Conventional and nonconventional Kramers-Kronig analysis in optical spectroscopy

This Master’s Thesis is dedicated to the investigation and testing conventional and nonconventional Kramers-Kronig relations on simulated and experimentally measured spectra. It is done for both linear and nonlinear optical spectral data. Big part of attention is paid to the new method of obtaining complex refractive index from a transmittance spectrum without direct information of the sample thickness. The latter method is coupled with terahertz tome-domain spectroscopy and Kramers-Kronig analysis applied for testing the validity of complex refractive index. In this research precision of data inversion is evaluated by root-mean square error. Testing of methods is made over different spectral range and implementation of this methods in future is considered.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Determinação de parâmetros ópticos de materiais por análise de Kramers-Kronig de espectros de infravermelho

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influence of cerium (IV) ions on the mechanism of organosilane polymerization and on the improvement of its barrier properties

In this work, the effect of cerium (IV) ammonium nitrate (CAN) addition on the polymerization of bis-[triethoxysilyl]ethane (BTSE) film applied on carbon steel was studied. The electrochemical characterization of the films was carried out in 0.1 mol L(-1) NaCl solution by open-circuit potential measurements, anodic and cathodic polarization curves and electrochemical impedance spectroscopy (EIS). Morphological and chemical characterization were performed by atomic force microscopy (AFM), contact angle measurements, infrared-spectroscopy, nuclear magnetic resonance and thermogravimetric analysis. The results have clearly shown the improvement on the protective properties of the Ce(4+) modified film as a consequence of the formation of a more uniform and densely reticulated silane film. A mechanism is proposed to explain the accelerating role of Ce(4+) ions on the cross-linking of the silane layer. (C) 2008 Elsevier Ltd. All rights reserved.

Cr3C2-NiCr and WC-Ni thermal spray coatings as alternatives to hard chromium for erosion-corrosion resistance

Cr3C2-NiCr and WC-Ni coatings are widely used for wear applications at high and room temperature, respectively. Due to the high corrosion resistance of NiCr binder, Cr3C2-NiCr coatings are also used in corrosive environments. The application of WC-Ni coatings in corrosive media is 14 not recommended due to the poor corrosion resistance of the (pure Ni) metallic matrix. It is well known that the addition of Cr to the metallic binder improves the corrosion properties. Erosion-corrosion performance of thermal spray coatings is widely influenced by ceramic phase composition, the size of ceramic particles and also the composition of the metallic binder. In the present work, two types of HVOF thermal spray coatings (Cr3C2-NiCr and WC-Ni) obtained with different spray conditions were studied and compared with conventional micro-cracked hard chromium coatings. Both as-sprayed and polished samples were tested under two erosion-corrosion conditions with different erosivity. Tungsten carbide coatings showed better performance under the most erosive condition, while chromium carbide coatings were superior under less erosive conditions. Some of the tungsten carbide coatings and hard chromium showed similar erosion-corrosion behaviour under more and less erosive conditions. The erosion-corrosion and electrochemical results showed that surface polishing improved the erosion-corrosion properties of the thermally sprayed coatings. The corrosion behaviour of the different coatings has been compared using Electrochemical Impedance Spectroscopy (EIS) and polarization curves. Total material loss due to erosion-corrosion was determined by weight loss measurements. An estimation of the corrosion contribution to the total weight loss was also given. (c) 2007 Elsevier B.V. All rights reserved.

Optical evidence for the proximity to a spin-density-wave metallic state in Na0.7CoO2

We present the optical properties of Na0.7CoO2 single crystals, measured over a broad spectral range as a function of temperature (T). The capability to cover the energy range from the far-infrared up to the ultraviolet allows us to perform reliable Kramers-Kronig transformation, in order to obtain the absorption spectrum (i.e., the complex optical conductivity). To the complex optical conductivity we apply the generalized Drude model, extracting the frequency dependence of the scattering rate (Gamma) and effective mass (m*) of the itinerant charge carriers. We find that Gamma(omega) at low temperatures and for similar to omega. This suggests that Na0.7CoO2 is at the verge of a spin-density-wave metallic phase.

Spectral characteristics of bacteriorhodopsin water solution

The object of the study is bacteriorhodopsin. This light-sensitive protein have been selected as perspective substance for optical and optoelectronic applications. Bacteriorhodopsin carries out pumping protons through the cell membrane. Biomolecule converts light into an electric signal when sandwiched between electrodes. These properties were utilized in this research to implement photosensors on the basis of BR layers. These properties were utilized in this research to the bR water solution. According to the absorption spectra and using Kramers – Kronig relation the extinction coefficient has been calculated, as well as the related change of the refractive index value.

