Principal Dielectric Constants Research Articles

Conical diffraction and the dispersion surface of hyperbolic metamaterials

Hyperbolic metamaterials are materials in which at least one principal dielectric constant is negative. We describe the refractive index surface, and the resulting refraction effects, for a biaxial hyperbolic metamaterial, with principal dielectric constants $\epsilon_1<0$, $0<\epsilon_2\neq\epsilon_3$. In this general case the two sheets of the index surface intersect forming conical singularities. We derive the ray description of conical refraction in these materials, and show that it is topologically and quantitatively distinct from conical refraction in a conventional biaxial material. We also develop a wave optics description, which allows us to obtain the diffraction patterns formed from arbitrary beams incident close to the optic axis. The resulting patterns lack circular symmetry, and hence are qualitatively different from those obtained in conventional, positive index materials.

On the Nature of Molecular Associations, Static Permittivity and Dielectric Relaxation in a Uniaxial Nematic Liquid Crystal

One fluorinated terphenyl compound was studied by polarizing microscopy, x-ray diffraction and dielectric spectroscopy. It exhibits the nematic phase over a range of 107.80. The average intermolecular distance was observed to be more than in systems without any lateral fluorine substitution. Apparent molecular length was found to be more than the molecular model length, suggesting presence of antiparallel molecular associations. Optimized geometry, obtained by molecular modeling, yielded a dipole moment of 6.68 D. The observed principal dielectric constants are consistent with respective components of dipole moments and show quite a high value of dielectric anisotropy. The threshold voltage and the splay elastic constant have also been determined. Flip-flop mode dielectric relaxation frequency is found to increase with temperature, and the activation energy for the process is found to be 35.53 kJ mol–1.

Optical properties of strongly anisotropic metamaterials

We study the behavior of wave propagation in strongly anisotropic metamaterials with different principal dielectric constants. Analytical expressions of the dispersion relation, Poynting vector, and group velocity are derived theoretically. The light propagation properties for TM and TE waves in these metamaterials are explored, in which the backward wave, negative refraction, phase-compensation effects, and far-field propagation wave carrying subwavelength information are discussed. These theoretical results are supported by numerical simulation.

Dielectric Constant of Ice Ih and Ice V: A Computer Simulation Study

In this work, we exploit an efficient algorithm for the sampling of hydrogen-bond networks in order to study the order/disorder transition and the dielectric properties of ice Ih. Our results show that all of the rigid point charge models studied, TIP4P/Ice, TIP4P/2005, TIP4P, and SPC/E, yield a very low dielectric constant as compared with experiment. The analysis of the polarization factor, G, reveals that the structure of ice Ih as predicted by the TIP4P family of models studied is very similar. For all such models, G approximately 2.5, the differences in the dielectric constant being given mainly by the different molecular dipole moments. The angular correlations in the SPC/E model are very different, however, yielding G approximately 1.8. Our study suggests that the dielectric anisotropy of ice Ih is very small and at any rate smaller than the statistical uncertainty of our results. We show that for sufficiently anisotropic structures, such as ice V, the method employed does indeed reveal a strong anisotropy. At 5000 bar and 180 K, we find that the principal dielectric constants of ice V according to the TIP4P/Ice model are 34, 164, and 76. The order/disorder transition could not be well characterized, because of very strong hysteresis. Whereas low temperature ordered phases were readily disordered at temperatures below 50 K, the high temperature phase remained disordered upon cooling. Nevertheless, our plots of dielectric constant versus temperature reveal a clear lambda-like shape and obey a Curie-Weiss law. All of the models studied show a higher stability of the antiferroelectric Pna2(1) phase than the experimental ferroelectric Cmc2(1) phase.

Electroconvection in a Homeotropic Bent-Rod Nematic Liquid Crystal Beyond the Dielectric Inversion Frequency

We characterize the structural transitions in an initially homeotropic bent-rod nematic liquid crystal excited by ac fields of frequency f well above the dielectric inversion point fi. From the measured principal dielectric constants and electrical conductivities of the compound, the Carr-Helfrich conduction regime is anticipated to extend into the sub-megahertz region. Periodic patterned states occur through secondary bifurcations from the Freedericksz distorted state. An anchoring transition between the bend Freedericksz (BF) and degenerate planar (DP) states is detected. The BF state is metastable well above the Freedericksz threshold and gives way to the DP state, which persists in the field-off condition for several hours. Numerous +1 and -1 umbilics form at the onset of BF distortion, the former being largely of the chiral type. They survive in the DP configuration as linear defects, nonsingular in the core. In the BF regime, not far from fi, periodic Williams-like domains form around the umbilics; they drift along the director easy axis right from their onset. With increasing f, the wave vector of the periodic domains switches from parallel to normal disposition with respect to the c vector. Well above fi, a broadband instability is found.

