Microscopic Polarizability Research Articles

A-site cation manipulation of exemplary second harmonic generation response and optical anisotropy in rare-earth borates.

Ultraviolet nonlinear optical (UV NLO) materials have garnered significant interest for their prospective applications in advanced laser technologies. However, tailoring the desired structure in these materials remains a formidable challenge. Here, we propose a simple yet effective strategy for synthesizing rare-earth borates, K x Na3-x La2B3O9 (x = 2-3), by manipulating the A-site cations to induce structural evolution. Notably, K x Na3-x La2B3O9 undergoes a phase transition from the Pnc2 to the Amm2 space group by adjusting the K+ content to reach x = 2.6. Moreover, the target compounds exhibit strong phase-matching second harmonic generation (SHG) efficiencies, ranging from 1.3 to 3.3 times that of KDP (KH2PO4), and feature short UV cutoff edges of around 204-208 nm. Additionally, the correlation between microscopic polarizability, optical anisotropy, and the structural evolution of these materials was characterized through structural and theoretical analyses. These findings highlight the potential applications of K x Na3-x La2B3O9 as UV NLO materials and underscore the viability of manipulating A-site cations to fabricate NLO crystals with desirable properties.

Atomic-scale electromagnetic theory bridging optics in microscopic world and macroscopic world

Atoms in the microscopic world are the basic building blocks of the macroscopic world. In this work, we construct an atomic-scale electromagnetic theory that bridges optics in the microscopic and macroscopic worlds. As the building block of the theory, we use the microscopic polarizability to describe the optical response of a single atom, solve the transport of electromagnetic wave through a single atomic layer under arbitrary incident angle and polarization of the light beam, construct the single atomic layer transfer matrix for light transport across the atomic layer. Based on this transfer matrix, we get the analytical form of the dispersion relation, refractive index, and transmission/reflection coefficient of the macroscopic medium. The developed theory can handle single-layer and few-layers of homogeneous and heterogeneous 2D materials, investigate homogeneous 2D materials with various vacancies or insertion atomic-layer defects, study compound 2D materials with a unit cell composed of several elements in both the lateral and parallel directions with respect to the light transport.

Reflection, transmission, and surface susceptibility tensor of two-dimensional materials

In a recent experiment, the out-of-plane surface susceptibility of a single-layer two-dimensional atom crystal in the visible spectrum has been measured. This susceptibility gives a measurable contribution to the reflectivity of two-dimensional materials. Here we provide a complete theoretical description of the reflective properties, considering incoming s and p polarized plane waves at any angle of incidence on the crystal, computing local, reflected and transmitted electromagnetic fields. We finally connect the microscopic polarizability to both the in-plane and the out-of-plane macroscopic surface susceptibilities.

A Simplified Method of Microscopic Polarizability Tensor Differential of Hyper-Raman Spectroscopy Based on the Bond Additivity Model

Coherent anti-Stokes Raman spectroscopy (CARS) and Ccherent anti-Stokes hyper-Raman spectroscopy (CAHRS), as other high-order nonlinear spectroscopy techniques, are widely exploited in many research fields, such as dynamic processes, gene expression spectrum screening, high-resolution spectroscopy, and nonlinear high-resolution imaging. However, it is difficult to make a quantitative analysis of the spectral signals that involve a large number of high-order micropolarizability tensors. It is reported that the CARS and CAHRS microscopic hyperpolarizability tensor elements can be decomposed into the product of the differentiation of Raman microscopic polarizability tensor α′i′j′ and hyper-Raman microscopic polarizability tensor β′i′j′k′ so that the high-order spectra can be simplified to the analysis of low-order spectra. In this paper, we use the bond additivity model (BAM) combined with experimental corrections to address the carbon dioxide (CO2) molecule and present the simplified scheme for differentiation of hyper-Raman microscopic polarizability tensor elements β′i′j′k′. Taking advantage of this approach, combined with the experimental correction, the differentiation of Hyper-Raman microscopic polarizability tensor elements β′i′j′k′ of the CO2 is obtained and the expressions of β′i′j′k′ for antisymmetric vibrations of CO2 are deduced. Finally, substituting the differentiation of Raman microscopic polarizability tensor elements α′i′j′ reported in the literature into the ratio above can obtain the proportional relationship between the microscopic polarizability tensor elements of CARS and CAHRS of the CO2. This method can provide the basis for the quantitative analysis of high-order nonlinear spectral profiles.