Far infrared reflectance and optical properties of organic superconductor (TMTSF)2ClO4 /

Polarized reflectance measurements of the quasi I-D charge-transfer salt (TMTSFh CI04 were carried out using a Martin-Puplett-type polarizing interferometer and a 3He refrigerator cryostat, at several temperatures between 0.45 K and 26 K, in the far infrared, in the 10 to 70 cm- 1 frequency range. Bis-tetramethyl-tetraselena-fulvalene perchlorate crystals, grown electrochemically and supplied by K. Behnia, of dimensions 2 to 4 by 0.4 by 0.2 mm, were assembled on a flat surface to form a mosaic of 1.5 by 3 mm. The needle shaped crystals were positioned parallel to each other along their long axis, which is the stacking direction of the planar TMTSF cations, exposing the ab plane face (parallel to which the sheets of CI04 anions are positioned). Reflectance measurements were performed with radiation polarized along the stacking direction in the sample. Measurements were carried out following either a fast (15-20 K per minute) or slow (0.1 K per minute) cooling of the sample. Slow cooling permits the anions to order near 24 K, and the sample is expected to be superconducting below 1.2 K, while fast cooling yields an insulating state at low temperatures. Upon the slow cooling the reflectance shows dependence with temperature and exhibits the 28 cm- 1 feature reported previously [1]. Thermoreflectance for both the 'slow' and 'fast' cooling of the sample calculated relative to the 26 K reflectance data indicates that the reflectance is temperature dependent, for the slow cooling case only. A low frequency edge in the absolute reflectance is assigned an electronic origin given its strong temperature dependence in the relaxed state. We attribute the peak in the absolute reflectance near 30 cm-1 to a phonon coupled to the electronic background. Both the low frequency edge and the 30 cm-1 feature are noted te shift towards higher frequcncy, upon cntering the superconducting state, by an amount of the order of the expected superconducting energy gap. Kramers-Kronig analysis was carried out to determine the optical conductivity for the slowly cooled sample from the measured reflectance. In order to do so the low frequency data was extrapolated to zero frequency using a Hagen-Ru bens behaviour, and the high frequency data was extended with the data of Cao et al. [2], and Kikuchi et al. [3]. The real part of the optical conductivity exhibits an asymmetric peak at 35 cm-1, and its background at lower frequencies seems to be losing spectral weight with lowering of the temperature, leading us to presume that a narrow peak is forming at even lower frequencies.

Infrared spectroscopy of Mg-doped SrRuO3 thin films /

The reflectance of thin films of magnesium doped SrRu03(Mg-SR0) produced by pulsed laser deposition on SrTiOa (100) substrates has been measured at room temperature between 100 and 7500 cm~^. The films were chosen to have wide range of thickness, stoichiometry and electrical properties. As the films were very thin (less than 300 nm), and some were insulating the reflectance data shows structures due to both the film and the substrate. Hence, the data was analyzed using Kramers-Kronig constrained variational fitting (VDF) method to extract the real optical conductivity of the Mg-SRO films. Although the VDF technique is flexible enough to fit all features of the reflectance spectra, it seems that VDF could not eliminate the substrate's contribution from fllm conductivity results. Also the comparison of the two different programs implementing VDF fltting shows that this technique has a uniqueness problem. The optical properties are discussed in light of the measured structural and transport properties of the fllms which vary with preparation conditions and can be correlated with differences in stoichiometry. This investigation was aimed at checking the VDF technique and also getting answer to the question whether Mg^"*" substitutes in to Ru or Sr site. Analysis of our data suggests that Mg^+ goes to Ru site.

Optical properties of organic superconductor K-(BETS)2FeBr4 /

/c-(BETS)2FeBr4 is the first antiferromagnetic organic superconductor with successive antiferromagnetic and superconducting transitions at Ta^=2.5K and Tc=l.lK respectively at ambient pressure. Polarized reflectance measurements were performed on three single crystalsamples of this material using a Briiker IFS66V/S Interferometer, and a Bolometer detector or an MCT detector, at seven temperatures between 4K and 300K, in both the far-infrared and mid-infrared frequency range. After the reflectance results were obtained, the Kramers-Kronig dispersion relation was apphed to determine the optical conductivity of /c-(BETS)2FeBr4 at these seven temperatures. Additionally, the optical conductivity spectra were fitted with a Drude/Lorentz Oscillator model in order to study the evolution of the optical conductivity with temperature along the a-axis and c-axis. The resistivities calculated from the Drude model parameters along the a-axis and c-axis agreed reasonably with previous transport measurements.

Far infrared optical properties of V and Cr doped Sb2Te3 /

The far infrared reflectance of Sb2Te3 , Sbi.97Vo.o3Te3 and Sbi.94Cr .o6Te3 was measured near normal incidence at different temperatures (between 45K and 300K). The direct current resistivities of the above samples were also measured between the temperatures of 4K and 300K. Also Kramers Kronig (KK) analyses were performed on the reflectance spectra to obtain the optical conductivities. In the doped samples, it was observed that a phonon at 62cm-1 softens to about 55cm-1 on decreasing the temperature from 295K to 45K. Also, it was observed that the plasma frequency of the doped samples is independent of doping. The scattering rate for the vanadium doped sample was seen to be greater than that for the chromium doped sample despite the fact that vanadium impurity density is less than that of chromium. The Drude-Lorentz model fits to the KK optical conductivity show that the samples used in this work are conventional metals. Definitive measurements of the temperature dependence of the scattering rate across the ferromagnetic transition await equipment changes allowing measurements at low temperature using the mercury cadmium telluride (MCT) detector.

