Group velocity dispersion in terahertz frequency combs within a generalized Maxwell-Bloch framework

As many molecules have their rotovibrational resonance frequencies in the mid-infrared or terahertz regime, efficient generation of corresponding frequency combs may lead to large progress in gas spectroscopy and sensing. Quantum cascade lasers (QCLs) are among the most promising candidates for a compact and cheap radiation source in this frequency range. This contribution presents a full-wave numerical solution of the Maxwell-Liouville-von Neumann equations, thus avoiding the limited applicability of the rotating wave approximation to moderate field strengths and spectral bandwidths. We include losses and chromatic dispersion of the optically active material in the QCL. The semiclassical approach uses the finite-difference time-domain (FDTD) method to derive update equations for the electric field, starting from the one-dimensional Maxwell equations. There, the optical full-wave propagation is coupled to the electronic quantum system via a polarization term that arises from the evolution of the density matrix. Furthermore, dispersion effects are considered through a classical polarization term and losses are introduced by a finite material conductivity. This work mainly focuses on the integration of group velocity dispersion (GVD) due to the bulk material and, if applicable, the waveguide geometry into the update equations. It is known to be one of the main degradation mechanisms of terahertz frequency combs, but has not yet been added to the existing full-wave solver. The implementation is carried out as Lorentz model and is applied to an experimentally investigated QCL frequency comb setup from the literature. The reported results are in good agreement with the experimental data. Especially, they confirm the need for dispersion compensation for the generation of terahertz frequency combs in QCLs.

Ability of Lewis Acids with Shallow σ-Holes to Engage in Chalcogen Bonds in Different Environments

Molecules of the type XYT = Ch (T = C, Si, Ge; Ch = S, Se; X,Y = H, CH3, Cl, Br, I) contain a σ-hole along the T = Ch bond extension. This hole can engage with the N lone pair of NCH and NCCH3 so as to form a chalcogen bond. In the case of T = C, these bonds are rather weak, less than 3 kcal/mol, and are slightly weakened in acetone or water. They owe their stability to attractive electrostatic energy, supplemented by dispersion, and a much smaller polarization term. Immersion in solvent reverses the electrostatic interaction to repulsive, while amplifying the polarization energy. The σ-holes are smaller for T = Si and Ge, even negative in many cases. These Lewis acids can nonetheless engage in a weak chalcogen bond. This bond owes its stability to dispersion in the gas phase, but it is polarization that dominates in solution.

The Importance of Strain (Preorganization) in Beryllium Bonds

In order to explore the angular strain role on the ability of Be to form strong beryllium bonds, a theoretical study of the complexes of four beryllium derivatives of orthocloso-carboranes with eight molecules (CO, N2, NCH, CNH, OH2, SH2, NH3, and PH3) acting as Lewis bases has been carried out at the G4 computational level. The results for these complexes, which contain besides Be other electron-deficient elements, such as B, have been compared with the analogous ones formed by three beryllium salts (BeCl2, CO3Be and SO4Be) with the same set of Lewis bases. The results show the presence of large and positive values of the electrostatic potential associated to the beryllium atoms in the isolated four beryllium derivatives of ortho-carboranes, evidencing an intrinsically strong acidic nature. In addition, the LUMO orbital in these systems is also associated to the beryllium atom. These features led to short intermolecular distances and large dissociation energies in the complexes of the beryllium derivatives of ortho-carboranes with the Lewis bases. Notably, as a consequence of the special framework provided by the ortho-carboranes, some of these dissociation energies are larger than the corresponding beryllium bonds in the already strongly bound SO4Be complexes, in particular for N2 and CO bases. The localized molecular orbital energy decomposition analysis (LMOEDA) shows that among the attractive terms associated with the dissociation energy, the electrostatic term is the most important one, except for the complexes with the two previously mentioned weakest bases (N2 and CO), where the polarization term dominates. Hence, these results contribute to further confirm the importance of bending on the beryllium environment leading to strong interactions through the formation of beryllium bonds.

