Isotropic Substrate Research Articles

Orientational self-organization in nematic thin film layer sandwiched between conducting isotropic substrates

The dependence of the anisotropic free energy of a nematic liquid crystal in contact with conducting substrates on the value of the angle between the director and the easy orientation axis was evaluated theoretically. The differences between the obtained form of the free energy's angular dependence mentioned above and the traditional form of the Rapini potential are discussed in detail. The peculiarities are mainly caused by the input of the two-component polarized liquid crystalline layer to the total surface energy. The coordinate dependences of ionic and dipolar polarizations are calculated, as well as the order parameter controlling the self-organization of the dipole momenta of the liquid crystal's molecules. The mutual influence of the interface polarization value and the self-consistent director orientation in the vicinity of the substrate surface was explained on the basis of the proposed model. The results obtained may be applied to the problem of the orientative influence of the substrate covered with various surfactants on the contrast and color demonstration scale in flat panel displays.

First and second order velocity shifts and reflection coefficients for periodic interdigital transducers by boundary condition matching

The method of boundary condition matching is utilized to determine reflection coefficients and velocity shifts for surface acoustic wave devices mechanically and electrically loaded by a periodic grating. The method has previously been limited to grooved gratings in isotropic substrates, but is here extended to allow for anisotropic and piezoelectric substrates as well as arbitrary overlay materials which allows for the modeling of metallic electrode interdigital transducers. Upper and lower stop band frequencies are determined by imposing the proper grating boundary conditions. From these frequencies is calculated both first and second order contributions in h/λ (where h is the grating finger height and λ the wavelength) to the reflection coefficient and velocity shift due to the loading of the substrate. The presence of the grating also couples the incident surface acoustic waves to evanescent and bulk modes. The attenuation of the incident Rayleigh waves due to bulk mode conversion is discussed as well. Numerical results for some common substrate and overlay materials are given and a comparison of the relative strengths of the first and second order contributions for specific values of h/λ is made. Some comparisons with experimental data are also given with good results for sufficiently small h/λ.

Thermal shock resistance of SiC compositionally graded C/C composites

Thermal shock resistance of SiC compositionally graded carbon fiber reinforced carbon composite (CFC) materials that are composed of a CVD SiC layer, a SiC/C graded layer and a CFC substrate was studied by thermal shock tests in air. Two types of CFCs were used: 1-D continuous fiber reinforced and 2-D felt reinforced composites. It was found that the SiC/C graded layer was to some extent effective to increase the resistance and that its effectiveness was larger when a difference in thermal expansion coefficient (CTE) between a substrate and β-SiC was smaller. The degree of an improvement of the thermal shock resistance for CFC substrates was lower than that for isotropic graphite substrate. The difference was attributed to the original cracks in CVD SiC layers on CFC substrates.

Analysis of binary diffraction gratings: Comparison of different approaches

Diffraction characteristics of periodic binary diffractive structures are studied using three different theoretical approaches. Namely rigorous coupled-wave analysis (RCWA), Kogelnik's two-wave method, and the scalar method of transmittance have been applied to study diffraction characteristics and have been compared, and their applicability has been determined. For comparison purposes, a binary surface-relief grating made from an isotropic non-absorbing substrate in the planar diffraction regime, and a transverse electric polarized incident wave, are considered in this paper. Additionally, by calculating the diffraction efficiency of such gratings using the RCWA method, with special respect to grating profile depth and period, it was possible to describe and explain the complex behaviour of diffraction efficiency, that is to find regions with typical diffraction regimes, of all gratings of a chosen kind, in this case given by the binary grating profile. Moreover, it has been shown how the classical scalar transmittance method for analysis of thin diffraction gratings can be modified by an estimation of the propagation process through the grating depth in order to describe the volume phase synchronism dependence on the relative grating period.

