Dielectric Susceptibility Tensor Research Articles

A molecular perspective on the emergence of long-range polar order from an isotropic fluid

The ferroelectric nematic phase (NF) has quickly become the most studied system in liquid crystal research. In this work, we investigate the origin of such polar structure by studying a compound for which the NF phase directly follows the isotropic liquid phase on cooling, making it a particularly interesting system. Our experimental results evidence the presence of polar correlations already in the high-temperature phase, in which ferroelectric order can be induced under a sufficiently strong electric field. In the NF phase, molecular dynamics and polar correlations are investigated through detailed dynamic dielectric measurements, while second harmonic generation experiments evidence a large value of the main coefficient of the second order dielectric susceptibility tensor. Lastly, experimentally determined parameters are employed for calculations based on a recently proposed theoretical model for the stability of the NF phase. The obtained results suggest that the parallel alignment of dipoles is driven by a subtle interplay between electrostatic and excluded volume interactions.

SECOND-HARMONIC GENERATION IN A THIN SPHERICAL LAYER OF A SMALL RADIUS BY COHERENT SOURCES OF ELLIPTICALLY POLARIZED RADIATION

Explicit forms of the power density and the total radiation power of the second-harmonic generation in a thin spherical layer of a small radius are determined. The conditions for a maximal total power of the second harmonic and the direction of observation of the maximum intensity of the second harmonic are found analytically for special cases of the second-order dielectric susceptibility tensor. A numerical maximization of the energy characteristics of the second-harmonic generated radiation is carried out using one and two coherent sources with the same ellipticity of radiation. The advantage of using several coherent sources compared to a single source of initial radiation is shown.

Генерация второй гармоники в поверхностном слое диэлектрической сфероидальной частицы. I. Аналитическое решение

The problem of second-harmonic generation by a plane elliptically polarized electromagnetic wave in a thin optically nonlinear surface layer of a dielectric particle shaped as an ellipsoid of revolution is solved. The generalized Rayleigh–Gans–Debye approximation is used for an analytical description with taking into account the difference in refractive indices of the medium corresponding to the frequencies of the exciting and generated radiation. The limiting forms of functions are obtained, with the use of which the electric field strength of the generated radiation is expressed. The order of dependence of these functions on the linear dimensions is found, when the lengths of the semiaxes of the particle are small compared to the wavelength of the exciting radiation and their ratio remains constant. It was found that the power density of the generated radiation in this case is determined to a greater extent by the chiral components of the nonlinear dielectric susceptibility tensor and is proportional to the fourth power of the length of the semiaxis of the particle, if the shape of the spheroidal particle differs significantly from the spherical one. The solution of this problem, obtained by other authors, is supplemented for the possibility of applying to the description of generation in the surface layer of a dielectric particle not only in the form of a prolate, but also in the form of an oblate spheroid. Corrections of inaccuracies and misprints made in similar works by other authors are proposed. The relationships between the formulas used in these works are found, taking into account the corrections and the formulas used in this work.

Second-harmonic generation in the surface layer of a dielectric spheroidal particle: I. Analytical solution

The problem of second-harmonic generation by a plane elliptically polarized electromagnetic wave in a thin optically nonlinear surface layer of a dielectric particle shaped as an ellipsoid of revolution is solved. The generalized Rayleigh-Gans-Debye approximation is used for an analytical description with taking into account the difference in refractive indices of the medium corresponding to the frequencies of the exciting and generated radiation. The limiting forms of functions are obtained, with the use of which the electric field strength of the generated radiation is expressed. The order of dependence of these functions on the linear dimensions is found, when the lengths of the semiaxes of the particle are small compared to the wavelength of the exciting radiation and their ratio remains constant. It was found that the power density of the generated radiation in this case is determined to a greater extent by the chiral components of the nonlinear dielectric susceptibility tensor and is proportional to the fourth power of the length of the semiaxis of the particle, if the shape of the spheroidal particle differs significantly from the spherical one. The solution of this problem, obtained by other authors, is supplemented for the possibility of applying to the description of generation in the surface layer of a dielectric particle not only in the form of a prolate, but also in the form of an oblate spheroid. Corrections of inaccuracies and misprints made in similar works by other authors are proposed. The relationships between the formulas used in these works are found, taking into account the corrections and the formulas used in this work. Keywords: second-harmonic generation, dielectric spheroidal particle, generalized Rayleigh-Gans-Debye model, small particle approximation, chiral component.

