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Tauc-Lorentz model is commonly used to describe the dielectric constant of amorphous semiconductors as a function of few parameters. However, this model is not fully analytic and presents other mathematical shortcomings. A modified self-consistent model based on the integration of [E'-(E + ia)]-1 functions using Tauc-Lorentz`s ε2 expression as a weight function is presented. This new model is analytic and meets all other mathematical requirements of optical constants. The main difference with TL model stands at photon energies close to or smaller than the bandgap energy. The new model has been satisfactorily tested on SiC optical constants. Additionally, an analytic extension of the new model has been also developed to include the Urbach tail. The complete model has been tested with Si₃N₄ optical constants, and it enables to extend the optical-constant characterization of materials down to zero energy.

Sum rules are a useful tool to evaluate the global consistency of a set of optical constants. We present a procedure to spectrally tune sum rules to evaluate the local consistency of optical constants. It enables enhancing the weight of a desired spectral range within the sum-rule integral. The procedure consists in multiplying the complex refractive index with an adapted function, which is named window function. Window functions are constructed through integration of Lorentz oscillators. The asymptotic decay of these window functions enables the derivation of a multiplicity of sum rules akin to the inertial sum rule, along with one modified version of f-sum rule. This multiplicity of sum rules combined with the free selection of the photon energy range provides a double way to tune the spectral contribution within the sum rule. Window functions were applied to reported data of SrF2 and of Al films in order to check data consistency over the spectrum. The use of window functions shows that the optical constants of SrF2 are consistent in a broad spectrum. Regarding Al, some spectral ranges are seen to present a lower consistency, even though the standard sum rules with no window function did not detect inconsistencies. Hence window functions are expected to be a helpful tool to evaluate the local consistency of optical constants.

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Causality implies that the optical constants of any material continue in the upper complex plane of photon energies or wavelengths as an analytic function. This is the basis for Kramers-Kronig dispersion relations to obtain ε 1 from ε 2 , or n from k. However, there have not been attempts to explore this continuation. This research focuses on such continuation and on applications thereof. An interesting property has been found: optical constants progressively smoothen when entering the upper complex plane. The continuation to complex energies is found to result in an average of the optical constants with a Lorentzian weight function. This optical-constant smoothening originated in a shift to the upper complex plane is naturally produced in optical constants that have been obtained by means of an optical instrument with a Lorentzian slit function. This smoothening results in reduced resolution through convolution with the slit function. A procedure that takes advantage of optical constants at complex energies is developed for optical-constant deconvolution. Deconvolution is performed locally, i.e., with no integration, and it consists of shifting the energy of the optical constants by an imaginary amount by means of a Taylor series expansion. The first correction term involves the derivative of the other optical constant. Even though deconvolution of optical constants measured with a Gaussian slit cannot be directly performed with the present method, an approach based on powers of the Lorentz function is also proposed. This procedure could be implemented as an analysis tool of a spectrophotometer or an ellipsometer; this tool would enable one to measure optical constants with a modest resolution and to improve it by post-processing them with the present scheme.

Mirrors are a subset of optical components essential for the success of current and future space missions. Most of the telescopes for space programs ranging from earth observation to astrophysics and covering the whole electromagnetic spectrum from x-rays to far-infrared are based on reflective optics. Mirrors operate in diverse and harsh environments that range from low-earth orbit to interplanetary orbits and deep space. The operational life of space observatories spans from minutes (sounding rockets) to decades (large observatories), and the performance of the mirrors within the mission lifetime is susceptible to degrading, resulting in a drop in the instrument throughput, which in turn affects the scientific return. Therefore, the knowledge of potential degradation mechanisms, how they affect mirror performance, and how to prevent them is of paramount importance to ensure the long-term success of space telescopes. In this review, we report an overview of current mirror technology for space missions with a focus on the importance of the degradation and radiation resistance of coating materials. Special attention is given to degradation effects on mirrors for far and extreme UV, as in these ranges the degradation is enhanced by the strong absorption of most contaminants.