Three polarization reflectometry methods for determination of optical anisotropy

Three novel methods for the determination of optical anisotropy are proposed and tested. The first, the special points method, may be applied to any uniaxially anisotropic medium and is based on the measurement of s- and p-polarized light reflectances under near-normal or grazing angles (or both) and of the Brewster angle. The second method is based on the use of the Azzam universal relationship between the Fresnel s- and p-reflection coefficients. For a flat surface and an isotropic medium, the Azzam combination of coefficients becomes zero and thus is independent of the incidence angle, whereas for a uniaxial or biaxial anisotropic sample it acquires a certain angular dependence, which may be used to determine the anisotropy of the sample. Finally, for those cases in which the anisotropy of the material of a film deposited on an isotropic substrate is itself of interest, a third method, the interference method, is suggested. This technique makes use of the different dependences of s- and p-polarized beam optical path-length changes on the variation of the angle of incidence.

An application of wavelet bases in the spectral domain analysis of transmission line discontinuities

The local support and vanishing moment property of wavelet bases have been recently used to obtain a sparse matrix representation of integral equations in the spatial domain. In this paper, an application of the cubic spline and the corresponding semi-orthogonal wavelets in the spectral domain is proposed for the evaluation of the reflection coefficient for open/short transmission lines. Because of the nearly optimal time (space)–frequency (wavenumber)–window product of the cubic spline and wavelet, the double spectral integrals appearing in the formulation can be computed more efficiently than with the commonly used piecewise sinusoidal (PWS) or triangular basis functions. It is shown that the time–frequency-window product of the triangular and PWS function are close to each other, whereas those of the cubic spline/wavelet are close to 0·5, the lowest possible value corresponding to functions of Gaussian class. Both the PWS and wavelet bases are applied to microstrip and coplanar waveguides with isotropic and anisotropic substrates, and the results are compared with published theoretical and experimental data. It is observed that even though the number of splines/wavelets required for an accurate representation of the current distribution in the transmission line is almost twice as high as the number of PWS functions, the overall computation time decreases significantly in the former case. © 1998 John Wiley & Sons, Ltd.

Surface acoustic wave technology for poisson ratio sensors

The phase velocity of surface acoustic waves (SAWs) propagating in structures consisting of an isotropic substrate and a thin isotropic layer is considered theoretically. The dependence of the change in the phase velocity on the Poisson ratio of a thin layer is presented. It is shown that the Poisson ratio of the layer may be determined from the results of the phase-velocity measurements. An appropriate analytic expression is given. Numerical simulations for LiNbO 3 and SiO 2 substrates with thin Al and W layers demonstrate a change of SAW velocity by (5–8)% under variation of the Poisson ratio of the layer from 0.1 to 0.4.

On the macroscopic and microscopic origin of the photovoltaic effect in YBCO thin films

The study of a photovoltaic component of the net voltage arising in illuminated YBCO thin films with different morphology was carried out. The anisotropy of the photovoltages in the film plane correlates with the anisotropy of such physical characteristics of the samples as resistivity and microwave absorption and implies the existence of a macroscopic preferential direction even in the film deposited on an isotropic MgO substrate. Disappearance of the photovoltaic signal below T c in the films exhibiting an appreciable residual resistivity is an unambiguous indication of its relation with extended defects inside the superconducting YBCO phase. A model for the microscopic asymmetry of the flow of the photocurrent generated at the boundaries of an isolated defect was proposed, and the contributions coming from some types of extended structural defects into the effect were estimated.

Microstrip transmission line tapers on ferrites

The spectral domain approach is employed to perform a theoretical investigation of tapered microstrip lines on magnetized ferrite substrates. A linear variation of the conducting strip width along the direction of propagation is considered. The analysis takes into account the effects of the applied dc magnetic bias field in the transmission characteristics of these structures. The properties of the taper are determined by a model based on a segmentation of the considered line into uniform microstrip line subsections. Normalized phase constants and characteristic impedances are obtained by using the Hertz vector potentials method and Galerkin numerical technique. Numerical results are presented to show the taper input parameters as a function of the load impedance, geometrical dimensions, operating frequency, and ferrite parameters, considering the orientation and magnitude changes of the biasing magnetic-field H0. The results agree fairly well with those available in the literature for tapered microstrip lines on isotropic dielectric substrates.