Second-harmonic generation in the surface layer of a dielectric spheroidal particle: II. Analysis of the solution

The vectors used in the solution of the problem of second-harmonic generation in the surface layer of a dielectric spheroidal particle are explicitly expressed in terms of the basis vectors of the spherical, cylindrical, and Cartesian coordinate systems. Three-dimensional directivity patterns characterizing the spatial distribution of the generated radiation in the far-field region and its polarization are constructed. It is found that for a small size of a spheroidal particle, the directivity pattern due to each of the non-chiral components of the nonlinear dielectric susceptibility tensor has its own individual shape. A proportional increase in the linear dimensions of the particle leads to separation of several directions of predominant radiation with a high directivity in the directivity pattern. If the exciting radiation has a linear polarization, then the generated radiation due to one (any) of the independent components of the tensor is also linearly polarized. Mathematical properties characterizing the spatial distribution of the generated radiation in the far-field region and properties associated with the change of problem parameters are found for the functions used in the solution. A relationship between the symmetries of the directivity patterns of doubled-frequency radiation and the indicated properties is revealed. The conditions under which the generation of radiation does not occur and the conditions under which the generated radiation has a linear polarization are found. The above conditions are related to the features of the spatial distribution of the generated radiation and its polarization, illustrated in the directivity patterns. Methods for estimating the independent components of the nonlinear dielectric susceptibility tensor using these conditions are proposed. Keywords: second-harmonic generation, spheroidal dielectric particle, symmetry of the spatial distribution of radiation, conditions for the absence of generation, conditions for the generation of linearly polarized radiation.

Генерация второй гармоники в поверхностном слое диэлектрической сфероидальной частицы: II. Анализ решения

The vectors used in the solution of the problem of second-harmonic generation in the surface layer of a dielectric spheroidal particle are explicitly expressed in terms of the basis vectors of the spherical, cylindrical, and Cartesian coordinate systems. Three-dimensional directivity patterns characterizing the spatial distribution of the generated radiation in the far-field region and its polarization are constructed. It is found that for a small size of a spheroidal particle, the directivity pattern due to each of the non-chiral components of the nonlinear dielectric susceptibility tensor has its own individual shape. A proportional increase in the linear dimensions of the particle leads to separation of several directions of predominant radiation with a high directivity in the directivity pattern. If the exciting radiation has a linear polarization, then the generated radiation due to one (any) of the independent components of the tensor is also linearly polarized. Mathematical properties characterizing the spatial distribution of the generated radiation in the far-field region and properties associated with the change of problem parameters are found for the functions used in the solution. A relationship between the symmetries of the directivity patterns of doubled-frequency radiation and the indicated properties is revealed. The conditions under which the generation of radiation does not occur and the conditions under which the generated radiation has a linear polarization are found. The above conditions are related to the features of the spatial distribution of the generated radiation and its polarization, illustrated in the directivity patterns. Methods for estimating the independent components of the nonlinear dielectric susceptibility tensor using these conditions are proposed.

Optimized Methodology for the Calculation of Electrostriction from First-Principles.