C(NH2)3]3PO4·2H2O: A new metal-free ultraviolet nonlinear optical phosphate with large birefringence and second-harmonic generation response

[PO4]3− possesses small microscopic second-order susceptibility and polarizability anisotropy, which inherently result in weak second-harmonic generation (SHG) and small birefringence. Herein, a new noncentrosymmetric phosphate, [C(NH2)3]3PO4·2H2O, was successfully designed and synthesized by a solution evaporation method. [C(NH2)3]3PO4·2H2O without metal ions is composed of planar conjugated guanidine cations and PO4 tetrahedrons, which are connected by hydrogen bonds, forming a three-dimensional network. Physical property measurements indicate that the title compound displays an SHG response of 1.5 × KH2PO4 (KDP) and a larger birefringence (0.055@546.1 nm) compared with most reported ultraviolet nonlinear optical phosphates. Furthermore, first-principles calculations reveal that the π-conjugated planar [C(NH2)3]+ cations and [PO4]3− groups are responsible for its excellent linear and NLO properties.

Crystal structures, intrinsic properties and phonon characteristics of non-stoichiometric Nd[Mg1/2(1+x)Sn1/2]O3 ceramics

The non-stoichiometric Nd[Mg1/2(1+x)Sn1/2]O3 (NMS, − 0.04 ≤ x ≤ 0.04) were synthesized through a routine solid-state reaction process. The phase composition, phonon characteristics, and microwave dielectric properties were investigated by X-ray diffraction patterns, Scanning electron microscopy Raman and Fourier transform far-infrared reflection. The best crystallinity with uniformly distributed grains and clear grain boundaries at x = 0.01. The intrinsic properties were calculated by four-parameter semi-quantum model based on far-infrared reflectivity data, which agree well with those values obtained from the microscopic polarizabilities & damping coefficient angle. The correlations between intrinsic properties and lattice vibrational modes were discussed in particular.

Intrinsic dielectric properties and vibration characteristics of La(Mg1/2Sn1/2)O3 ceramic

La(Mg1/2Sn1/2)O3 (LMS) ceramic was synthesized via the conventional solid-state reaction method. The main phase of the sample is LMS with a double perovskite structure (monoclinic P121/n1 symmetry), which is confirmed by X-ray diffraction. Scanning electron microscopy shows the sample is well-crystallized with dense and uniform grains as well as clear grain boundaries. The Raman scattering and Fourier transform far-infrared reflection spectroscopies were employed to analyze the lattice vibrational modes of the sample. The Raman active modes were fitted by the Lorentz function, and the lattice vibrational modes were assigned and illustrated accurately. The four-parameter semiquantum model was applied to simulate the intrinsic dielectric properties, which agree well with the data calculated from the microscopic polarizability & damping angles. The A1g(La) Raman mode in A-site has a great impact on the dielectric loss, and F3u(2) mode makes the largest contribution to the dielectric constant and the dielectric loss.

On the theory of light propagation in crystalline dielectrics

A synoptic view on the long-established theory of light propagation in crystalline dielectrics is presented, where charges, tightly bound to atoms (molecules, ions) interact with the microscopic local electromagnetic field. Applying the Helmholtz-Hodge decomposition to the current density in Maxwell’s equations, two decoupled sets of equations result determining separately the divergence-free (transversal) and curl-free (longitudinal) parts of the electromagnetic field, thus facilitating the restatement of Maxwell’s equations as equivalent field-integral equations. Employing a suitably chosen basis system of Bloch functions we present for dielectric crystals an exact solution to the inhomogenous field-integral equations determining the local electromagnetic field that polarizes individual atoms or ionic subunits in reaction to an external electromagnetic wave. From the solvability condition of the associated homogenous integral equation then the propagating modes and the photonic bandstructure for various crystalline symmetries Λ are found solving a small sized matrix eigenvalue problem. Identifying the macroscopic electric field inside the sample with the spatially low-pass filtered microscopic local electric field, the dielectric tensor of crystal optics emerges, relating the accordingly low-pass filtered microscopic polarization field to the macroscopic electric field, solely with the individual microscopic polarizabilities of atoms (molecules, ions) at a site R and the crystalline symmetry as input into the theory. Decomposing the microscopic local electric field into longitudinal and transversal parts, an effective wave equation determining the radiative part of the macroscopic field in terms of the transverse dielectric tensor is deduced from the exact solution to the field-integral equations. The Taylor expansion around q = 0 provides then insight into various optical phenomena connected to retardation and non-locality of the dielectric tensor, in full agreement with the phenomenological reasoning of Agranovich and Ginzburg in ‘Crystal Optics with Spatial Dispersion, and Excitons’ (Springer Berlin Heidelberg, 1984): the eigenvalues of the tensor describing chromatic dispersion of the index of refraction and birefringence, the first order term specifying rotary power (natural optical activity), the second order term shaping the effects of a spatial-dispersion-induced birefringence. In the static limit an exact expression for the dielectric tensor is deduced, that conforms with general thermodynamic stability criteria and reduces for cubic symmetry to the Clausius-Mossotti relation. Considering various crystals comprising atoms with known polarizabilities from the literature, in all cases the calculated indices of refraction, the rotary power and the spatial-dispersion-induced birefringence coincide well with the experimental data, thus illustrating the utility of the theory.