An application of FDTD in studying the end effects of slotline and coplanar waveguide with anisotropic substrates

In this paper, the finite-difference time-domain (FDTD) method is applied in conjunction with the generalized pencil of function (GPOF) technique to evaluate the reflection coefficient from shorted slotlines and coplanar waveguides (CPW) on anisotropic substrates, and to extract the propagation constant along the line from these data. For each frequency, the field solutions at different locations are processed by using the GPOF technique to extract two complex exponents that correspond to the forward and backward traveling waves, which provide all the information about the reflection coefficient and the dispersion characteristic of the transmission line. The advantage of combining the GPOF technique with the FDTD method is that the reflection coefficients can be obtained with a single run. Recognizing that there is a dearth of results for the reflection coefficients of slotline and CPW-line discontinuities with anisotropic substrates, the present problem is also solved by using the spectral-domain method for the purpose of validation, and the two results are found to compare quite well with each other. For further validation, the FDTD and GPOF solutions are derived for isotropic substrates, and are compared with the published theoretical and experimental results.

Modeling variations of Rayleigh wave velocity due to distributions of one-dimensional surface-breaking cracks

A model describing changes of Rayleigh wave velocity caused by distributions of one-dimensional, surface-breaking cracks is presented. The concept of effective medium and the assumption of noninteracting cracks are used in the model. This approach is developed in the low-frequency limit. A real cracked surface is modeled by a homogeneous, anisotropic layer on top of an isotropic substrate. The substrate’s elastic properties are those of the original isotropic half-space, whereas those of the layer are modified by the presence of the crack distribution. Distributions are considered where parameters such as crack density, crack depth, crack depth distribution, and crack orientation are varied. Variations of surface acoustic wave (SAW) velocity are reported for all these cases. SAW velocity is shown to be most sensitive to changes in crack density and crack depth. Negative variations of Rayleigh wave velocity are predicted to be up to 3% even for distributions of rather shallow cracks. These results show that variations of SAW velocity caused by crack distributions are much larger than those due to other forms of surface damage such as surface roughness or residual stresses.

First-order velocity shift and reflection coefficient for surface acoustic wave propagation

Design of surface acoustic wave (SAW) devices requires accurate values of velocity shift q and reflection coefficient r associated with finger overlays placed on the substrate material. In previous treatments variational and perturbative approaches have been developed for calculating first-order reflection coefficients and velocity shifts; however, the anisotropic substrate materials have until now been modeled by an effective isotropic substrate. We extend the variational and perturbative calculations of the first-order quantities to fully anisotropic crystals for several standard SAW substrate and overlay materials. Moreover, we report results obtained with both electrically free and shorted trial functions, and suggest optimum parametrizations of q and r, to first order in h/λ, where h is the finger thickness and λ is the Rayleigh wavelength.

Application of GIBCs to the computation of resonant frequencies for uniaxial cylindrical resonators

Numerical analysis for computing resonant frequencies of uniaxially anisotropic cylindrical resonators is presented. The resonator is placed on a grounded isotropic substrate and is covered with a metallic tuning plate. The generalized impedance boundary conditions are employed along the axis of the resonator to simplify the boundary-value problem. Ample numerical results are presented, explicitly showing the dependent of the resonant frequency on the variation in the elements of the permittivity tensor. © 1996 John Wiley & Sons, Inc.

Electromagnetically Coupled Dipole Antennas in Nonreciprocal Microstrip

ABSTRACT An integral equation approach is used to study the radiation and matching characteristics of an electromagnetically coupled dipole antenna. The dipole is located on top of a generalized anisotropic superstrate, which is itself on top of a grounded isotropic substrate. The feeding transmission line lies at the interface between these two layers. The integral equation is solved rigorously using the method of moments to find the current distribution on both conductors. Nonreciprocal transmission line analysis is then used to quantify how well the microstrip dipole and transmission line are matched based on the current distribution. Special considerations and advantages in the design of this type of antenna are discussed.

Existence of a leaky dominant mode on microstrip line with an isotropic substrate: theory and measurements

A newly discovered leaky dominant mode is reported for conventional microstrip line on an isotropic substrate, at higher frequencies. The existence of this leaky mode has been confirmed both numerically and experimentally. This new mode exists independently of, and in addition to, the customary bound dominant mode. It leaks power away from the line into the fundamental TM/sub 0/ surface wave of the surrounding grounded substrate, and may therefore be responsible for spurious microstrip circuit performance at higher frequencies. This could have important implications for millimeter-wave circuits.