In this work a new method for the calculation of the electrostrictive properties of materials using density functional theory is presented. The method relies on the thermodynamical equivalence, in a dielectric, of the quadratic mechanical responses (stress or strain) to applied electric stimulus (electric or polarization fields) to the strain or stress dependence of its dielectric susceptibility or stiffness tensors. Comparing with current finite-field methodologies for the calculation of electrostriction, it is demonstrated that this presented methodology offers significant advantages of efficiency, robustness, and ease of use. These advantages render tractable the high throughput theoretical investigation into the largely unknown electrostrictive properties of materials, and the microscopic origins of giantelectrostriction.

Генерация второй гармоники-суммарной частоты в тонком сферическом слое. I. Аналитическое решение

The problem of the simultaneous second–harmonic and sum–frequency generation by two coherent plane electromagnetic waves with elliptical polarizations and equal frequencies in a thin spherical layer is solved in the Rayleigh–Gans–Debye model. The second–order dielectric susceptibility tensor is chosen in a form containing four independent components (including one chiral component). Fundamental differences are shown between the problem statements as well as between solutions to the problem of second–order nonlinear generation by several coherent electromagnetic waves and the problem of sum–frequency generation in the limiting case of equality of the frequencies of the incident waves. Combinations of parameters are determined at which the spatial distribution of the radiation generated as a result of incidence of two plane waves coincides with the distribution of second–harmonic radiation generated by one plane wave. The limiting cases of the obtained solution are considered: small and large radii of the spherical particle. In these cases the contributions of the chiral and non-chiral anisotropy coefficients to the generated radiation are determined.

Генерация второй гармоники-суммарной частоты в тонком сферическом слое: III. Свойства решения

Mathematical properties of functions characterizing symmetries of spatial distribution of second harmonic–sum frequency radiation are determined. The conditions at which there occurs no generation and the conditions at which the polarization of the generated radiation is linear are found. The revealed properties are systematized by their manifestations in the directivity patterns of the generated radiation. Methods based on these properties for determining the components of the nonlinear dielectric susceptibility tensor are proposed. The relationship is described between the revealed properties as well as conditions and previously found similar properties and conditions for the phenomena of second–harmonic generation and sum–frequency generation.

Second-Harmonic Generation from a Thin Cylindrical Layer: II. Analysis of Solution

The problem of second-harmonic generation by a plane elliptically polarized electromagnetic wave from a thin optically nonlinear layer on the surface of a cylindrical dielectric particle of finite dimensions placed in a dielectric medium has been solved analytically in the Rayleigh–Gans–Debye approximation. The result has been presented in the tensor and vector forms in the general case, in which the nonlinear dielectric susceptibility tensor has four independent components (one chiral component and three nonchiral components). It has been shown for the first time that the contribution of chiral components to the generation from the butt-end surfaces of a cylindrical particle differs in phase from the contribution of nonchiral components. It has also been revealed that, if the linear dimensions of a cylindrical particle (height and base radius) are small, the radiation determined by the chiral component of the second-order nonlinear dielectric susceptibility tensor makes a predominant contribution to the second-harmonic generation from a nonlinear cylindrical layer (butt-end and lateral surfaces).

Генерация второй гармоники от тонкого цилиндрического слоя. I. Аналитическое решение

In the Rayleigh–Gans–Debye approximation an analytical solution is obtained for the problem of second harmonic generation by a plane electromagnetic wave with elliptical polarization from a thin optically nonlinear layer on the surface of a cylindrical dielectric particle of finite size placed in a dielectric. The result is presented in tensor and vector forms in general case, in which the nonlinear dielectric susceptibility tensor has four independent components (one chiral and three non-chiral). For the first time it is shown that at generation from the end plane surfaces of a cylindrical particle the contribution of chiral components differs in phase from that of non-chiral components. It is also found that for small linear dimensions of the cylindrical particle (height and radius of the base), the radiation due to the chiral component of the second-order nonlinear dielectric susceptibility tensor makes a dominant contribution to the second harmonic generation from a non-linear cylindrical layer (end and side surfaces).

Sum-Frequency Generation from a Thin Cylindrical Layer

In the Rayleigh–Gans–Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.

