Isotropic Substrate Research Articles

Reflection from an oriented thin film

Expressions for the amplitude reflection and transmission coefficients for light incident on a dielectric thin film that is biaxially anisotropic and situated on an isotropic substrate are presented for the special case where one of the principal axes of the film is parallel to the surface of the film and perpendicular to the plane of incidence of the light. This is one of a few special cases for reflection from anisotropic materials that contains no cross-coupling between the p and s polarizations of the light.

Perturbation analysis of finlines containing anisotropic media

The simple perturbation method is applied to obtain the propagation characteristics of finlines loaded with anisotropic material. Starting from the analysis of a finline on isotropic dielectric substrate, we obtain the propagation constants of finlines having dielectric anisotropy in the substrate and finlines containing magnetised ferrite. The main feature of the perturbation method is its simplicity. Since the anisotropies encountered in practice are small deviations about some mean isotropic value, the results obtained show good agreement with those obtained using the rigorous methods reported in the literature.

Ellipsometric study of the optical anisotropy of lead arachidate Langmuir films

The reflection matrix of lead arachidate Langmuir films on silicon was measured by means of a generalized ellipsometric technique. The lateral anisotropy of the films was determined. The problem of light reflection from a uniaxial film on an isotropic substrate with arbitrary axis orientation was solved and used for the interpretation of the measurements. A simple generalized ellipsometric technique for measuring the non-diagonal reflection matrix of a weakly anisotropic medium is described. Film refraction indices, monolayer thickness and the angle between the optical axis of the film and the normal to the surface were determined. Models of molecular packing with lateral anisotropy are discussed. A difference between the wetting angles of odd and even monolayers is supposed to be the origin of the non-centrosymmetric structure of the bilayer, resulting in lateral anisotropy of the film.

The focusing of surface-acoustic-waves launched from a slanted chirped transducer. I. Isotropic substrate

The focusing behavior of surface acoustic waves launched from a slanted chirped transducer (SCT) is explored using both a continuum model and a discrete model for sources associated with a linear FM chirp transducer on a substrate with isotropic properties. The continuum model leads to the prediction of an understanding of effects that would arise in the radiation field of an SCT on an isotropic substrate. It is based on a representation of the transducer as a continuum of sources, with the radiation field determined by applying the stationary phase method, and is presented for infinitesimally short fingers. It is compared with a more direct and exact but less revealing method of determining the field based on a discrete array of sources. The effects of increasing finger lengths are considered. The results are related to the focusing of radiation by a lens.

An improved design of systems based on three coupled microstrip lines

The design parameters of three coupled equal-mode-impedance microstrip lines on an alumina substrate are introduced in a manner that gives a convenient systematic design procedure. The use of equal-mode-impedance lines greatly facilitates the design of the system. The design procedure for two configurations of this system is presented. A coupler satisfying the requirements of one of these configurations is realized and its practical performance is shown to be in good agreement with theory. The design procedure is applicable to any such system on any other isotropic substrate material. >

Analysis of reflective SAW gratings for SH‐type modes using finite‐element method

AbstractA solution based on the finite‐element method (FEM) is presented for the analysis of SH‐type surface acoustic wave gratings. Although the FEM has already been applied to the discontinuities in elastic waveguides for SH‐type modes, only the isotropic substrate has been treated. Also, it is difficult to apply the FEM directly to many discontinuities such as grating reflectors due to excessive computation time and computer memory requirements.This paper presents a numerical approach to the analysis of SH‐type surface acoustic wave gratings on anisotropic substrates. To apply the FEM directly to many discontinuities, the substructure method is introduced. As a result, mutual interaction between surface waves and bulk waves is automatically taken into account over the entire discontinuity region. To show the validity and usefulness of this approach, examples are computed for various gratings on PZT‐4, 41° Y‐X LiNbO3, and 36° Y‐X LiTaO3 substrates.

