547 research outputs found

    The transfer matrix: a geometrical perspective

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    We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical resonators. In all these cases, the transfer matrix has the same algebraic properties as the Lorentz group in a (2+1)-dimensional spacetime, as well as the group of unimodular real matrices underlying the structure of the abcd law, which explains many subtle details. We elaborate on the geometrical interpretation of the transfer-matrix action as a mapping on the unit disk and apply a simple trace criterion to classify the systems into three types with very different geometrical and physical properties. This approach is applied to some practical examples and, in particular, an alternative framework to deal with periodic (and quasiperiodic) systems is proposed.Comment: 50 pages, 24 figure

    Hyperbolic reflections as fundamental building blocks for multilayer optics

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    We reelaborate on the basic properties of lossless multilayers by using bilinear transformations. We study some interesting properties of the multilayer transfer function in the unit disk, showing that hyperbolic geometry turns out to be an essential tool for understanding multilayer action. We use a simple trace criterion to classify multilayers into three classes that represent rotations, translations, or parallel displacements. Moreover, we show that these three actions can be decomposed as a product of two reflections in hyperbolic lines. Therefore, we conclude that hyperbolic reflections can be considered as the basic pieces for a deeper understanding of multilayer optics.Comment: 7 pages, 7 figures, accepted for publication in J. Opt. Soc. Am.

    Bioerosion and palaeoecological association of osteophagous insects in the Maastrichtian dinosaur Arenysaurus ardevoli

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    Bioerosions produced by the osteophagous diet of animals that fed on dinosaur bones are very scarce in the European fossil record. Herein we present bioerosion on hadrosaurid remains from the Maastrichtian Tremp Formation of the Pyrenean Basin, which is only the second such case recorded from the Iberian-Occitan Plate besides a sauropod from the Jurassic-Cretaceous of Valencia. The hadrosaurid fossil record is particularly rich in the Blasi sites of the Tremp Formation located in the municipality of Arén (Huesca, Spain). In this article, bones referred to the hadrosaurid Arenysaurus ardevoli from the Blasi-3 site are analysed to shed light on the palaeoenvironment and on the presence of a palaeoecological interaction between the hadrosaurid carcase and osteophagous tracemakers. Bioerosions recorded on the bones comprise tunnels, roundish holes, and straight notches, similar to the traces attributed to necrophagous insects (cf. Cuniculichnus seilacheri). Here, we record the first instance of the activity of these animals on dinosaur bones in the Upper Cretaceous of the Ibero-Occitan Plate. The results presented lead us to infer that the Arenysaurus bones were possibly transported by a storm or similar event to the Blasi-3 site, where they were exposed to post-mortem biotic interactions (eaten and partially decomposed by dermestid beetles) for a prolonged time period before they were completely buried. © 2021 The Authors. Lethaia published by John Wiley & Sons Ltd on behalf of Lethaia Foundatio
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