Uniaxial Substrate Research Articles

Full-wave analysis of microstrip lines on ferrite and anisotropic dielectric substrates

Microstrip lines on ferrimagnetic and uniaxial anisotropic dielectric substrates are examined. Hertz vector potentials oriented along the magnetization direction for the ferrimagnetic substrate and along the optical axis for the uniaxial anisotropic dielectric substrate are used to obtain the dyadic Green's functions in the Fourier transform domain. Galerkin's method is used to obtain the frequency behavior of the propagation constant. Curves for a few cases are shown as examples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Generalized spectral analysis of planar lines on layered media including uniaxial and biaxial dielectric substrates

The spectral-domain analysis is generalized to compute the dispersive properties of a wide variety of planar and quasiplanar transmission lines (microstrips and finlines) printed on a stratified dielectric medium. Uniaxial and biaxial dielectric anisotropy can be easily manipulated due to the definition of a transverse propagation matrix characterizing each dielectric layer. The whole boundary value problem is reduced to two simpler problems involving only one or two dielectrics, and the spectral dyadic Green's function is derived by a recurrence algorithm. The dispersion equation is derived by using the Ritz-Galerkin method. The numerical convergence is substantially improved taking into account the asymptotic behavior of the series. A number of illustrative examples are included to emphasize the power of the method. >

Lumped capacitance and open end effects of striplike structures in multilayered and anisotropic substrates

An accurate calculation of the lumped capacitance of a rectangular microstrip patch and the edge capacitance of an open-circuit microstrip or stripline is carried out. Variational expressions in the spectral domain are developed to analyze these conductors when they are embedded in a multilayered anisotropic substrate. A recurrence algorithm, easy to compute, is proposed to determine the three-dimensional spectral Green's function characterizing the sort of substrates employed. The method makes it possible to study biaxial substrates in the case of the rectangular patch and uniaxial substrates with tilted optical axis in the transverse plane in the case of open-circuit striplike transmission lines. A detailed study of trial functions to approximate the charge density on the conductors is carried out, taking into account the physical features of each problem. The results obtained are compared with those appearing in the literature. Original design graphs are presented, with special emphasis on the use of inhomogeneous and anisotropic substrates.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Characterization of the Finline Step Discontinuity on Anisotropic Substrates

An analysis of the finline step discontinuity in either uniaxial or biaxial substrates is presented. The method is based on a spectral-domain hybrid-mode expansion in an enclosed finline cavity in conjunction with Galerkin's method. A numerically stable scattering matrix formulation is used. The effect of substrate anisotropy is described. The results are also compared with published experimental data or those by the modal matching method when the substrate is isotropic. The comparison shows very good agreement.

Dynamic Analysis of Microstrip Lines and Finlines on Uniaxial Anisotropic Substrates

Dyadic Green's functions in the Fourier transform spectral domain are obtained for open microstrip lines and bilateral finlines on uniaxial anisotropic substrates. These functions are written in an impedance matrix form by expressing the electric and magnetic fields in terms of Hertz vector potentials oriented along the optical axis. In combination with Galerkin's method, they are used to obtain the propagation characteristics of single and parallel coupled microstrip lines on uniaxial anisotropic substrates having the optical axis in an arbitrary direction in a transverse plane and of bilateral finlines with the three optical axis orientations of the uniaxial anisotropic substrate that result in the diagonal permittivity tensor.

Zigzag ray model of hybrid modes in thin-film optical waveguides with uniaxial anisotropic substrates

We give a model of zigzag rays of hybrid modes propagating in a thin-film optical waveguide on uniaxial anisotropic substrates. The oblique power flow of the hybrid modes, which depends on the polarization, is represented by introducing a transverse shift as well as a longitudinal shift of the rays. The polarization of the zig-zag rays in the film is given. The transverse component of power flow in the film (but not in the top layer or the substrate) is ignored in this model. It is numerically shown that near the degenerate points the oblique direction of the ray propagation obtained by the present zigzag ray model is in agreement with that of the power flow.

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.

Uniaxial and Biaxial Substrate Effects On Finline Characteristics

The effect of uniaxial and biaxial substrates on the frequency-dependent properties of a bilateral finline is investigated in this article. The finline characteristics are obtained by using the spectral-domain procedure in conjunction with the Galerkin method. Investigation of uniaxial substrates indicates that there is a particular optical axis direction for which the permittivity component in that direction dominates the finline behavior. In addition, a study has been carried out which determines the error which results when the material layer anisotropy is neglected.

