What is the Brillouin Zone of an Anisotropic Photonic Crystal?

The concept of the Brillouin zone (BZ) in relation to a photonic crystal fabricated in an optically anisotropic material is explored both experimentally and theoretically. In experiment, we used femtosecond laser pulses to excite THz polaritons and image their propagation in lithium niobate and lithium tantalate photonic crystal (PhC) slabs. We directly measured the dispersion relation inside PhCs and observed that the lowest bandgap expected to form at the BZ boundary forms inside the BZ in the anisotropic lithium niobate PhC. Our analysis shows that in an anisotropic material the BZ - defined as the Wigner-Seitz cell in the reciprocal lattice - is no longer bounded by Bragg planes and thus does not conform to the original definition of the BZ by Brillouin. We construct an alternative Brillouin zone defined by Bragg planes and show its utility in identifying features of the dispersion bands. We show that for an anisotropic 2D PhC without dispersion, the Bragg plane BZ can be constructed by applying the Wigner-Seitz method to a stretched or compressed reciprocal lattice. We also show that in the presence of the dispersion in the underlying material or in a slab waveguide, the Bragg planes are generally represented by curved surfaces rather than planes. The concept of constructing a BZ with Bragg planes should prove useful in understanding the formation of dispersion bands in anisotropic PhCs and in selectively tailoring their optical properties.Comment: 9 pages, 6 figure

Causes of Corruption:History, Geography, and Government

Corruption, which remains a serious problem in many countries, has prompted considerable research in recent years. This paper adds to the extant literature with insights on factors influencing corrupt activity. Using cross-country data for about 100 nations, the roles of national history, geography, and government are examined to see how they affect conditions for corruption, both qualitatively and quantitatively. The innovative aspects of this research include use of a wide set of historical, geographical, and governmental determinants of corruption, as well as detailed assessment of several previously considered determinants. The main issues addressed are the effects of the size and scope of government on the incidence of corruption across countries, and the significance of historical and geographic factors in corruption. Regarding the first question, the authors find the size and scope of government can significantly affect corruption. On the second, it is shown that historical institutional inertia in older countries and new rent-seeking opportunities in younger nations can encourage corruption, while certain geographic factors can mitigate corruption. The paper ends with discussion aimed at the policymaker.corruption; bribery; government size; government scope; rent-seeking; history; geography

Analysis of an F.M. Discriminator with Fading Signal plus Additive Gaussian Noise

Fading signal plus additive Gaussian noise applied to frequency modulation discriminator for determining fading effects on threshol

Dust obscuration studies along quasar sight lines using simulated galaxies

We use the results of a set of three-dimensional SPH-Treecode simulations which model the formation and early evolution of disk galaxies, including the generation of heavy elements by star formation, to investigate the effects of dust absorption in quasar absorption line systems. Using a simple prescription for the production of dust, we have compared the column density, zinc abundance and optical depth properties of our models to the known properties of Damped Lyman alpha systems. We find that a significant fraction of our model galaxy disks have a higher column density than any observed DLA system. We are also able to show that such parts of the disk tend to be optically thick, implying that any background quasar would be obscured through much of the disk. This would produce the selection effect against the denser absorption systems thought to be present in observations.Comment: 7 pages, 8 figures, to be published in MNRA

Quantum geometry from 2+1 AdS quantum gravity on the torus

Wilson observables for 2+1 quantum gravity with negative cosmological constant, when the spatial manifold is a torus, exhibit several novel features: signed area phases relate the observables assigned to homotopic loops, and their commutators describe loop intersections, with properties that are not yet fully understood. We describe progress in our study of this bracket, which can be interpreted as a q-deformed Goldman bracket, and provide a geometrical interpretation in terms of a quantum version of Pick's formula for the area of a polygon with integer vertices.Comment: 19 pages, 11 figures, revised with more explanations, improved figures and extra figures. To appear GER

Towards an understanding of nanometric dielectrics

Dielectric studies are described aimed at providing an understanding of the charge storage and transport of an epoxy resin containing TiO2 nanoparticles. Comparative results for conventionally filled composites are given, and the results discussed in terms of the underlying physics. It is shown that nanometric fillers mitigate the interfacial polarization characteristic of conventional materials with a reduction in the internal field accumulations