Hyperbolic reflections as fundamental building blocks for multilayer optics

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.

Simple trace criterion for classification of multilayers

The action of any lossless multilayer is described by a transfer matrix that can be factorized in terms of three basic matrices. We introduce a simple trace criterion that classifies multilayers in three classes with properties closely related with one (and only one) of these three basic matrices.Comment: To be published in Optics Letter

A geometrical setting for the classification of multilayers

We elaborate on the consequences of the factorization of the transfer matrix of any lossless multilayer in terms of three basic matrices of simple interpretation. By considering the bilinear transformation that this transfer matrix induces in the complex plane, we introduce the concept of multilayer transfer function and study its properties in the unit disk. In this geometrical setting, our factorization translates into three actions that can be viewed as the basic pieces for understanding the multilayer behavior. Additionally, we introduce a simple trace criterion that allows us to classify multilayers in three types with properties closely related to one (and only one) of these three basic matrices. We apply this approach to analyze some practical examples that are representative of these types of matrices.Comment: 8 pages, 5 figures. To be published in J. Opt. Soc. Am.

Fresnel coefficients as hyperbolic rotations

We describe the action of a plane interface between two semi-infinite media in terms of a transfer matrix. We find a remarkably simple factorization of this matrix, which enables us to express the Fresnel coefficients as a hyperbolic rotation.Comment: 6 pages, 3 figure

Constructing Fresnel reflection coefficients by ruler and compass

A simple and intuitive geometical method to analyze Fresnel formulas is presented. It applies to transparent media and is valid for perpendicular and parallel polarizations. The approach gives a graphical characterization particularly simple of the critical and Brewster angles. It also provides an interpretation of the relation between the reflection coefficients for both basic polarizations as a symmetry in the plane

In situ generation of COx-free H2 by catalytic ammonia decomposition over Ru-Al-monoliths

Ru catalysts supported on alumina coated monoliths has been prepared employing three different precursor, which are ruthenium chloride, ruthenium nitrosyl nitrate and ruthenium acetyl acetonate, by an equilibrium adsorption method. The Ru particle sizes could be controlled varying the metal precursor salt. Among the prepared catalysts, Ru catalyst prepared from nytrosyl nitrate exhibited the highest activity which is concomitant to the largest mean Ru particle size of 3.5 nm. The values of the apparent activation energy calculated from the Arrhenius equation are according to the Temkin-Phyzev model, indicating that the recombinative desorption of N ad-atoms is the rate-determining step of the reaction. However, the ratio between the kinetic orders with respect to ammonia and hydrogen (-a/ß), is not in agreement to the valued predict by Temkin formalism. This fact could be related to the different operational conditions used during the reaction, and/or catalyst nature, but not to any change on the controlling step of the reaction

Synthesis of graphenic nanomaterials by decomposition of methane on a Ni-Cu/biomorphic carbon catalyst. Kinetic and characterization results

This work addresses the preparation and application of the synthesis of graphene in Ni-Cu catalysts supported on carbonaceous materials. The catalysts have been prepared by a biomorphic mineralization technique which involves the thermal decomposition, under reductive atmosphere, of commercial cellulose previously impregnated with the metallic precursors. The characterization results indicate that the preparation method leads to the formation of carbonaceous supports with a moderate microporosity (ca. 33% pore volume) and adequate surface area (343 m2/g), maintaining the original external texture. The catalytic performance of these materials was previously tested in liquid phase reactions (Zampieri et al., 2007 [7]). In order to extend the use of these catalysts, in this work we present a study corresponding to a gas phase reaction: the synthesis of graphenic nanomaterials by catalytic decomposition of methane (CDM). The influence of the reaction temperature and of the feed composition (i.e.%CH4 and%H2) has been studied. The graphenic nanomaterials obtained after reaction were characterized by nitrogen adsorption-desorption isotherms, Raman spectroscopy and transmission electron microscopy (TEM). The results indicate that the carbonaceous nanomaterial with the highest quality is obtained operating at 950 °C and feeding 28.6% of CH4 and 14.3% of H2. The evolution of the carbon mass during the reaction time was analysed using a phenomenological kinetic model that takes into account the main stages involved during the formation of carbonaceous nanomaterials (NCMs). The results obtained from the kinetic model along with the characterization results enable the influence of the operating variables on each stage of the carbonaceous nanomaterial formation to be discerned

Hydrophobic RWGS catalysts: Valorization of CO2-rich streams in presence of CO/H2O

Nowadays, the majority of the Reverse Water Gas Shift (RWGS) studies assume somehow model feedstock (diluted CO2/H2) for syngas production. Nonetheless, biogas streams contain certain amounts of CO/H2O which will decrease the obtained CO2 conversion values by promoting the forward WGS reaction. Since the rate limiting step for the WGS reaction concerns the water splitting, this work proposes the use of hydrophobic RWGS catalysts as an effective strategy for the valorization of CO2-rich feedstock in presence of H2O and CO. Over Fe-Mg catalysts, the different hydrophilicities attained over pristine, N- and B-doped carbonaceous supports accounted for the impact on the activity of the catalyst in presence of CO/H2O. Overall, the higher CO productivity (4.12 μmol/(min·m2)) attained by Fe-Mg/CDC in presence of 20 % of H2O relates to hindered water adsorption and unveil the use of hydrophobic surfaces as a suitable approach for avoiding costly pre-conditioning units for the valorization of CO2-rich streams based on RWGS processes in presence of CO/H2O