Internal Relations between Crystal Structures and Intrinsic Properties of Nonstoichiometric Ba1+ xMoO4 Ceramics.

Ba1+ xMoO4 (-0.03 ≤ x ≤ 0.03) ceramics were fabricated by a conventional two-step sintering technique. X-ray diffraction patterns show that there appeared new diffraction peaks when x > 0, which were identified as Ba2MoO5. The Rietveld refinement results indicate that the unit cell volume is the largest at x = -0.02, because it has the lowest packing fraction and covalency. The far-infrared reflectivity (IR) spectra were fitted and analyzed for calculating the intrinsic properties, which comply well with the data obtained from microscopic polarizabilities and damping coefficient angle. The proportion of each mode in the dielectric response demonstrates that the Ba-O8 polyhedra have a decisive role on the dielectric properties. And based on the Raman modes, the internal relations of the structural-properties were revealed with the changes of Ba2+ content.

Refracting properties of lyotropic nematic calamitic mesophase under magnetic field

The present study found the time-dependent extraordinary refractive index and birefringence of lyotropic nematic calamitic mesophase for different temperatures during its orientation under magnetic field. Based on the experimental results, the average angle between the mesophase directors and magnetic field was calculated to estimate the orientation dynamics of the mesophase during the director rotation from planar to homeotropic orientations. On the other hand, the textural properties were investigated during the orientation. The ordinary and extraordinary refractive indices were also measured depending on temperature to obtain the orientational order parameter of the mesophase. Using the macroscopic refractive index results, the microscopic polarizability was studied as well.

Three alkaline-rare earth cations carbonates with large birefringence in the deep UV range

Three new alkaline-rare earth carbonate and carbonate fluorides, KY(CO3)2, Na2Gd(CO3)F3 and NaGd0.25Lu0.75(CO3)F2, were synthesized through the subcritical hydrothermal method. The three crystals crystallize in the centrosymmetric space groups C2/c, Pbca and Pnma, respectively. All the three compounds were structurally characterized by X-ray single crystal diffraction. The ultraviolet–visible–near-infrared diffuse reflectance spectra indicate that the absorption edges of all crystals are below 200 nm. The first-principles calculations show that the birefringences of KY(CO3)2, Na2Gd(CO3)F3 and NaGd0.25Lu0.75(CO3)F2 are 0.105, 0.084 and 0.198, respectively. The birefringences for all compounds originate from a geometrical addition of the microscopic anisotropic polarizability of the planar [CO3] groups. And the smaller the angle between the [CO3] group and the crystal axis is, the larger the structure factor C will be, and the corresponding birefringence will also be larger.

Reinterpreting the magnetoelectric coupling of polarizability tensors of infinite cylinders using symmetry: A simple TM/TE view

Recently, Strickland et al retrieved dynamic polarizabilities of infinitely long wires at oblique incidence, reporting non-zero magnetoelectric coupling, seemingly defying existing theorems which forbid this in centrosymmetric scatterers. We reconcile this finding with existing symmetry restrictions on microscopic polarizabilities using a property of line dipoles. This motivates a reformulation of cylinder polarizability, yielding diagonal tensors that decompose the response into TM and TE contributions, simplifying subsequent treatment by homogenization theories. A transformation is derived between Strickland et al.'s formulation and our reformulation, allowing magnetoelectric coupling to be identified as the contrast between TM and TE responses, and enabling simple geometric insights into all its scaling and symmetry properties.