Revealing modes from controlling an off-optical axis conical diffraction laser

Thanks to controlling the off-optical axis propagation in the monoclinic KGd(WO4)2:Nd biaxial crystal used as a laser gain medium, we exhibited remarkable crescent laser modes and mode switching, demonstrating the preservation of the conical diffraction. We revealed an optical singularity in addition to the optical axis: the directions of polarization changed abruptly to the highest emission cross-section mode, which leads to un-polarized lasing. The key explanation is a severe mode selection due to the threshold behavior of lasing. This is confirmed by a theoretical model taking into account a two-axes crystal rotation and including the conical diffraction behavior. The rotation around the two-fold b crystallographic axis of the frame, which makes the imaginary part of the dielectric susceptibility tensor diagonal, is exhibited.

Dynamic dielectric and magnetic properties of a spontaneously polarized single layer of the polar dielectric

In the framework of the Debye–Smoluchowski theory and in local electric field approximation, an expression of the dielectric susceptibility tensor is derived for a single layer of spontaneously polarized polar dielectric in the field of a monochromatic radiation. It is shown that the AC radiation also generates or induces magnetic moments with a density that is expressed by the components of the dielectric susceptibility tensor of the layer.

Second-harmonic generation from a thin spherical layer and No-generation conditions

In the Rayleigh–Gans–Debye approximation, we solve the problem of second-harmonic generation by an elliptically polarized electromagnetic wave incident on the surface of a spherical particle that is coated by an optically nonlinear layer and is placed in a dielectric. The formulas obtained characterize the spatial distribution of the electric field of the second harmonic in the far-field zone. The most general form of the second-order dielectric susceptibility tensor is considered, which contains four independent components, with three of them being nonchiral and one, chiral. Consistency and inconsistencies between the obtained solution and formulas from works of other authors are found. We analyze the directivity patterns that characterize the spatial distribution of the generated radiation for the nonchiral layer and their dependences on the anisotropy and ellipticity coefficients of the incident wave. It is found that, with increasing radius of the nonlinear layer, the generated radiation becomes more directional. Combinations of parameters for which no radiation is generated are revealed. Based on this, we propose methods for experimental determination of the anisotropy coefficients.

Dielectric properties of crystalline organic molecular films in the limit of zero overlap.

We present the calculation of the static dielectric susceptibility tensor and dipole field sums in thin molecular films in the well-defined limit of zero intermolecular overlap. Microelectrostatic and charge redistribution approaches are applied to study the evolution of dielectric properties from one to a few molecular layers in films of different conjugated molecules with organic electronics applications. Because of the conditional convergence of dipolar interactions, dipole fields depend on the shape of the sample and different values are found in the middle layer of a thick film and in the bulk. The shape dependence is eliminated when depolarization is taken into account, and the dielectric tensor of molecular films converges to the bulk limit within a few molecular layers. We quantify the magnitude of surface effects and interpret general trends among different systems in terms of molecular properties, such as shape, polarizability anisotropy, and supramolecular organization. A connection between atomistic models for molecular dielectrics and simpler theories for polarizable atomic lattices is also provided.

Counter-Ions Near a Charged Wall: Exact Results for Disc and Planar Geometries

Macromolecules, when immersed in a polar solvent like water, become charged by a fixed surface charge density which is compensated by ``counter-ions'' moving out of the surface. Such classical particle systems exhibit poor screening properties at any temperature and the trivial bulk regime (far away from the charged surface) with no particles, so the validity of standard Coulomb sum rules is questionable. In the present paper, we concentrate on the two-dimensional version of the model with the logarithmic interaction potential. We go from the finite disc to the semi-infinite planar geometry. The system is exactly solvable for two values of the coupling constant $\Gamma$: in the Poisson-Boltzmann mean-field limit $\Gamma\to 0$ and at the free-fermion point $\Gamma=2$. We show that the finite-size expansion of the free energy does not contain universal term as is usual for Coulomb fluids. For the coupling constant being an arbitrary positive even integer, using an anticommuting representation of the partition function and many-body densities we derive a sequence of sum rules. As a result, the contact density of counter-ions at the wall is available for the disc. The amplitude function, which characterizes the asymptotic inverse-power law behavior of the two-body density along the wall, is found to be related to the particle density profile. The dielectric susceptibility tensor, calculated exactly for an arbitrary coupling and the particle number, exhibits the anticipated disc value in the thermodynamic limit, in spite of zero contribution from the bulk region. Some of the results obtained in the Poisson-Boltzmann limit are generalized to an arbitrary Euclidean dimension.