Physical characterisation of 4′-butyl-4-heptyl- bicyclohexyl-4-carbonitrile

We report measurements of birefringence, bend elastic constant, principal dielectric constants and conductivities as functions of temperature in the nematic phase of 4′-butyl-4-heptyl-bicyclohexyl-4-carbonitrile (CCN-47). The compound exhibits a small birefringence and a large negative dielectric anisotropy. Surprisingly, it shows a negative conductivity anisotropy, which probably owes its origin to the structural details of the molecules. The orientational order parameters (S) are estimated from both birefringence and dielectric anisotropy, and they agree well in the entire nematic range. The experimental results are compared with those on CCH7, which has a similar core structure but with a longitudinal dipole moment, in place of the transverse one of CCN-47.

Optimization of antiferroelectric liquid crystal devices at the degeneration point

Antiferroelectric liquid crystals (AFLCs) with 45° tilt angle have been shown recently [K. D’hav’e, Per Rudquist, S. T. Lagerwall, H. Pauwels, W. Drzewinski, and R. Dabrowski, Appl. Phys. Lett. 76, 3528 (2000)] to exhibit true dark state between crossed polarizers at normal incidence. We show that this situation is possible at any incidence or any tilt angle depending on the principal dielectric constants ε1–3. In particular, when the deviation of ε1 from the average (ε2+ε3)/2 is small, the medium behaves nearly as isotropic medium. Hence using this class of AFLC materials it will be possible to build full color, high-resolution displays with large viewing angular range. The optimum viewing angular cone will be obtained when the degeneracy point corresponds to 45° incidence angle and tilt angle anywhere from 0 to 45° depending on the values of the principal dielectric constants and, in particular, on the biaxiality. For the uniaxial case this angle is practically 41°–42° without dependence on the optical anisotropy.

Long-wavelength limit (homogenization) for two-dimensional photonic crystals

Using the Fourier expansion method in the low-frequency limit we develop an effective-medium theory for two-dimensional (2D) periodic composites. We give a rigorous proof that, in this limit, a periodic medium behaves like a homogeneous one and we derive compact analytical formulas for the effective dielectric constants of a 2D photonic crystal, i.e., a periodic arrangement of infinite cylinders. These formulas are very general, namely the Bravais lattice, the cross-sectional form of cylinders, their filling fractions, and the dielectric constants are all arbitrary. So is the direction of propagation of the Bloch wave---out of plane in general, with special attention paid to the limiting cases of propagation in the plane of periodicity and parallel to the cylinders. In the latter case we report a behavior that is qualitatively different from that encountered in natural crystals and in 3D photonic crystals. Namely, for propagation along the cylinder axes, the wave fronts are not plane but rippled, with the distribution of the ripples following the pattern of the 2D Bravais lattice. We also demonstrate that the other long-wavelength optical properties can be described by means of the index ellipsoid. This allows us to apply the classification used in the optics of natural crystals (``crystal optics'') to photonic crystals. Namely, we characterize the photonic crystal entirely in terms of its three ``principal'' dielectric constants. One of these is associated with the direction parallel to the cylinders, and is given simply by the spatially averaged dielectric constant. For the two in-plane principal dielectric constants we derive three representations that are equivalent in principle, however, give rise to different rates of numerical convergence, depending on whether the dielectric constant or its reciprocal have been expanded in a Fourier series (respectively, $``\ensuremath{\varepsilon}$ representation'' and ``\ensuremath{\eta} representation''). Numerical results are given for a uniaxial (biaxial) photonic crystal with square (rectangular) lattice and circular cylinders. We conclude that for dielectric cylinders in air the \ensuremath{\eta} representation leads to much better convergence than the $\ensuremath{\varepsilon}$ representation. The opposite holds for air cylinders in a dielectric. The accuracy is checked by applying Keller's theorems to conjugate structures.

