Arbitrary Dielectric Profiles Research Articles

Universal behavior of a dispersive Dirac cone in gradient-index plasmonic metamaterials

We demonstrate analytically and numerically that the dispersive Dirac cone emulating an epsilon-near-zero (ENZ) behavior is a universal property within a family of plasmonic crystals consisting of two-dimensional (2D) metals. Our starting point is a periodic array of 2D metallic sheets embedded in an inhomogeneous and anisotropic dielectric host that allows for propagation of transverse-magnetic (TM) polarized waves. By invoking a systematic bifurcation argument for arbitrary dielectric profiles in one spatial dimension, we show how TM Bloch waves experience an effective dielectric function that averages out microscopic details of the host medium. The corresponding effective dispersion relation reduces to a Dirac cone when the conductivity of the metallic sheet and the period of the array satisfy a critical condition for ENZ behavior. Our analytical findings are in excellent agreement with numerical simulations.

Second-Order Perturbative Solution of Scattering From Two Rough Surfaces With Arbitrary Dielectric Profiles

Analytical expressions for the cross-polarization components of the normalized radar cross sections (NRCS) of three-dimensional stratified media with two rough surfaces are presented. In a recent paper, the zeroth- and the first-order scattering solutions of a two-rough-surface structure with arbitrary dielectric profiles were presented using the small perturbation approach based on the extended boundary conditions (EBC). In this study, the proposed method is extended to obtain the second-order solutions including cross-polarized fields. Unlike copolarizations, the main contribution of cross-polarizations is determined by the second-order solutions. A direct extension of the recently proposed formulation leads to difficult and lengthy manipulations; hence, first a compact recursive matrix formulation for the unknown surface fields of an arbitrary order is derived. Then, for the second-order fields, the matrix system is efficiently and straightforwardly solved. Finally, the cross-polarized scattered fields and the normalized radar cross sections are derived. The final solutions are given in simple, compact, and closed-form expressions that make the computations very easy. The derived expressions are validated against known solutions of special cases, available in the literature. The results are shown to be exactly consistent with existing ones, both analytically and numerically.

Scattering From Two Rough Surfaces With Inhomogeneous Dielectric Profiles

A rigorous analytical technique to derive the scattering coefficients of three-dimensional (3-D) two rough surfaces with arbitrary dielectric profiles is presented. The proposed method applies a perturbation approach to a surface integral equation (IE) formulation that is derived from the extended boundary conditions (EBC). First, using EBC or the surface equivalence principle (SEP) and the dyadic Green’s functions of the resulting simpler geometries, a system of IEs for the surface fields of the two rough interfaces is established. Then, the Fourier-domain surface fields are derived using a perturbation method. The scattered fields are subsequently determined by a second application of SEP. In general, the approach could be used to present the general formulation for multiple rough layers and also higher order solutions. But, the focus of this paper is on deriving compact closed-form solutions for inhomogeneous dielectric profiles and thus, only two rough interfaces are considered. Accordingly, the first-order closed-form scattered fields are represented in a remarkably compact form that is suitable for physical interpretation and also extension to higher orders. Finally, the derived expressions are compared to known solutions of special cases, available in the literature. The results are shown to be exactly consistent with existing ones and hence validated analytically and numerically.

Field of a short dipole above a dielectric half‐space with rough interface

The accurate prediction of radiowave coverage at high frequency-ultra high frequency over irregular terrain features is of importance in the design and development of low-cost and low-power communication systems. This study studies the problem of electromagnetic wave propagation, excited by a short dipole, above a dielectric ground plane with an arbitrary dielectric profile and an irregular interface. This investigation is a natural extension of the classical Sommerfeld problem with the exception of the random surface irregularities at the interface between the two dielectric media. It is assumed that the interface profile height variations are small compared with the wavelength. First, the bistatic scattering of a plane wave illuminating the rough surface is solved using a perturbation solution of an integral equation for the induced polarisation current. Analytical expressions for the coherent field and incoherent scattered power at an arbitrary observation point are obtained. Then, the solutions for the coherent and incoherent scattered power generated by a small dipole of arbitrary orientation and position are derived by expanding the field of the dipole in terms of a continuous spectrum of plane waves and using superposition. The effects of the rough interface on the surface waves and on depolarisation are studied.

Electromagnetic Scattering From Multilayer Rough Surfaces With Arbitrary Dielectric Profiles for Remote Sensing of Subsurface Soil Moisture

Radar remote sensing of soil moisture content at low frequencies requires an accurate scattering model of realistic soils, which often involves multilayer rough surfaces and dielectric profiles. In this paper, a hybrid analytical/numerical solution to two-dimensional scattering from multilayer rough surfaces separated by arbitrary dielectric profiles based on the extended boundary condition method (EBCM) and scattering matrix technique is presented. The reflection and transmission matrices of rough interfaces are constructed using EBCM. The dielectric profiles are modeled as stacks of piecewise homogeneous dielectric thin layers, whose scattering matrices are computed by recursively cascading reflection and transmission matrices of individual dielectric interfaces. The interactions between the rough interfaces and stratified dielectric profiles are taken into account by applying the generalized scattering matrix technique. The scattering coefficients are obtained by combining the powers computed from the resulting Floquet modes of the overall system. The bistatic scattering coefficients are validated against existing analytical and numerical solutions. Field-collected soil moisture data are then used for numerical simulations to investigate the penetration capability at different frequencies and to address the potential of low-frequency radar systems in estimating deep soil moisture. In particular, soil moisture profiles during dry ground, wet ground, and wet subsurface layer conditions are examined. The results show that both backscattering coefficients and copolarized phase difference at low frequencies are sensitive to the roughness of subsurface interfaces and deep soil moisture. Also, much larger depth sensitivity can be achieved using copolarized phase difference than scattering coefficients

