Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction

The boundary integral equation method (BIM) was one of the first methods in grating theory. It has been used for the investigation of diffraction gratings of extremely different kinds as well as for photonic crystal diffraction gratings. Besides an overview of three of the most important BIMs for in-plane diffraction, we present a new BIM for gratings in a conical mounting with one profile as well as for separated multilayer gratings with photonics inclusions using a common description for both approaches. In numerical examples, (1) blazing in conical mounting is demonstrated at a photonic crystal diffraction grating, (2) the excellent conical efficiency convergence for a plasmonic structure of two stacked silver rod gratings is shown, and (3) the transmission for conical incidence is studied at a blazed grating with large period-to-wavelength ratio.

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