Multipurpose S-shaped solvable profiles of the refractive index: application to modeling of antireflection layers and quasi-crystals

A class of four-parameter solvable profiles of the electromagnetic admittance has recently been discovered by applying the newly developed Property & Field Darboux Transformation method (PROFIDT). These profiles are highly flexible. In addition, the related electromagnetic-field solutions are exact, in closed-form and involve only elementary functions. In this paper, we focus on those who are S-shaped and we provide all the tools needed for easy implementation. These analytical bricks can be used for high-level modeling of lightwave propagation in photonic devices presenting a piecewise-sigmoidal refractive-index profile such as, for example, antireflection layers, rugate filters, chirped filters and photonic crystals. For small amplitude of the index modulation, these elementary profiles are very close to a cosine profile. They can therefore be considered as valuable surrogates for computing the scattering properties of components like Bragg filters and reflectors as well. In this paper we present an application for antireflection layers and another for 1D quasicrystals (QC). The proposed S-shaped profiles can be easily manipulated for exploring the optical properties of smooth QC, a class of photonic devices that adds to the classical binary-level QC.Comment: 14 pages, 18 fi

RAMPAC: a program for analysis of complicated Raman spectra

A computer program for the analysis of complicated (e.g. multi-line) Raman spectra is described. The program includes automatic peak search, various procedures for background determination, peak fit and spectrum deconvolution and extensive spectrum handling procedures

Optimal binning of X-ray spectra and response matrix design

A theoretical framework is developed to estimate the optimal binning of X-ray spectra. We derived expressions for the optimal bin size for model spectra as well as for observed data using different levels of sophistication. It is shown that by taking into account both the number of photons in a given spectral model bin and their average energy over the bin size, the number of model energy bins and the size of the response matrix can be reduced by a factor of $10-100$. The response matrix should then contain the response at the bin centre as well as its derivative with respect to the incoming photon energy. We provide practical guidelines for how to construct optimal energy grids as well as how to structure the response matrix. A few examples are presented to illustrate the present methods.Comment: 16 pages, 7 figures, accepted for publication in Astronomy and Astrophysic