Analytical Modeling In Applied Electromagnetics

The Maxwell-Garnett mixing formula, previously well known for dielectric mixtures, is generalised for the first time to cover chiral materials. The mixing formula expresses the permittivity, permeability and chirality of a two-component mixture with spherical inclusions as functions of the material parameters of the components. The result gives the classical Maxwell-Garnett formula as a special case. The mixing formula can be applied for the design of chiral composites that have attracted keen interest in recent years.

Chiral Maxwell-Garnett mixing formula

The paper discusses wave propagation and field distributions in slab dielectric waveguides having homogeneous isotropic chiral material. The analysis is based on field expansions in the guide and in the upper and lower half spaces. Enforcing the boundary conditions at the waveguide interfaces result in eigenvalue equations for the hybrid propagating and guided modes. The theory is illustrated by calculating dispersion curves and field distributions for weakly guiding chiral slab waveguides.

Dispersion curves and fields for a chiral slab waveguide

The optical radiation force experienced by a cylinder material of circular cross section exhibiting circular dichroism (known also as rotary polarization) in an electric line source illumination is considered. An exact analytical expression for the radiation force (per length) valid for any frequency range is derived assuming an electric line source radiating cylindrically diverging TM-polarized waves without any approximations. The partial-wave series expansion method in cylindrical coordinates utilizing standard Bessel and Hankel functions is used to derive the electric and magnetic field expressions and a dimensionless radiation force function (or efficiency), which depends on the scattering coefficient of the cylinder as well as the distance from the radiating source. To illustrate the analysis, numerical computations for the dimensionless radiation force function for a perfect electromagnetic conductor (PEMC) cylinder are performed with emphasis on its dimensionless size parameter and source distance, which clearly draw attention to the contribution of the cross-polarized scattered waves (resulting from the rotary polarization effect) to the total force. The numerical predictions demonstrate the possibility to pull a circular-shaped cylinder material with rotary polarization toward the illuminating electric line source with TM-polarized waves using a curved wavefront depending on the PEMC material admittance, distance to the source, and size of the cylinder.

Induced radiation force of an optical line source on a cylinder material exhibiting circular dichroism.

This paper presents a comparison of results of coherent and incoherent sampling measurements of complex ratios of sinusoidal voltages, obtained with the use of an ellipse-fitting algorithm (EFA) and with the use of discrete Fourier transform (DFT). The EFA algorithm has not been yet used in the measurements of the complex voltage ratio. Known applications of EFA in impedance measurements were based on simultaneous sampling of two voltages by a two-channel aquisition card. Measurements presented in this paper were made with an automated measurement system consisting of Keysight 3458A multimeter operating in the DC voltage sampling mode. The internal 20-MHz clock generator of this multimeter was replaced with a custom-made clock module dividing the clock frequency by 2 and providing fiber optic 10–MHz synchronization signal. This signal was used as the reference frequency of the Keysight 33250A generator which served as a reference frequency clock for the dual-channel source of digitally synthesized sinusoidal voltage. Because the output frequency of the Keysight 33250A generator can be adjusted with very high resolution and accuracy, it was possible to perform coherent and incoherent sampling measurements with controlled frequency deviation.

Application of Ellipse Fitting Algorithm in Incoherent Sampling Measurements of Complex Ratio of AC Voltages

A wire grid is assumed to be composed of parallel infinitely long thin perfectly conducting or conducting wires. Effects of random positioning errors upon grid impedance, reflection and transmission characteristics are analyzed theoretically for such a grid. It is studied that increasing random errors in positioning of wires increases the magnitude of wire grid impedance. Also, it reduces reflection from a wire grid. This reduction is more dominant at normal incidence. Likewise, increasing error in positioning of wires increases transmission through a wire grid.

Effects of Random Positioning Errors Upon Electromagnetic Characteristics of a Wire Grid

An analytical theory has been developed to find the general effective parameters of a nonlocal medium. The medium is nonlocal due to presence of spatial dispersion. The proposed theory is based upon the dipolar scattering model of the inclusions comprising the medium. The bianisotropy stemming from the magnetoelectric coupling at the inclusion and lattice level has been discussed. The developed theory is then applied to a medium which consists of coated spheres with realistic materials. Effects of different values of wavevector upon the effective permittivity, effective permeability, and magnetoelectric coefficient stemming from lattice effects have been studied for a coated sphere medium. It is shown that a coated sphere medium with a weak spatial dispersion gives rise to a broader range of frequencies, where real parts of the effective permittivity and permeability are negative. On the other hand, this range of frequencies becomes smaller when the spatial dispersion of the medium is not weak.

Nonlocal effective parameters of a coated sphere medium

Accurate amplitude and phase difference estimation is desired for impedance measurements where two common frequency sine signals are acquired. One of the proposed algorithms for amplitude and phase estimation is the ellipse fitting algorithm. This algorithm, due to its simplicity, is a prime candidate for implementation in standalone impedance measurement systems based on DSPs. However, the phase difference estimation of the ellipse fit method is biased when the signals approach in phase or in phase-opposition. In this paper, a modified ellipse fit method is proposed to improve phase difference estimation. The performance of the algorithm is tested on simulated data. It is found that the proposed method is better for phase difference estimation than the ellipse fit method.

Improvement of phase difference estimation using modified ellipse fit method

The reflection and transmission properties of a wire grid embedded in lossless Single Negative (SNG) or Single Zero (SZ) medium have been analytically studied. The wires of the grid are taken to be lossless as well as lossy. It is shown that a lossy grid has approximately identical reflection characteristics for the Transverse Magnetic incident wave with Epsilon Negative and Mu Negative background medium. The lossy grid with Epsilon Zero background medium acts as a perfect reflector for the normally incident wave. Likewise, it is further studied that a lossy wire grid embedded in Mu Zero medium can be cloaked for the incoming normally incident wave.

Reflection and transmission properties of a wire grid embedded in a SNG or SZ medium

A considered metasurface is assumed to consist of a two-dimensional periodic arrangement of inductively loaded wires. The effects of incident angles and inductive loads upon equivalent surface impedance, reflection, and transmission properties of this metasurface have been investigated using numerical simulations. It is shown that at a particular frequency and angle, a metasurface can be cloaked for the incoming incident wave with nearly zero reflection. It is further studied that this approximate zero reflection is independent of the inductances of the inductively loaded wire dipoles.

Reflection and transmission properties of a metasurface composed of resonant loaded wire dipoles.

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