and Dielectric Measurement Techniques #Numerical Analysis (math.NA) #Optical Coatings and Gratings
paper · pdf · doi:10.48550/arxiv.1203.3025
openalex publication_date 2012/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Transverse magnetic (TM) scattering of an electromagnetic wave from a\nperiodic dielectric diffraction grating can mathematically be described by a\nvolume integral equation. This volume integral equation, however, in general\nfails to feature a weakly singular integral operator. Nevertheless, after a\nsuitable periodization, the involved integral operator can be efficiently\nevaluated on trigonometric polynomials using the fast Fourier transform (FFT)\nand iterative methods can be used to solve the integral equation. Using\nFredholm theory, we prove that a trigonometric Galerkin discretization applied\nto the periodized integral equation converges with optimal order to the\nsolution of the scattering problem. The main advantage of this FFT-based\ndiscretization scheme is that the resulting numerical method is particularly\neasy to implement, avoiding for instance the need to evaluate quasiperiodic\nGreen's functions.\n