Salinity dependence of complex conductivity of unconsolidated and consolidated materials: Comparisons with electrical double layer models

We examined the dependence of imaginary conductivity ([Formula: see text]) on pore fluid conductivity ([Formula: see text]) for an extensive database of 67 samples acquired from twelve independent studies. We compared fitting of functions describing the salinity dependence of [Formula: see text] for two models of the electrical double layer (EDL) polarization, both of which predict asymptotic behavior of [Formula: see text] at high [Formula: see text]. We define these models as the diffuse layer polarization (DLP) and Stern layer polarization (SLP) models based on the physical description of the salinity dependence of the surface polarization. We also examined the database for evidence of a high salinity decrease in [Formula: see text] not predicted by either model. The dependence of [Formula: see text] on [Formula: see text] prior to the polarization plateau predicted by both models approximates a simple empirical power law with an average exponent of 0.34. The salinity dependence predicted by the DLP model adequately describes most data sets. A fitting parameter representing the high salinity [Formula: see text] asymptote is strongly correlated ([Formula: see text]) with pore normalized specific surface ([Formula: see text]). The SLP model describes well the observations when a recently proposed additive polarization term representing the contribution of the protons is included. In this case, the SLP model provides an excellent fit to the data sets, including a low salinity asymptote (in log-log conductivity space) seen in some samples. Predicted values of the fitting parameters of the SLP model generally are consistent with the values expected based on the theory; the fitting parameter describing the high salinity asymptote of the SLP model is also strongly correlated ([Formula: see text]) with [Formula: see text]. The SLP and DLP models neglect a high salinity decrease in the polarization that is observed in numerous data sets from independent studies. New data acquired on a sandstone sample demonstrate that this high salinity decrease is likely not attributable to the limited phase accuracy of earlier measurements.

Induced polarization measurements on unsaturated, unconsolidated sands

Induced polarization (IP) measurements were obtained on unsaturated, unconsolidated sediments during (1) evaporative drying and (2) pressure drainage followed by subsequent imbibition (water reentry). Porous ceramic discs were used with existing laboratory IP instrumentation to permit accurate IP measurements on unsaturated samples. Polarization magnitude during evaporative drying approximates a power law dependence on saturation. Saturation exponents for the polarization term were consistently less than Archie conduction exponents, although no clear relationship between the exponents was observed. The polarization measured over a pressure drainage and imbibition cycle exhibits a complex (yet similar between tested samples) saturation dependence, being a function of saturation range and saturation history. Polarization is observed to increase with saturation over certain saturation intervals, yet decrease with saturation over others. High polarization observed during sample imbibition is consistent with a model for the development of a continuous charged air‐fluid interface as previously proposed to explain hysteresis in resistivity measurements. The saturation dependence of the phase angle measured in IP in large part results from changes in conduction as pores fill and drain. Models of low‐frequency polarization based on grain‐size‐controlled and pore‐size‐controlled relaxation both support dependence of IP measurements on saturation. Our results suggest that saturation dependent polarization must be considered for effective interpretation of IP measurements from the vadose zone.

Dynamic Finite Element Analysis of a Piezoelectric Bimorph Beam Deflector With Consideration of Hysteresis Effect

This study is devoted to propose a method of finite element technique to account for the hysteresis effect of a piezoelectric bimorph beam deflector. To this end, the constitutive equations of a general piezoelectric material are first modified to include the hysteresis effect by adding a polarization term in one of constitutive equations. Based on these modified constitutive equations and employment of Preisach model for hysteresis, the governing equations of the bimorph beam are derived through the utilization of Hamilton’s principle and calculus of variation. In addition, according to the common physical rules, boundary, transition and continuous conditions are next formulated to complement the governing equations. Simulations are finally conducted to show the effectiveness of the proposed modeling technique and decipher the dynamic behavior of the piezoelectric beam with consideration of hysteresis effect.