We report what is believed to be the first demonstration of optical fiber gratings written in photonic crystal fibers. The fiber consists of a germanium-doped photosensitive core surrounded by a hexagonal periodic air-hole lattice in a silica matrix. The spectra of these gratings allow for a detailed characterization of the fiber. In particular, the gratings facilitate coupling to higher-order leaky modes. We show that the spatial distribution and the effective index of these modes are determined largely by the design of the lattice and that the grating spectra are unaffected by the refractive index surrounding the fiber. We describe these measurements and corresponding simulations and discuss their implications for the understanding of such air-hole structures.
Angle-resolved photoelectron spectroscopy ͑ARPES͒ is commonly applied to map the shape of Fermi surfaces. Here we quantify the errors of simple criteria for extracting Fermi vectors by ARPES that are induced by strongly varying matrix elements. Sophisticated methods for determining the three-dimensional Fermi vector based on temperature and photon energy dependent photoemission are discussed with reference to data of the quasi-two-dimensional system 1T-TiTe 2 .
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