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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. [ABSTRACT FROM AUTHOR]

General properties of solid core photonic bandgap fibers are presented as well as general guidelines, found thanks to numerical investigations, helpful for designing this kind of fibers. We give two examples of applications and a new fiber design with interstitial air holes that lead to a significant reduction of both confinement and bend losses. This design allows the light to be guided in the fiber core thanks to a modified total internal reflection mechanism at long wavelengths and by photonic bandgap at short wavelengths. Furthermore, this new design satisfies the phase index matching condition for either second- or third-harmonic generation between two fundamental modes. [ABSTRACT FROM AUTHOR]