First-principles approach to dielectric response of graded spherical particles

We have studied the effective response of composites of spherical particles each having a dielectric profile which varies along the radius of the particles. We developed a first-principles approach to compute the dipole moment of the individual spherical particle and hence the effective dielectric response of a dilute suspension. The approach has been applied to two model dielectric profiles, for which exact solutions are available. Moreover, we used the exact results to validate the results from the differential effective dipole approximation, recently developed to treat graded spherical particles of an arbitrary dielectric profile. Excellent agreement between the two approaches were obtained. While the focus of this work has been on dielectric responses, the approach is equally applicable to analogous systems such as the conductivity and elastic problems.

Wave Propagation in a Curved Waveguide with Arbitrary Dielectric Transverse Profiles

A rigorous approach is derived for the analysis of electromagnetic (EM) wave propagation in dielectric waveguides with arbitrary profiles, situated inside rectangular metal tubes, and along a curved dielectric waveguide. The first objective is to develop a mode model in order to provide a numerical tool for the calculation of the output fields for radius of curvature 0.1 m ≤ R ≤∞ . Therefore we take into account all the terms in the calculations, without neglecting the terms of the bending. Another objective is to demonstrate the ability of the model to solve practical problems with inhomogeneous dielectric profiles. The method is based on Fourier coefficients of the transverse dielectric profile and those of the input wave profile. These improvements contribute to the application of the model for inhomogeneous dielectric profiles with single or multiple maxima in the transverse plane. This model is useful for the analysis of dielectric waveguides in the microwave and the millimeter-wave regimes, for diffused optical waveguides in integrated optics, and for IR regimes.

Exact quantum calculation of polariton dispersion in semiconductor microcavities

We develop a general quantum mechanical method to calculate the dispersion relations of polariton modes for a quantum well embedded in a semiconductor planar microcavity. The method is based on the properties of the Green's function of the electromagnetic field in a one dimensional dielectric structure. By means of this approach it is possible to express the dispersion relations in a compact form once the eigenmodes of the electromagnetic field in the region where the quantum well is placed are known. We discuss the specific example of a microcavity with equal distributed Bragg reflectors at the two ends. The dispersion relation in this case is calculated analytically. The method can in principle be applied to dielectric one dimensional structures of arbitrary dielectric profile.

Light in periodically stratified media

A pedagogical presentation of the propagation of electromagnetic waves in stratified media is given. The usual 2 × 2 matrix analysis is simplified and generalized. A Bloch factor eigenvalue equation is obtained, valid for all periodic stratifications. The implications of the band structure of an infinite periodic structure for reflection by a finite structure are demonstrated. Some features of the reflectivity are shown to be universal. In the long-wave limit, a periodic stratification with an arbitrary dielectric function profile ∊(z) within a unit cell is shown to be equivalent to a homogeneous anisotropic medium, with ordinary and extraordinary dielectric constants given by ∊o = 〈∊〉 and ∊e−1 = 〈∊−1〉.

Series solutions to the arbitrary profile 1-D waveguide and quantum-well problems

The 1D waveguide of arbitrary dielectric profile is solved for TE and TM modes by a method based on series solutions. It is a guess-propagate-iterate scheme. The profile is approximated by small segments of either constant or linearly changing dielectric constant. The method is accurate, generally significantly faster than other methods, and can cope with modes near cutoff; and with lossy, or gain-guided modes. Series solutions are also given to solve the 1D Schrodinger equation. >

Numeric reconstruction of smooth dielectric profiles

The one-dimensional inverse scattering problem can be solved in principal by use of the Gel'fand-Levitan integral equation. However, explicit solutions of this equation are seldom easy to obtain. Here we develop an iterative numeric procedure to reconstruct arbitrary smooth dielectric profiles. Several cases exemplify the simplicity and economy of the technique.

Measurements of Dispersion Characteristics and Field Distributions in Rectangular-Dielectric Waveguide and its Modifications

The author has previously numerically analyzed transmission characteristics of several dielectric waveguides by applying generalized telegraphist's equations. The technique may be applicable to a wide class of dielectric waveguides with arbitrary dielectric profile and cross section. In this paper, the dispersion characteristics and the field distributions in rectangular-dielectric waveguides and in single material fibers have been measured at X-band frequencies to verify the validity of the analysis. Good agreement between measured and calculated results shows that the analysis is useful to study the transmission characteristics of dielectric waveguides.

Numerical Analysis of the Rectangular Dielectric Waveguide and its Modifications

Dielectric waveguides suitable for millimeter and submillimeter wave integrated circuits are analyzed by applying the generalized telegraphist's equations. The dielectric waveguides treated in this paper are the rectangular dielectric image line, the cladded rectangular dielectric image line, the insulated image guide, and the strip dielectric guide. Numerical results of the propagation constant, the power distribution, and the field configuration in these dielectric waveguides are presented. Values for the propagation constants obtained by our method are compared with other theoretical results. Although this work is based on a closed waveguide model, it may be applicable to wide classes of dielectric waveguides with arbitrary dielectric profiles and cross sections.