Crystal growth, Raman scattering and optical properties of the superconductor Cd2Re2O7(16O, 18O)/

Using the Physical Vapor Transport method, single crystals of Cd2Re207 have been grown, and crystals of dimensions up to 8x6x2 mm have been achieved. X-ray diffraction from a single crystal of Cd2Re207 has showed the crystal growth in the (111) plane. Powder X-ray diffraction measurements were performed on ^^O and ^^O samples, however no difference was observed. Assigning the space group Fd3m to Cd2Re207 at room temperature and using structure factor analysis, the powder X-ray diffraction pattern of the sample was explained through systematic reflection absences. The temperatiure dependence of the resistivity measurement of ^^O has revealed two structural phase transitions at 120 and 200 K, and the superconducting transition at 1.0 K. Using Factor Group Analysis on three different structiures of Cd2Re207, the number of IR and Raman active phonon modes close to the Brillouin zone centre have been determined and the results have been compared to the temperature-dependence of the Raman shifts of ^^O and ^*0 samples. After scaling (via removing Bose-Einstein and Rayleigh scattering factors from the scattered light) all spectra, each spectrum was fitted with a number of Lorentzian peaks. The temperature-dependence of the FWHM and Raman shift of mode Eg, shows the effects of the two structurjil phase transitions above Tc. The absolute reflectance of Cd2Re207 - '^O single crystals in the far-infrared spectral region (7-700 cm~^) has been measured in the superconducting state (0.5 K), right above the superconducting state (1.5 K), and in the normal state (4.2 K). Thermal reflectance of the sample at 0.5 K and 1.5 K indicates a strong absorption feature close to 10 cm~^ in the superconducting state with a reference temperature of 4.2 K. By means of Kramers-Kronig analysis, the absolute reflectance was used to calculate the optical conductivity and dielectric function. The real part of optical conductivity shows five distinct active phonon modes at 44, 200, 300, 375, and 575 cm~' at all temperatures including a Drude-like behavior at low frequencies. The imaginary part of the calculated dielectric function indicates a mode softening of the mode 44 cm~' below Tc.

Far infrared spectroscopy of heavy fermion superconductor CeCoIn5

The optical response to far infrared radiation has been measured on a mosaic of heavy fermion CeColnssingle crystals. The superconducting transition temperature of the crystals has been determined by van der Pauw resistivity and ac-susceptibility measurements as Tc = 2.3 K. The optical measurements were taken above and below the transition temperature using a 3He cryostat and step and integrate Martin-Puplett type polarizing interferometer. The absolute reflectance of the heavy fermion CeColns in the superconducting state in range (0, 100)cm-1 was calculated from the measured thermal reflectance, using the normal state data of Singley et al and a low frequency extrapolation for a metallic material in the Hagen-Rubens regime. By means of Kramers-Kronig analysis the absolute reflectance was used to calculate the optical conductivity of the sample. The real part of the calculated complex conductivity 0-(w) ofCeColns indicates a possible opening of an energy gap close to 50 em-I.

Far infrared spectroscopy of heavy fermion superconductor CeCoIn5 /

The optical response to far infrared radiation has been measured on a mosaic of heavy fermion CeCoIns single crystals. The superconducting transition temperature of the crystals has been determined by van der Pauw resistivity and ac-susceptibility measurements as Tc = 2.3 K. The optical measurements were taken above and below the transition temperature using a ^He cryostat and step and integrate Martin-Puplett type polarizing interferometer. The absolute reflectance of the heavy fermion CeCoIns in the superconducting state in range (0, 100)cm~^ was calculated from the measured thermal reflectance, using the normal state data of Singley et al and a low frequency extrapolation for a metallic material in the Hagen-Rubens regime. By means of Kramers-Kronig analysis the absolute reflectance was used to calculate the optical conductivity of the sample. The real part of the calculated complex conductivity a{u)) of CeCoIns indicates a possible opening of an energy gap close to 50 cm~^.

Optical Properties of Sb2Te3, and Dilute Magnetic Semiconductors Sb1.97 VO.03 Te3 and Sb1.94 CrO.06 Te3

This thesis reports on the optical properties of the dilute magnetic semiconductors, Sb1.97 V 0.03 Te3 and Sb1.94Cr0.06Te3, along with the parent compound Sb2Te3' These materials develop a ferromagnetic state at low temperature with Curie temperatures of 22 K and 16 K respectively. All three samples were oriented such that the electric field vector of the light was perpendicular to the c-axis. The reflectance profile of these samples in the mid-infrared (500 to 3000 cm-1) shows a pronounced plasma edge which retracts with decreasing temperature. The far-infrared region of these samples exhibits a phonon at ~ 60 cm-1 which softens as temperature decreases. Kramers-Kronig analysis and a Drude-Lorentz model were employed to determine the optical constants of the bulk samples. The real part of the optical conductivity is shown to consist of intraband contributions at frequencies below the energy gap (~0.26 eV) and interband contributions at frequencies above the energy gap. The temperature dependence of the scattering rate show that a mix of phonon and impurity scattering are present, while the signature of traditional spin disorder (magnetic) scattering was difficult to confirm.