Analysis of the Coupling Between Rectangular Microstrip Patches on Uniaxial Anisotropic Substrates

The effect of the dielectric anisotropy in the behavior of the resonant frequencies of coupled microstrip patches is investigated. In the analysis, the Hertz vector potentials technique, in the spectral domain, is used to determine the field components expressions, while the moment (Galerkin) method is used to solve the matrix equation obtained by imposing the boundary conditions of the structure under consideration. The microstrip patches substrates are composed by two uniaxial anisotropic dielectric materials. The optical axes in these dielectric layers are oriented perpendicularly to the ground plane. Numerical results are presented for the resonant frequency for the geometry under consideration. Excellent agreement was observed with results available in the literature for coupled microstrip patches on isotropic substrates.

Harmonic heat flow in anisotropic thin films

The three-dimensional equation of heat conduction is solved to obtain the time-dependent (harmonic) temperature field in an opaque, thermally anisotropic layer on a thermally thick and isotropic substrate when the system is heated by a modulated Gaussian laser beam. The influence of the anisotropy on the amplitude and phase response of the temperature variation as a function of the position on the surface and depth in the layer is studied. The limiting case of one-dimensional heat diffusion in highly anisotropic media is discussed. For one example the influence of thermal anisotropy on the frequency dependence of the surface temperature distribution is studied.

Microstrip Open End and Gap Discontinuities Including Anisotropic Substrates

ABSTRACT A dynamic source reversal method, based on potential theory, is developed to determine the parameters of the equivalent circuit for capacitive gaps in microstrip lines with anisotropic substrates. The open circuit end capacitance is found as a special case by letting the gap spacing go to infinity. It is also shown that since the discontinuity is essentially characterized by the excess charge in the vicinity of the gap an equivalent problem with an isotropic substrate and an effective substrate thickness can be formulated that gives accurate results for the equivalent circuit capacitances.

The speed of a wave along a fluid/solid interface in the presence of anisotropy and prestress

The classical solution for the Scholte wave along a fluid and isotropic substrate is well known. However, when the substrate is either a weakly anisotropic solid, or the adjoining fluid is subject to a hydrostatic pressure, the analysis of Scholte wave propagation becomes rather complex and lengthy computations are required to obtain the solution. The purpose of this paper is to apply simple and computationally efficient expressions in the determination of Scholte wave speeds for substrates with either weak anisotropy or in the presence of uniform initial stresses and strains in the substrate and fluid media. Both of these two simple expressions are for the incremental change in the Scholte wave speed Δv/v from an appropriately selected isotropic, reference substrate and adjoining fluid under no hydrostatic pressure. The predictions of the Scholte wave speeds from the derived expressions agree to well within 1%–2% with the other approximation techniques for the high-frequency asymptotes of the Stoneley wave velocity dispersions in a fluid-filled borehole traversing either a weakly anisotropic formation or a formation with initial stresses and strains caused by a borehole pressurization.

The Phenomenological Functions that Characterize the Surface Free Energy Density of Nematic Liquid Crystals: A Microscopic Analysis

In a recent paper, Faetti proposed a new phenomenological expression for the surface free energy density Fs of a nematic liquid crystal m contact with an isotropic substrate. Fs depends on director n, on the unit vector k orthogonal to the interface and on their gradients at the interface. Five different terms appear in the expression of Fs. The first term is the standard anchoring energy contribution, the second and third terms are elastic contributions that depend on the surface tangential director gradients, the fourth and fifth terms are new geometrical contributions that account for the effect of a local curvature of the interfaces. The expression of the surface free energy density is characterized by five phenomenological functions W(nk), K13(nk), K14(nk), Ai(nk) and A2(nk) where nk is the scalar product n. k. In this paper we give the first microscopic calculation of these new surface functions by using a simplified microscopic model of intermolecular interactions. Surface functions Ai(nk), A2(nk), and K14(nk) are found to be of the same order of magnitude of the Frank bulk elastic constants, whilst K13(nk) = 0. The geometric surface functions Ai(nk) and A2(nk) satisfy the simple relation Ai(nk) = -n( A2(nk). Both the results K13(nk) = 0 and Ai(nk) = -n( A2(nk) are shown to be a direct consequence of the invariance with respect to the transform n - -n of the interaction energy between molecules.