Clausius-Mossotti Lorentz-Lorenz relations and retardation effects for two-dimensional crystals

The macroscopic surface electric susceptibility determines the linear optical properties of an insulating single-layer two-dimensional atomic crystal, and can be expressed in terms of the microscopic polarizability of the atoms. We compute the local electric field acting on a single atom, both for the static and the dynamic case, as the superposition of the external applied electric field and the fields generated by the induced dipoles in the crystal. We find that, in the dynamic case, retardation effects dephase the local electric field with respect to the incident one. This explains why the Fresnel coefficients of a single-layer two-dimensional atomic crystal are intrinsically complex quantities, even when a null macroscopic surface conductivity is assumed.

Theoretical study on the polarizability properties of liquid crystal in the THz range

Terahertz (THz) technology developed rapidly in recent years. Liquid crystals (LCs) are one of the most promising base materials to construct switchable devices in THz range because of their high optical anisotropies. However, the practical applications of the devices are hampered by the relationships between birefringence, thickness and LCs switching time. Due to the long wavelength, THz device requires a larger birefringence LC than the device operated at optical frequencies. Yet, in order to design an efficient switchable LC-THz device, it is crucial to find or synthetize LC material which will still display a useful birefringence at THz frequencies. The birefringence properties of LC are determined by the molecular polarizability of the relevant material. Knowledge of the LC molecular polarizability and its dependence on the molecular structure is important for designing LC molecules with desired THz properties. The prediction of the photoelectric characteristics could save a considerable quantity of the man-power and materials needed for the design or synthesis of new LC compounds. A priori screening of materials and the prediction of the optoelectronic properties would make a vast opportunity for expanding the LC material application scope. Hence, the main purpose of the present work is to provide a theoretical method of calculating and analyzing the THz polarizability properties of LC single compounds for LC-THz device applications. In this work, the frequency dependent molecule polarizability values of liquid crystal PCH5, 5CB and 5OCB in THz range are calculated by the density functional theory method. The geometries of the studied LCs are optimized at B3 LYP levels with the standard 6-311G(d) basis set. From the optimized geometries the molecule THz polarizabilities of LCs are calculated by the M06-2x functional with 6-311++G(2d, p) basis set, and they are found to be in good agreement with experimental data. By plotting the polarizability density analysis (PDA), the spatial contributions of electrons to the longitudinal polarizability are presented. The influences of alkyl chain and core structure on the microscopic polarizability of the LC molecule are investigated and explained by using the finite field approach and PDA. The results show that the unsaturated group, such as benzene ring or cyanobenzyl, makes great contribution to the polarizability of LC. In the design process, the new type of LC molecule must be extended the length of up electron conjugated system, to reduce the energy gap between HOMO and LUMO, and hence improving LC molecule polarizabilty. We hope that the present work could give a useful guide in screening or designing LC molecules for THz applications, and offer an effective way to understand fundamental optoelectronic characteristic of LC materials in the THz frequency range.

Electric Property Variations in Nanosized Hexagonal Boron Nitride/Graphene Hybrids

Within the realm of hybrid materials built from graphene and white graphene (hexagonal boron nitride (h-BN)), this paper attempts to shed light on some unknown aspects concerning essential structure–property relationships one might come across in h-BN/graphene hybrids of finite size. To do so, we present and analyze the outcomes of a systematic study focalized on the electric properties and, more particularly, on the microscopic dipole polarizabilities and first hyperpolarizabilities of purposely chosen h-BN/graphene nanosized molecular hybrids comprising h-BN segments of increasing size. Quantum chemical computations reveal that size modifications of a h-BN segment confined in a given graphene host may induce dramatic electric property variations which vary in a rather surprising manner as a function of the graphene host. For instance, it is shown how a given h-BN fragment may induce precisely the reverse effect on band gap related properties when embedded in graphene hosts of apparently similar features...