First principles investigations of structural, electronic, elastic, and dielectric properties of KMgF3

An ab initio study of structural, electronic, elastic, and dielectric properties of KMgF3 in cubic perovskite structure is presented in the framework of density functional theory. The calculations presented here employ generalized gradient approximation with projector augmented wave method. The fully relaxed structural parameters are found to be in reasonable agreement with available experimental data and with previous theoretical work. The independent elastic constants of cubic KMgF3 are derived from the derivative of total energy as a function of lattice strain in full detail. The bulk modulus and its first pressure derivative are obtained by fitting total energy versus volume data to a Murnaghan equation of state. The electronic band structure, total density of states, and projected density of states on each of the K, Mg, and F atoms are calculated and found to be in good agreement with previous theoretical results. First principles computed phonon dispersions for the cubic KMgF3 are reported for the first time. The imaginary part of frequency-dependent dielectric function is determined by summing over all possible transitions from occupied to unoccupied states and taking the appropriate transition matrix element into account. The Born effective charges computed by linear response within density functional perturbation theory are used together with the mode eigenvectors to decompose the lattice dielectric susceptibility tensor into contributions arising from individual IR-active phonon modes. Our results for the static and optical dielectric constant are in good agreement with previously reported experimental results.

Magnetoelectric susceptibility tensor of multiferroic TbMnO3 with cycloidal antiferromagnetic structure in external field

Magnetoelectric, dielectric, and magnetic susceptibility tensors of multiferroic TbMnO3 with cycloidal antiferromagnetic structure in external electric and magnetic fields have been investigated with taking into account dynamics of spin, electro-dipole, and acoustic subsystems. All components of tensors depend on values of external electric and magnetic fields. The possibility of control of electrodynamic properties of multiferroic TbMnO3 with cycloidal antiferromagnetic structure by external electric and magnetic fields has been shown. The resonant interaction of spin, electro-dipole, electromagnetic, and acoustic waves in such material is observed.

Refraction indices of spatially nonuniform magnetic systems and nanostructures from the first principles

An equilibrium two-time temperature Green’s function (TTGF)-based, quantum statistical mechanical approach has been used to derive from the first principles an explicit expression for the tensor of “local” refraction indices of spatially nonuniform systems in weak external electromagnetic (EM) fields in the linear approximation with regard to the field magnitudes. Written in terms of the TTGF-based, first-principle tensorial dielectric and magnetic susceptibilities, the obtained formula for the local tensor of refraction indices (TRI) is applicable to any system, including individual nanoscale objects, such as quantum dots and wires, magnetic nanostructures, composite materials, or spatially nonuniform, bulk magnetic materials. An explicit expression for the space-time Fourier transform (STFT) of the dielectric susceptibility tensor used in TRI is derived in terms of STFTs of the charge density—charge density TTGFs, while the corresponding STFT of the magnetic susceptibility tensor also includes STFTs of the microcurrent—microcurrent TTGFs. The STFTs of the equilibrium TTGFs featuring in the susceptibilities, and thus necessary to calculate TRI, can be obtained by equilibrium quantum statistical mechanical means, modeling and simulations, or from experimental data. Two TRI regimes of significant interest for applications that can be realized in spatially inhomogeneous magnetic systems have been identified.