Rapidly convergent two-dimensional quasi-periodic Green function throughout the spectrumincluding Wood anomalies
We introduce a new methodology, based on new quasi-periodic Green functions which converge rapidly even at and around Wood-anomaly configurations, for the numerical solution of problems of scattering by periodic rough surfaces in two-dimensional space. As is well known the classical quasi-periodic Green function ceases to exist at Wood anomalies. The approach introduced in this text produces fast Green function convergence throughout the spectrum on the basis of a certain finite-differencing approach and smooth windowing of the classical Green function lattice sum. The resulting Green-function convergence is super-algebraically fast away from Wood anomalies, and it reduces to an arbitrarily-high (user-prescribed) algebraic order of convergence at Wood anomalies.
quasi-periodic green function wood anomaly lattice sums rough-surface scattering diffraction grating ewald summation method scattering by periodic surfaces time-harmonic helmholtz equation time-harmonic maxwell equations integral equation methods boundary integral methods