Space observations in the far ultraviolet (FUV, are aimed at providing essential information for astrophysics, solar physics, and atmosphere physics. There are key spectral lines and bands in the FUV for the above disciplines. Despite various developments in the recent decades, yet many observations are not possible due to technical limitations, of which one of the most important is the lack of efficient optical coatings. Hence for solar physics applications there are needs of narrowband coatings for key wavelengths such as H Lyman β (102.6 nm) and OVI lines (103.2 and 103.8 nm). For atmosphere physics, narrowband coatings are required for observations at spectral lines such as OI (135.6 nm) and at the N 2 Lyman-Birge-Hopfield band (LBH,.In solar corona observations, often the intensities of the target lines are weak, and this radiation may be masked by more intense lines, such as H Lyman α at 121.6 nm. Until now, no narrowband multilayers peaked in the ~100-105 nm range have been reported, which is due to the absorption of materials at these wavelengths. When efficient narrowband coatings are not possible, an option is the use of coatings with high reflectance at the target wavelength and simultaneously low reflectance at the undesired wavelength, such as Lyman α.We have developed novel multilayers to address this target, with combinations of these materials: Al, LiF, SiC and C. We developed multilayers based on the following three systems, Al/LiF/SiC, Al/LiF/SiC/C, and Al/LiF/SiC/LiF. Their reflectance was measured both when fresh and after some storage in a desiccator. Al/LiF/SiC and Al/LiF/SiC/C systems displayed a high Lyman β/Lyman α reflectance ratio when fresh, although they resulted in an undesired reflectance increase at Lyman α for the aged samples and the reflectance ratio Lyman β/Lyman α became small; this behavior turned these systems useless for the present application. The most promising multilayers were the ones based on the Al/LiF/SiC/LiF system, which resulted in a good performance and a limited evolution after months of storage in a desiccator.Five samples based on the Al/LiF/SiC/LiF system were prepared and measured in the 50-190 nm spectral range. These samples resulted in high reflective and narrowband coatings peaked at 100-101 nm, with a promising reflectance ratio Lyman β/Lyman α when fresh. Some efficiency degradation was observed after the sample storage in a desiccators; however all samples retained a narrowband performance over time and a high Lyman β/Lyman α ratio. The same system can be designed to be an efficient narrowband coating peaked in the target spectral range and not constrained to a specific performance at Lyman α. Hence an 8-month aged sample exhibited a reflectance as high as 61% at the peak wavelength of 100.9 nm, at near-normal incidence, the highest experimental reflectance reported in this range for a narrowband coating.We have also prepared narrowband transmission coatings tuned either at 135.6 nm or at the center of the LBH band (~160 nm), with the requirement to ...

Optical-constant data of a material typically come from various sources, which may result in inconsistent data. Sum rules are tests to evaluate the self-consistency of optical constant data sets. Standard sum rules provide collective self-consistency evaluation of an optical-constant set in the full electromagnetic spectrum, but they give no information on the specific spectral range originating the inconsistency. Spectrally-resolved self-consistency information can be obtained with the use of window functions (WFs). Window functions can give more weight to the desired spectral range in the calculation of the sum rule. A previously developed WF was successfully used to evaluate self-consistency over the spectrum, but since it involves steep transition at the window edges and center, it has a trend to turn unstable in the calculation of sum-rule integrals for a fast decaying WF outside the window band. Two new WFs have been developed to reduce such instability. They use weight functions that smoothly cancel at the two window edges and center. The two new WFs use a weight function with three straight lines or with two 4-degree polynomials. The new WFs have been tested on exact optical constants with a coarse sampling, and they provide a strong instability reduction in self-consistency evaluation compared with the old WF. The new WFs have been also tested on experimental data sets of Al and Au reported in the literature, which unveils ranges of inconsistency. The large stability of the new WFs compared with the old one helps decide that the inconsistency calculated with the new WFs on experimental data must be attributed to inconsistency of the data sets, and not to poor sampling rate. A WF that has been used in the literature in the calculations of the dielectric function at imaginary energies for the thermal Casimir effect is also analyzed in terms of self-consistency when it is applied to sum rules involving optical constant at real (not imaginary) energies.