Anisotropic Dielectrics Research Articles

Attenuated total reflection method for measurements of optical properties of metallic films bordering anisotropic dielectrics

Thin-film assemblies of magnesium fluoride/aluminium/BK7-glass (MgF2/Al/BK7) and rutile/aluminium/BK7-glass (TiO2/Al/BK7) are experimentally studied, both by a direct coupling of evanescent waves and by a coupling of guided waves into surface plasmon waves (SPWs). Anisotropic effects of the prism coupler as well as the MgF2 and the TiO2 films on the phase-matching condition are examined theoretically and experimentally. The dielectric function of the Al films is recovered from SPW experiments with an uncertainty <10%.

Dispersion characteristics of asymmetric coupled anisotropic dielectric waveguides using FDFD

The formulation is developed in the frequency domain and the finite difference method is used for the numerical solution of the scalar wave equation, written in terms of the transverse components of the magnetic field. As a result a conventional eigenvalue problem is obtained without the presence of spurious modes due to the implicit inclusion of the divergence of the magnetic field equal to zero. The formulation is developed to include biaxial anisotropic dielectrics with an index profile varying arbitrarily in the cross section of the waveguide under analysis. This formulation is then applied to the analysis of the influence on the dispersion characteristics of the dimensions of asymmetric coupled rectangular uniaxial anisotropic dielectric waveguides. As expected, the reduction of the height or the width of one of the rectangular dielectric waveguides causes the dispersion curves to move towards higher frequencies.

Radiation Properties of a Biaxially Anisotropic Dielectric Sphere Excited by a Dipole

ABSTRACT The radiation properties of a dielectric sphere with biaxial anisotropy are investigated. The excitation source is assumed to be an elementary dipole of arbitrary orientation illuminated at the centre of the anisotropic sphere. The primary field is defined and computed in terms of the convenient spherical vector wave functions, by solving the wave equation in the phase space. The boundary conditions at the sphere surface are satisfied and following the method of moments, Fourier series and spherical vector wave functions series are employed to express the unknown reflected and scattered fields at the sphere inner and outer region respectively. Although main emphasis is given to theoretical analysis, some numerical results are computed and presented.

A theoretical model of solvation in continuum anisotropic dielectrics

A new formulation of the polarizable continuum method (PCM) is presented to describe the electrostatic interaction between molecular solutes and anisotropic media (e.g., liquid crystals, crystalline matrices). The main features of the PCM (ab initio treatment of solute, cavity of arbitrary shape, dielectric reaction described with apparent charges) are maintained, though in this case polarization charges are present both on the cavity surface and in the bulk of the dielectric. A simplified method, saving about half of the computational time, is also presented.

Vectorial finite element modelling of 2D leaky waveguides

An accurate finite element method is described for the analysis of leaky optical waveguides with arbitrary cross-section and inhomogeneous anisotropic dielectrics including loss or gain. The method leads to the iterative solution of a nonlinear matrix eigenvalue problem without compromising the sparsity of the resultant matrices which depend only on the mesh topology. >

A Wiener-Hopf-type analysis of microstrips printed on uniaxial substrates: effects of the substrate thickness

A Wiener-Hopf-type analysis of the canonical problem of a TEM wave obliquely incident at the edge of the truncated upper conductor of a parallel plate waveguide loaded with a uniaxial anisotropic dielectric is presented. A numerical integration scheme as well as a thin substrate approximation for the reflection coefficient is given. The influence of the dielectric anisotropy and the slab thickness on the reflection coefficient and the edge admittance are investigated. Numerical results show the importance of the dielectric anisotropy and the expected effects in microstrip applications. >

High accuracy formulas for calculation of the characteristic impedance of microstrip lines