MICROSTRIP ELEMENTS ON CYLINDRICAL SUBSTRATES-GENERAL ALGORITHM AND NUMERICAL RESULTS–Invited Paper

Abstract A highly accurate and efficient numerical algorithm for the computation of the near-field characteristics of microstrip elements on cylindrical substrates is presented in this paper. The algorithm is applicable for any homogeneous, isotropic, and linear substrate material, including lossy materials of arbitrary substrate thickness. The numerical and mathematical limiting cases, such as the low or high frequency limits, are described analytically and numerically to illustrate the functional behavior of the cylindrical Green's function.

Attenuation distortion of transient signals in microstrip

Attenuation distortion, and combinations of dispersion and attenuation distortions, of transient signals in microstrip lines are investigated. Conduction losses are considered for the general case where the strip conductor resistivity is different from that of the ground plane. Dielectric losses are examined for commonly used isotropic substrates. Attenuation and dispersion distortions of short pulses are shown to vary as microstrip and pulse parameters are changed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Finite element analysis of dispersion in waveguides with sharp metal edges

The dispersion characteristics of arbitrarily shaped waveguides with sharp metal edges are found by a finite-element method in which the usual polynomials are supplemented by singular trial functions. As in recent approaches, the method solves for the three components of the magnetic field and can thereby avoid spurious modes. Results for a rectangular waveguide with two double ridges and for shielded microstrip on isotropic and anisotropic substrates are presented. >

Normalized transverse current distributions of microstrip lines on anisotropic substrates

The normalized transverse current distributions are obtained for microstrip lines on anisotropic substrates, and their dependence on epsilon */sub y/, w/h, and the anisotropy ratio AR is explained. These distributions are classified into five cases. There are cases in which the normalized transverse current distribution can be approximated by that obtained already for the cases of isotropic substrate. >

Numerical Spectral Matrix Method for Propagation in General Layered Media: Application to Isotropic and Anisotropic Substrates

A full-wave analysis technique for generalized artisotropic layered media based on a 4x4 field matix method is applied to calculate the propagation constant of a number of microstriplike transmission structures. This technique is very versatile, and allows simultaneous permittivity, permeability, and optical activity anisotropy. Data for higher order modes of single and coupled strip lines in isotropic layered media in the millimeter-wave region are presented. New dispersion data for both low- and high-anisotropy dielectric layered structures are generated for different principal axis crystallographic orientations.

Microstrip Dispersion Including Anisotropic Substrates

A perturbation-iteration solution based on potential theory is developed for determining the effective dielectric constant, characteristic impedance, and current-charge distribution on a microstrip transmission line with isotropic and anisotropic substrates. The numerical implementation of the theory is described and is suitable for use on a personal computer. Computed data for several common substrate materials are included.

Radiation and scattering from a microstrip patch on a uniaxial substrate

The problem of a rectangular microstrip antenna printed on a uniaxially anisotropic substrate is treated. The effect of anisotropy on the resonant frequency and surface wave excitation of the antenna is considered, and the radar cross section (RCS) of the antenna is calculated. The RCS calculation includes the effect of the load impedance (antenna mode scattering). Results for the resonant frequency of a patch on a uniaxial substrate are compared with measurements, and the RCS of a patch on an isotropic substrate is compared with measurements. The derivation of the uniaxial Green's function in spectral form, the associated moment method analysis for the input impedance and scattering of the microstrip patch, and the expressions for the far-zone fields of a source on a uniaxial substrate are presented.

Quasi-Static Characteristics of Asymmetrical and Coupled Coplanar-Type Transmission Lines

In this paper, variational expressions for the capacitances of' asymmetrical and coupled coplanar-type transmission lines are derived. The methods employed are quite general, and are useful for analyzing various types of coplanar-type transmission lines, with either an isotropic or anisotropic substrate. An accurate and efficient method of calculation is provided for the variational expressions, and some numerical results are presented.