Contribution prom thermoelastic and electroelastic fields to effective properties of multilayer piezoelectric textures of the piezoceramics/metal type

Abstract Exact solutions have been obtained in terms of a model of the thermoelectroelastic medium characterized by one-dimensional nonuniformity of its physical properties for principal effective piezoelectric, dielectric, elastic and pyroelectric constants of a multilayer structure of the piezoceramics/metal type. A case is discussed of the ceramic poled orthogonal to the plane of the layers which can be used as sensitive elements of piezoceramic sensors.

A Method for Determination of Elastic Constants K1, K2, K3 of a Nematic Liquid Crystal Only Using a Homogeneously Aligned Cell

It is shown that three Frank elastic constants K1, K2 and K3 of a nematic liquid crystal can be determined by measuring the capacitance change with a magnetic field of a homogeneously aligned cell. The splay elastic constant K1 is determined from the threshold magnetic field strength Hc1 when the magnetic field is applied normal to the cell. The bend elastic constant K3 is determined from the slope of the linear dependence between the inverse of the capacitance 1/C and the inverse of the magnetic field strength 1/H in the high field region H/Hc1> 3. The twist elastic constant K2 is determined from the threshold field strength when the magnetic field is applied oblique to the cell normal but perpendicular to the initial director. In these procedures, principal dielectric constants ε//, ε⊥, dielectric anisotropy Δε, anisotropy of the magnetic susceptibility Δχ can be determined simultaneously.

Characteristic Impedance of the Slab Line with an Anisotropic Dielectric (Short Papers)

The characteristic impedance of the slab line with a circular conductor having an anisotropic dielectric is presented by rising the affine and conformal transformations. Moreover, a simpler approximate formula of the impedance expressed in term of epsilon /spl par/, epsilon /spl perp/, and r/h is also presented, where epsilon /spl par/, epsilon /spl perp/ r, and h, are the principal axes-relative dielectric constants of the anisotropic dielectric, the inner conductor radius, and the half Iength between ground planes, respectively.

The low temperature electrical properties of some anisotropic crystals

The principal complex dielectric constants have been studied at audio frequencies over the temperature range 5.5–380K for α-quartz, sapphire, magnesium fluoride, and calcite. For some samples, the imaginary part of the dielectric constant revealed the presence of dipolar or thermally activated loss mechanisms which are attributed to trace impurities. The effects of these impurities are considered in arriving at values of the real part of the dielectric constants for each of the materials.

Dielectric properties of 4′-n-alkyl-4-cyanobiphenyls in their nematic phases

The principal dielectric constants of the pentyl to octyl derivatives of 4′-n-alkyl-4-cyanobiphenyl have been measured as functions of temperature in their nematic and isotropic phases. All the compounds exhibit a strong positive dielectric anisotropy due to the presence of a large dipole moment along the major molecular axis. The principal dielectric constantse ‖ ande ⊥ as well as the anisotropy Δe decrease with increasing alkyl chain length. The experimental value of $$\bar \in = \frac{1}{3}$$ (e‖+2e⊥) decreases with decreasing temperature, and is throughout less than the extrapolated isotropic value, in conformity with the model of antiferroelectric short range order proposed by Madhusudana and Chandrasekhar.

The dielectric constants of axially isotropic composite materials

An exact expression is obtained for the principal dielectric constants of a macroscopically homogeneous and axially isotropic two-phase composite material. This is compared with the result obtained in the isotropic case. Upper and lower bounds are given. They are shown to be attainable and are found to depend upon the direction of the applied field. Approximate power-law formulae are derived and their applicability discussed in terms of the internal geometry of the sample. It is suggested that these approximate formulae may be usefully applied to polymer-polymer mixtures. It is further shown that except for the Looyenga third-power formula they are not applicable to isotropic samples.

Optical Properties of Calcite in the Vacuum Ultraviolet

The reflection spectra of calcite single crystal have been measured in the region 5-12 eV with polarized light normally incident upon the cleaved surface (10\bar11). The principal dielectric constants are determined from the spectra using Fresnel's equation as well as the Kramers-Kronig relation. For the ordinary ray, a strong absorption band is found around 8 eV in the e 2 spectrum, whereas almost no absorption below 9 eV for the extraordinary ray. From the temperature dependence of the spectra this dichroic absorption band is attributed to the intramolecular dipole transition A 1 '→ E ' in the planar CO 3 - radical. It is concluded that the high birefringence in the transparent region (<6 eV) is almost due to the strong dichroic absorption band at 8 eV.