Local field effects in anisotropic metamaterials

We consider dielectric and magnetic properties of metamaterials consisting of single particles. Local field effects are taken into account. The so called method of multiscale consideration is realized: the macroscopic quantities of permittivity and permeability are expressed through the microscopic polarizability and magnetization of single particles. We obtain the generalized Clausius-Mossotti relations for the case of magnetic medium and with anisotropic particles in the long wave approximation. In cases of isotropic magnetic and nonmagnetic particles our results coincide with published results of other authors.

Ferroelectric instability of two-dimensional crystals

The macroscopic dielectric permittivity of dielectric crystals is related to the microscopic atomic polarizability of constituent atoms by the known Clausius-Mossotti relation obtained in the middle of 19th century. We derive a similar relation for recently discovered two-dimensional crystals (mono- and bilayer graphene, boron nitride, etc) and show that, in contrast to three-dimensional materials, much stronger electron-electron interaction in two dimensions leads to a spontaneous electric polarization of the ground state of two-dimensional crystals. The predicted ferroelectric transition may have interesting applications in electrodynamics and optics.

Cyanine‐Like Dyes with Large Bond‐Length Alternation

Herein, the synthesis and properties of alkyne-bridged carbocations, which are analogous in structure to cyanine dyes, are reported. An alkene-bridged dye, linked at the third position of the indole, was also synthesized as a reference compound. These new carbocations are stable under ambient conditions, allowing characterization by UV/Vis and NMR ((1)H and (13)C) spectroscopies. These techniques revealed a large degree of delocalization of the positive charge, similar to a previously reported porphyrin carbocation. The linear and nonlinear optical properties are compared with cyanine dyes and triarylmethyl cations, to investigate the effects of the bond-length alternation and the overall molecular geometry. The value of Re(γ), the real part of the third-order microscopic polarizability, of -1.3×10(-33) esu for the alkyne-linked cation is comparable to that of a cyanine dye of similar length. Nondegenerate two-photon absorption spectra showed that the alkene-bridged dye exhibited characteristics of cyanines, whereas the alkyne-bridged dye is reminiscent of octupolar chromophores, such as the triarylmethyl carbocation brilliant green. Such attributes were confirmed and rationalized by quantum chemical calculations.

Effects of Dendronization on the Linear and Third-Order Nonlinear Optical Properties of Bis(thiopyrylium) Polymethine Dyes in Solution and the Solid State

Effects of the size and attachment position of benzyl aryl ether dendrons covalently attached to bis(thiopyrylium) penta- and heptamethines on the optical properties of these dyes in solution and in solid films have been investigated. In dilute solution the low-energy absorption bands of some of the dendronized species differ from those of the parent compounds in having much smaller transition dipole moments, this effect possibly due to differences in ion pairing, while at higher concentrations, dye–dye interactions lead to a decrease in the transition dipole moments of the nondendronized species, but not of the dendronized ones. Consequently, in the high concentration range, dendronized and nondendronized species exhibit similar values of the real part of the microscopic third-order polarizability at 1550 nm. Solid-state film absorption spectra suggest that the dendrons significantly disrupt the chromophore–chromophore interactions seen for the nondendronized species, reducing, but not eliminating, linea...

Calculation of the Casimir-Polder interaction between Bose-Einstein condensates and microengineered surfaces: a pairwise-summation approach

Understanding the Casimir-Polder (CP) attraction between ultracold atoms and dielectric surfaces is of fundamental importance to the design and miniaturization of atom chips [1] and for understanding quantum reflection from, and sticking to, the surface [2 – 6]. So far, calculations have focussed on planar dielectrics, either semi-infinite or of finite width [7–9], and non-planar geometries including corrugated surfaces [10], spheres and carbon nanotubes [11–12]. Here, we present a simple scheme, based on the Pairwise-Summation (PWS) approximation, for estimating the CP interaction between a ground-state alkali atom and a dielectric volume of arbitrary shape. The PWS approximation integrates the van der Waals interaction between two ground-state atoms over the many atoms in the surface volume. We relate the microscopic polarizability of atoms in the surface to the bulk dielectric constant via the Clausius-Mossotti relation within the Lorentz local-field theory. We find that the CP potential depends strongly on both the geometry and density of the surface, which modify the fluctuation spectrum of the electromagnetic field that couples the alkali atoms to the dielectric. We compare our results with known analytical expressions for the CP potential near planar surfaces and use them to investigate how BECs interact with, and may quantum reflect from, curvilinear surface structures.