Shear‐wave vibrator signals in transversely isotropic shale

The experiments of Robertson and Corrigan (1983) on shale are among the first three‐component field observations of shear waves in transversely isotropic media to be published. Their data are reprocessed to highlight the effects of the shale’s anisotropy on shear waves. Two results emerge. First, shear‐wave splitting in a transversely isotropic substrate is most easily observed when the vibrator baseplate is oriented so that both SH‐ and SV‐waves reach the geophone. Second, the SV‐wave polarization deviates significantly from perpendicular to the raypath. Both results may significantly affect the interpretation. Both are found to agree with theoretical results and are modeled successfully by synthetic seismograms.

The influence of the symmetry of the piezoelectric crystal on love acoustic waves

The Love acoustic waves have been analytically studied for two systems: 1) the piezoelectric substrate loaded by the isotropic layer and 2) the isotropic substrate loaded by the piezoelectric layer. Piezoelectric crystals of classes 6, 4, 6mm, 4mm, 622, 422 were considered for both systems. It has been shown that two different types of the Love waves (the usual waves and the channel waves) are possible. The channel Love waves can exist both for the soft and for the hard layers in each system. Their existence is due to the piezoeffect. For the usual Love waves in the first system the silent zone of the thickness is obtained for 6, 4, 622, 422 classes. In this zone the Love wave cannot exist unless the thickness of the layer exceeds a definite thickness.

Analysis of thermal generation of Rayleigh waves

We have developed an analysis for thermal generation of surface acoustic waves (Rayleigh waves) valid for anisotropic materials. The analysis, based on the complex reciprocity relation, provides expressions for the mechanical displacement, the electrical potential, and the acoustic power density of the Rayleigh waves launched by harmonic heating of zones on the surface. These quantities are evaluated for an isotropic substrate. They are compared with those obtained by R. M. White in his work on thermal generation of bulk waves. Our theoretical results are in good agreement with two previous experiments carried out with a piezoelectric crystal of lithium niobate.

Frequency Dependent Characteristics of Microstrips on Anisotropic Substrates

Frequency dependent characteristics are discussed for the microstrip line on anisotropic substrate (original line) from the extension of the results obtained in an isotropic substrate case. In approximating the original line by the equivalent line on an isotropic substrate, it is best to maintain h and w of the equivalent line equal to those of the original line. The reason is that the inflection frequency f/sub i/ is a function of w and h and that f/sub i/ plays an important role in calculating the dispersion. Three approximate dispersion formulas are derived owing to this idea. The results obtained by these formulas are compared with the other available theoretical and experimental results for sapphire substrates. Good agreement is seen.

An Analysis of Transverse Modes in Acoustic Surface Wave Resonators

A system of approximate surface wave equations employed in an earlier treatment of the reflection of straight‐crested surface waves by arrays of reflecting strips is extended to the case of variable‐crested surface waves. Although the basic straight‐crested surface wave velocities are determined as in the previous treatment, in the present case a reduction in straight‐crested surface wave velocity in the unplated region due to the adjacent plated regions, which is essential for the existence of the guided transverse modes, is determined by means of a perturbation procedure. The attendant depth dependence for each region is employed in the variational principle as in the earlier treatment, but now the variable cresting relation for the isotropic substrate is incorporated in the description. The resulting equations are applied in the determination of both the transverse modes in each region and the transmission line representation of each mode. The transverse wave numbers in a given mode are taken to be the...

Polarization-selective lateral waveguiding in layered dielectric structures

A riblike waveguide structure consisting of three isotropic transparent layers on an isotropic transparent substrate is shown to be capable of selectively guiding only the TE-like (TM-like) mode if the waveguide axis is defined by a trough (ridge) in the low-index middle layer. Guidance in the film plane arises from the joint dependence of the planar waveguide mode-propagation constants on the strength of evanescent coupling between high-index layers and on the difference between the propagation constant for the three-layer structure and that for a single, isolated layer on the same substrate. The mode with polarization opposite the guided one radiates away from the guide axis in the film plane. Because the insertion loss arises only from scattering and mode conversion at boundaries, it is expected that high extinction ratios, accompanied by tolerable insertion losses, will be realized.