Electric Effects in MBBA/PEBAB Mixtures

Abstract The principal low-frequency dielectric constants have been measured for the binary mixture (MBBA)1-x (PEBAB) x' , for mole fractions up to x = 0.21. In this range Δ∊ varies linearly with x changing sign at x∼ 0.02, and a room-temperature mesophase is preserved. Eor Δ∊ 0, we study the Freedericksz transition, using an approximation which leads to a closed-form expression for the variation of phase retardation with voltage. Electrohydrodynamic instabilities are observed in the positive regime.

Optical Properties of Sodium Nitrate in the Vacuum Ultraviolet Region

The reflectivity spectra of NaNO 3 single crystal have been measured in the region from 4 to 12 eV with polarized light normally incident upon the cleaved surface (10\bar11). Two principal dielectric constants, \(\hat{\varepsilon}_{\text{o}}\) and \(\hat{\varepsilon}_{\text{e}}\), have been derived from the spectra with the application of the Kramers-Kronig relation and the equation of dielectric ellipsoid for uniaxial crystals. The profile of the absorption spectrum derived from the reflectivity is in good agreement with the absorption spectrum of thin films, particularly with respect to the bands at about 6 eV and 10.5 eV. It is found that the 6 eV band is active to light polarized perpendicularly to the c axis and the oscillator strength of the band is 0.4 9 per NO 3 - molecule. These facts support the previous assignment that the absorption is due to π 2 →π * ( A 1 '→ E ') in NO 3 - . The 10.5 eV band is found to be active to light polarized perpendicularly to the c axis, and is assigned to the electron transfer from the n 2 ( e ') orbitals of NO 3 - to the Na + –3s orbital.

Selective Reflection by Cholesteric Liquid Crystals

Abstract Selective light reflection at the plane structure of a cholesteric liquid crystal is treated by the theory of de Vries(1) for normal incidence only. A more general approach is outlined for arbitrary angles of incidence. Conditions for the borders of the reflection bands are given. Also the cases of ordinary total reflection are included. Using the derived formula, the two principal dielectric constants are determined from the angles of total reflection measured with a refrectometer. Their values are used to calculate ther eflection spectrum of a layer of finite thickness at normal incidence which is compared with an experimental spectrum. In agreement with the experimental curve the calculated spectrum shows a central band with a nearly rectangular shape flanked by a series of maxima and minima due to interferences, the positions of which depend strongly on the dielectric constants.

The measurement of the principal dielectric constants of sapphire by a mechanical action method

A new mechanical action method for the determination of the principal dielectric constants of synthetic sapphire is described. It is based on measurements of the couple experienced by a sphere of the material suspended in a uniform electric field. The values were found to be [perpendicular] = 79 ± 05 and [parallel] = 65 ± 04 when measured at a frequency of 50 Hz, and these values compare favourably with those obtained by other methods. The method may be applied to anisotropic crystals in general, and it is suggested that with slight modification it may be used for the corresponding electrical conductivity determinations.

Dielectric Relaxation in Nematic Liquid Crystals

Abstract In homogeneously ordered liquid crystals of the nematic type, two principal dielectric constants can be measured: ϵ1 parallel and ϵ2 perpendicular to the symmetry axis of the liquid crystal. The two dielectric constants may show a very different relaxation behavior. With alkoxy derivatives of azobenzene, only the normal Debye dispersion region at microwave frequencies has been observed. With alkoxy derivatives of azoxybenzene, ϵ2 shows again only the normal Debye dispersion region at microwave frequencies, but ϵ1 has an additional dispersion at very unusually low frequencies in the radio region. This dispersion is due to the permanent electric dipole momment of the azoxy group, more exactly to its component parallel to the long molecular axis. The reorientation of this component in direction 1 is hindered by a potential barrier due to intermolecular forces. The corresponding relaxation time is increased by a factor g. Starting from a modification of the Debye theory of dielectric relaxation, this retardation factor may be used to calculate the height of the potential barrier. Numerical values are in satisfactory agreement with other values, calculated from the observed long range order.