An analytical formula for determination of the characteristic impedance of a microstrip line assuming the quasi-TEM mode of propagation is presented. The new form of the final formulas contains only integrals which can be numerically performed by means of the Gauss-Laguerre quadrature. The method can be applied to multilayer lines and also to the case of anisotropic dielectrics. By using some suitable conformal mappings the formulas obtained can be used to determine the characteristic impedance of some cylindrical microstrip lines. We have compared the results given by the proposed formulas with the finite analytical solution available in a particular case and also with results obtained by the substrip method. All the performed tests indicate that the proposed formulas are highly accurate and efficient relations for determining the characteristic impedance of microstrip lines.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The measurement of complex permittivity of anisotropic dielectrics by means of an electromagnetic open resonator

By applying the perturbation method and the complex-source-point theory, the theoretical research of measurement of complex permittivity of uniaxial anisotropic materials by means of an electromagnetic open resonator has been made, and the double refraction phenomenon due to anisotropy of measured dielectric materials has been quantitatively analyzed. Finally, measurements have been made on some single-crystal quartz specimens using an automated open resonator measurement system at 8mm band.

Analysis of coupled anisotropic dielectric waveguides using the frequency domain finite‐difference method

AbstractA rigorous general and versatile finite‐difference formulation for the analysis of the propagation characteristics in structures, having the dielectric waveguide as the basic element, is presented here. In this formulation, the finite‐difference method is used in the numerical solution of the scalar wave equation, written in terms of the transverse components of the magnetic field. As a result, a conventional eigenvalue problem is obtained without the presence of spurious modes (present in previous formulations), due to the implicit inclusion of the divergence of the magnetic field equal to zero. The general case of biaxial anisotropic dielectrics is considered, with the refractive index profile varying arbitrarily in the waveguide cross section. Dispersion characteristics for isolated and parallel coupled dielectric waveguides are calculated. The theoretical development was then used to solve particular problems and the results agree with those available from other methods. Results were obtained for a variety of waveguide structures of much interest, particularly for the development of integrated optics. © 1994 John Wiley &amp; Sons. Inc.

Analysis of a microstrip crossover embedded in a multilayered anisotropic and lossy media

The equivalent circuit and the scattering parameters of the orthogonal microstrip crossover discontinuity are determined by assuming that the conducting strips are embedded in a multilayered substrate which may contain both anisotropic dielectrics and materials with a nonnegligible conductivity. The equivalent circuit of the crossover is obtained in terms of the complex excess charge densities on the strips. These excess charge densities are computed by means of the Galerkin method in the spectral domain. Comparison is carried out with previously existing results for microstrip crossovers on lossless isotropic substrates and original results are presented for crossovers on anisotropic and lossy substrates.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Temperature dependence of the moduli of elasticity of NaClO3 and NaBrO3 single crystals

The temperature dependences of the moduli of elasticity cik(T) of single crystals of sodium chlorate NaClO3 and sodium bromate NaBrO3 in the temperature range 77–300 K were investigated experimentally with the help of the resonance method. It is shown that these compounds are elastically anisotropic dielectrics with elastic anisotropy factor A E110>E111 and G100<G110<G111. The experimental data on cik(T) were interpreted using a lattice model taking into account the central and noncentral interactions of ions in two coordination spheres. The force constants of these interactions are presented. It is shown that the model chosen describes well the temperature dependences cik(T), if both the noncentral interaction of the ions and the contribution of the vibrational part of the free energy to the moduli of elasticity are taken into account.

Laminated polarization splitter with a large split angle

A new spatial walk-off polarizer with a large polarization-splitting angle is fabricated. The polarizer, which utilizes artificial anisotropic dielectrics, is composed of layers of periodically laminated a-Si:H/SiO2 thin films. The thickness of each layer is 67 nm, while the total number of the layers amounts to 1440. The measured polarization-splitting angle is 15.5° at λ=1.55 μm, which is 2.7 times larger than that of existing polarizers.

On the quasimomentum of light and matter and its conversion

It is shown that, in nonlinear electrodynamics of macroscopically homogeneous anisotropic dielectrics, there exists a conserved vector quantity which has the physical meaning of quasimomentum. Its density is expressed in terms of the field variables as ( 1 4 π)D × B . If electromagnetic excitations are coupled to elastic excitations the sum of their quasimomenta is conserved. The connection of the conservation law, via Noether's theorem, with invariance properties of homogeneous media is indicated. As an example of where the concept of quasimomentum proves to be useful the well-known radioelectric effect is considered: When an electromagnetic wave propagates in a semiconductor or a semimetal, in the process of its absorption its quasimomentum is transferred to the electrons and a dc voltage is built up. Based on quasimomentum conservation, a formula for this voltage in terms of the intensity of the wave is given. Further examples of application are mentioned.

