Abstract

Traditional periodic PDE formulations for infinite diffraction gratings are studied using the Wiener—Hopf technique or Green’s function representations. The limitations present in both methods restrict consideration to specific types of gratings if computable solutions are desired. This talk presents an extension to the Fokas method (also known as the Unified Transform method) to periodic domains – then numerically computable by a spectral collocation method. The resulting global relation for the periodic problem features an extra term to accompany what is otherwise the global relation for the unit cell in free space. Links to the periodic Wiener—Hopf method are also discussed.