Magneto-optical transverse Kerr effect in a film-substrate system

The problem of electromagnetic reflection at an oblique angle of incidence in a system consisting of an isotropic ambient, a magnetic film and a thick magnetic substrate is studied. The magnetizations in both the film and substrate are assumed normal to the plane of incidence (transverse geometry). The results are expressed in terms of the reflection matrix. The solution includes the conditions for guided wave propagation in the system. As a special case of the general formulae the reflection matrix in a system consisting of a uniaxial film and a uniaxial substrate optical axes of which are oriented normal to the plane of incidence are obtained.

Magneto-optical longitudinal Kerr effect in a film-substrate system

The problem of electromagnetic reflection at an arbitrary angle of incidence in a system consisting of an isotropic ambient, a magnetic film and a thick magnetic substrate is considered. The magnetization in both the film and substrate is assumed parallel to the planar interfaces and to the plane of incidence. The analysis provides the dispersion relation for the guided wave propagation in the system. The obtained general formulae are applied to the special cases of (a) normal incidence, (b) oblique incidence on a uniaxial film on a uniaxial substrate, both optical axes being parallel to the interfaces and to the plane of incidence, and (c) to the case when the permittivity tensor diagonal elements are the same and the off-diagonal element is small. The possible practical applications of the present analysis are in the ellipsometry of thin-film — substrate structures displaying magnetic order and in the theory of magneto-optic thin-film devices for integrated optics.

Magneto-optical polar Kerr effect in a film-substrate system

The problem of electromagnetic reflection at an arbitrary angle of incidence in a system consisting of an isotropic ambient, a magnetic film and a thick magnetic substrate is studied. The magnetizations in both the film and substrate are assumed normal to the planar interfaces. The results are expressed in terms of the reflection matrix which is directly connected to the experimentally observed quantities: ellipsometric ratio and magneto-optical rotation and ellipticity. The general condition for guided wave propagation in the system is obtained. The theory is applied to the special cases of (a) normal incidence, (b) oblique incidence on a uniaxial film on a uniaxial substrate, both optical axes being normal to the interfaces, and (c) oblique incidence on a system consisting of an isotropic ambient, a magnetic film and a thick magnetic substrate assuming the diagonal elements of the permittivity tensor in a particular magnetic medium (film or substrate) equal to each other and the corresponding off-diagonal elements much smaller with respect to them. The possible practical applications of the present analysis are in the optimum design of film-substrate structures in magneto-optic devices and in the optical studies of the surface effects in magnetic materials.

Dyadic Green's function for microstrip-like transmission lines on a large class of anisotropic substrates

In the paper simple and compact expressions for the dyadic Green&apos;s function in the spectral domain for microstrip-like transmission lines on anisotropic substrates are developed. The method can be used in microstrip and related structure analysis, with the unique assumption that the direction perpendicular to the ground plane of the line must also be a main axis of substrate anisotropy. Hence, the scope of the method covers microstrip-like lines on biaxial and uniaxial dielectric substrates, provided the condition mentioned above is fulfilled, as well as plasma and ferrite substrates magnetised in the direction perpendicular to the ground plane. As a first application, some original structures, i.e microstrip and bilateral finlines printed on an uniaxial substrate, are numerically analysed.

TM-polarized nonlinear waves guided by asymmetric dielectric layered structures

We found the field structure, exact dispersion relations and power flow ofp-polarized nonlinear guided and surface waves travelling along a three-component layered structure consisting of a film of thicknessd with dielectric constanteb bounded at the negativez-side by a linear medium with dielectric constantea and at the positivez-side by a nonlinear uniaxial substrate characterized by the diagonal dielectric tensore11 =e22 =\(\varepsilon _ \bot\) + α(|E1|2 + |E2|2),e33 =e∥, α<0 (self-defocusing medium),E1 andE2 being the components of the electric field in thex andy-direction, respectively. It is shown that for sufficiently smalld/λ (λ: wavelength) the nonlinear wave may exist only at power flows exceeding some certain minimum values. For sufficiently larged/λ to some values of the power flow there correspond two distinct values of the propagation constant. In this case with increasing of the power flow the number of waveguide modes is decreasing and for higher-order modes the film-waveguide exhibits an optical-power limiter from the above behaviour.