Analysis of an infinite array of rectangular anisotropic dielectric waveguides using the finite-difference method

The finite-difference method is used in the analysis of the propagation characteristics of an infinite array of rectangular dielectric waveguides. Particular attention is devoted to the mode coupling analysis and a comparison with results from an integral equation method is presented. The wave equation is solved in terms of the transverse components of the magnetic field, resulting in an eigenvalue problem with the elimination of spurious modes. The formulation is general and may be applied to the solution of other problems, including those with anisotropic dielectrics and with a continuous variation of the index of refraction profile in the waveguide cross section.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Microwave reflection measurements on doped semiconductors with picosecond transient radiation

Broadband microwave reflection spectroscopy using the COMITS (coherent microwave transient spectroscopy) method is described. COMITS is particularly suited to reflection studies because the picosecond transient radiation emitted from planar antennas is strongly linearly polarized. The validity of the technique is verified by reflection measurements on isotropic and anisotropic dielectrics. Reflection studies on a series of doped silicon samples demonstrate that the carrier dynamics in the 15-140-GHz frequency range are well described by a simple Drude model. >

Experimental verification of a form-birefringent polarization splitter

Experimental verification is made of a new polarization splitter which utilizes artificial anisotropic dielectrics. The splitter is composed of layers of periodically laminated SiO2/TiO2 thin films. The SiO2 and TiO2 films are alternately deposited by rf sputtering and reactive dc sputtering, respectively. The thickness of each layer is 50 nm, while the total number of the layers amounts to 2000. The measured polarization split angles are 5.7° (λ=0.63 μm) and 5.1° (λ=1.3 μm), being roughly the same as those predicted.

Variational finite element analysis of dielectric waveguides with no spurious solutions

A new variational formulation for the analysis of dielectric waveguides is presented. This formulation provides a direct solution for the propagation constant using only the transverse components of the magnetic field and avoids spurious solutions. It allows treatment of lossy anisotropic dielectrics and leads to a canonical sparse matrix eigenvalue problem.

Spatial walk-off polarizer utilizing artificial anisotropic dielectrics

We propose a new spatial walk-off polarizer that utilizes artificial anisotropic dielectrics. The polarizer is composed of two kinds of periodically laminated dielectric layer. We calculated the characteristics of the polarizer composed of periodically laminated a-Si/SiO(2) layers and found that the split angle between the ordinary wave and the extraordinary wave in the polarizer is more than three times larger than that in well-known birefringent crystals, e.g., rutile and calcite. The polarizer holds promise for the miniaturization of polarization beam splitters and polarization-independent isolators.

Modal analysis of the second-harmonic electromagnetic field generated by the Cherenkov effect in optical waveguides

A model analysis of the second-harmonic electromagnetic wave generated by the Cherenkov effect in an optical channel waveguide made of an anisotropic dielectric is discussed. With the effective-refractive-index method the waveguide is modeled by two slab-type waveguides. Both TE and TM waves are considered, and the polarization dependence of the second-harmonic power is studied. Numerical results for the configuration giving maximum second-harmonic power are in close agreement with experimental results. >

A K-space method of moments solution for the aperture electromagnetic fields of a circular cylindrical waveguide radiating into an anisotropic dielectric half-space

A method of moments solution is presented for the problem of determining the electromagnetic aperture fields that occur when a circular cylindrical waveguide radiates into an anisotropic dielectric-covered ground plane. The method of moments solution is derived by using a reaction matching technique and by using K-space theory to develop the aperture matrix elements of the system. An example of radiation into an anisotropic dielectric is given. The anisotropic dielectric for this example is assumed to be formed by the presence of a static magnetic field placed within a plasma.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>