Phase transitions in monolayers adsorbed on uniaxial substrates

The phase diagram of a $p\ifmmode\times\else\texttimes\fi{}1$ uniaxial adsorbed layer is investigated theoretically, including the possibility of incommensurate phases. For $p=3 \mathrm{and} 4$ we determine the incommensurability crossover exponents at the commensurate-fluid multicritical point. We then argue that due to a strong renormalization of the dislocation core energy the incommensurate phase should be stable up to the multicritical point for $p&gt;~3$. Possible phase diagrams for general $p$ are discussed.

Effect of subband splitting on Si inversion layers

The subband structure of (100)Si inversion layers can be altered by either uniaxial stress or substrate bias due to deformation potential and quantizing surface field, respectively. The reduced splitting between E 0 and E 0 caused by compressive stress is shown to be exactly compensated by the additional surface field via substrate bias at high compressive stress. At low compressive stress (≲ 10 9 dyn cm −2) and low carrier concentration (< 10 12 cm 2) we observe a marked decrease of electron mobility at 4.2 K. The decrease in mobility can be recovered by suitable negative substrate bias. We attribute these results to the influence of the density of state tails of E 0 subband on the free electrons in the E 0 subband. At high stress, E 0 and E 0 cross. The measured E f crossing point from E 0 to mixed subband at various stresses and depletion charges agrees well with Takada and Ando's calculation. The results for [001] and [011] stresses indicate further splitting of the E 0 subband for the former. For (111) surfaces, the mobility increases with either eompressive or tensile stress in [011] direction. From the point of view of the influence of tail states of the higher subbands, this even function dependence of μ( P) seems to support 6-valley degeneracy in the absence of sttess.

Effect of subband splitting on Si inversion layers

Abstract The subband structure of (100)Si inversion layers can be altered by either uniaxial stress or substrate bias due to deformation potential and quantizing surface field, respectively. The reduced splitting between E0 and E0 caused by compressive stress is shown to be exactly compensated by the additional surface field via substrate bias at high compressive stress. At low compressive stress (≲ 109 dyn cm−2) and low carrier concentration (

Analysis of coplanar striplines on an anisotropic substrate using Galerkin's method

AbstractA unified analysis approach is shown for obtaining the quasistatic and dispersive characteristics of coplanar Striplines on a uniaxial anisotropic substrate. Galerkin's method is adopted in the numerical calculations and the basis functions are determined systematically by use of Chebyshev polynomials with the result that solutions with desired accuracy can be obtained efficiently. In general, in coupled striplines large errors occur when the current distribution function is to be determined solely by its fringing effect. In the case of sapphire substrate, the accuracy of solution is investigated and its propagation wavelength as well as characteristic impedance are obtained and shown in graph. In these graphs the quasistatic characteristics obtained from the electrostatic approximation and the hybrid mode dispersion are compared so that a rough criterion of the error due to the electrostatic approximation can be estimated. The quasi‐static characteristics of a uniaxial anisotropic substrate line can be characterized by its effective and equivalent isotropic substrate [1]. The dispersion of the isotropic substrate line is obtained and compared with that of the original anisotropic line.

Commensurate-Incommensurate Transitions in Two Dimensions: Discrete Models and Square Symmetric Substrates

The phase diagram and the critical behavior of a discrete two-dimensional model of the commensurate-incommensurate transition is determined with use of an approximate mapping onto the six-vertex model. For an uniaxial substrate the critical behavior is that of the continuum case. For a square substrate either a single first-order transition or a second-order transition followed by a first-order transition is found.

Guided and semileaky modes in anisotropic optical waveguides of the LiNbO 3 type

Light propagation in anisotropic optical waveguides formed by an isotropic or a uniaxial layer onto a uniaxial substrate is studied theoretically. Special attention is paid to semileaky modes which are lossy due to the radiation of energy into the substrate. Both their propagation constants and loss coefficients are calculated numerically for waveguide parameters close to As-S glass layer onto LiNbO 3 substrate and to LiNbO 3 out-diffused and in-diffused waveguides.

Deposition of Permalloy with Varying Degrees of Anisotropy

Some of the physical properties of 81/19 Permalloy films with different degrees of uniaxial anisotropy have been studied. Such films were produced by vacuum deposition in rotating magnetic fields with varying ellipticity, keeping all other deposition parameters constant during one test series. Substrate temperatures were 300°, 200°, 100°C, and room temperature. Explanations for the observed dependence of angular anisotropy dispersion and easy-axis coercivity on uniaxial anisotropy and substrate temperature are presented.