Surface Impedance Boundary Condition Research Articles

Scattering coefficients of surface plasmon polaritons impinging at oblique incidence onto one-dimensional surface relief defects

We present a theoretical analysis of surface plasmon polariton (SPP) scattering by shallow one-dimensional surface relief defects for oblique incidence, applying both surface impedance boundary conditions and Rayleigh expansion. Using this method, nontrivial angular dependences for transmission, reflection, and out-of-plane scattering are obtained. For the case of a defect with rectangular shape, we give an analytical description of the interference phenomena caused by the SPP diffraction for both a single defect (either protrusion or indentation) and a finite array of them.

On the Applicability of the Surface Impedance Integral Equation for Optical and Near Infrared Copper Dipole Antennas

The applicability of the surface impedance integral equation (SI-IE) method for the analysis of optical and near-infrared copper dipole antennas is assessed, and some issues relative to resonant half-wavelength optical dipoles are highlighted. Since at these frequencies the conductivity of copper (and of all metals) is relatively small, the appropriateness of using the standard integral equation method for imperfectly conducting wires, based on a surface impedance boundary condition, needs to be examined. Here it is found that the SI-IE method yields accurate results in the near-infrared regime, and for suitably small wire radius values at low optical frequencies. For the middle and upper optical frequencies the approximate SI-IE is not generally valid. Some results are presented for a half-wave dipole resonant in the upper near-infrared/low optical range, and a discussion of the trade-off between maintaining good polarization selectivity and radiation efficiency is provided

Modeling of Lossy Curved Surfaces in 3-D FIT/FDTD Techniques

A conformal first-order or Leontovic surface-impedance boundary condition (SIBC) for the modeling of lossy curved surfaces in a Cartesian grid is presented for the finite-integration technique (FIT). Equivalently, the model can be derived using the contour-path formulation of the finite-difference time domain (FDTD) method. The SIBC is based on a lumped-element representation of the impedance combined with a conformal modeling scheme. The validity of the proposed model is evaluated by investigating the quality factors of rectangular, cylindrical and spherical cavity resonators. The convergence rate of the conformal SIBC model is shown to be of second order

Transmission of light through a single rectangular hole in a real metal

A theory is presented to describe the optical transmission through a rectangular hole in a real metal film. The previous theory of the transmission through a rectangular hole in a perfect electric conductor is extended to include the effects associated with having a real metal by adding surface-impedance boundary conditions and an effective index mode calculation. Both the peak and amplitude of the Fabry-P\'erot resonance of the fundamental mode agree quantitatively with experiments. Finite-difference time-domain calculations are used to verify the theoretical findings as well as to show the effects of including loss, which is not included in the theory. The localized nature of the transmission resonances is also revealed by analyzing the electric field maps associated with the enhanced transmission process.

Broadband lossy conductor wall processing using lumped constant circuit and recursive formulas on FDTD method

AbstractA practical conductor boundary processing method using the surface impedance boundary condition in the FDTD method is presented. In the present method, the surface impedance on the conductor is first replaced by an approximate equation. This approximation can easily suppress the approximation errors in the frequency range of interest in the analysis. Next, by means of inverse Laplace transform, the approximate equation is expressed in the time domain. In this way, the problem can be replaced by the excellent recursive operation previously proposed and a new update equation can be derived. Also, as a confirmation of the validity of the present conductor boundary processing method, an FDTD analysis is carried out for propagation of the TEM wave between the conductors and the results are compared with the theoretical values of the analysis model. As a result, remarkable agreement with the theoretical values is obtained over a broad frequency range. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 89(6): 8–13, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20172

An FDTD Model for Low and High Altitude Lightning-Generated EM Fields

To explore lightning-generated electromagnetic wave behavior and lightning-related ionospheric phenomena, a full-wave two-dimensional cylindrical finite-difference time-domain (FDTD) model was developed to simulate lightning-generated electromagnetic wave propagation in the ionosphere with high altitude and long distance capabilities. This FDTD model removes the approximations made in other similar models to extend its applicability, and incorporates a variety of existing methods and new techniques. A dispersive and anisotropic realization of the nearly perfectly matched layer (NPML) absorbing boundary condition is adopted in this numerical model for ease of implementation. Earth curvature is included in the model through the modified refractive index method. The surface impedance boundary condition is adopted to treat arbitrary but homogeneous ground parameters. We quantify the errors through dispersion relations, and the solution convergence is analyzed. Comparisons between our simulation, numerical waveguide mode theory, and experimental data validate this model and show its capabilities compared to other methods. Although this FDTD model was developed for the lightning-generated electromagnetic field simulation, it is also applicable for other very low frequency (VLF, 3-30 kHz) and extremely low frequency (ELF, 3-3000 Hz) wave propagation problems

Surface impedance boundary conditions for the finite integration technique

Approximate time-domain relations between the electric field integrated along the edge and the magnetic flux density integrated over the facet of the computational cell at the dielectric/conductor interface are derived and implemented into the finite integration technique to accurately eliminate the conducting region from the computational mesh. Both Cartesian and tetrahedral grids are considered. A numerical example is included to illustrate the method

Modelling of lossy curved surfaces in the 3-D frequency-domain finite-difference methods

A conformal first-order or Leontovic surface-impedance boundary condition (SIBC) for the modelling of fully three-dimensional (3-D) lossy curved surfaces in a Cartesian grid is presented for the frequency-domain finite-difference (FD) methods. The impedance boundary condition is applied to auxiliary tangential electric and magnetic field components defined at the curved surface. The auxiliary components are subsequently eliminated from the formulation resulting in a modification of the local permeability value at boundary cells, allowing the curved 3-D surface to be described in terms of Cartesian grid components. The proposed formulation can be applied to model skin-effect loss in time-harmonic driven problems. In addition, the impedance matrix can be used as a post-processor for the eigenmode solver to calculate the wall loss. The validity of the proposed model is evaluated by investigating the quality factors of cylindrical and spherical cavity resonators. The results are compared with analytic solutions and numerical reference data calculated with the commercial software package CST Microwave Studio™ (MWS). The convergence rate of the results is shown to be of second-order for smooth curved metal surfaces. The overall accuracy of the approach is comparable to that of CST MWS™. Copyright © 2006 John Wiley & Sons, Ltd.

Reconstruction of transient currents from magnetic data

Purpose – To provide a time domain formulation for reconstruction of transient currents flowing in massive parallel conductors from magnetic data collected in the dielectric space surrounding the conductors.Design/methodology/approach – A boundary integral equation (BIE) formulation involving Mitzner's and Rytov's high order surface impedance boundary conditions (SIBCs) is used. Input data of the inverse problem are the magnetic fields at given locations near the conductors. In order to validate the inversion algorithm, the magnetic field data are computed solving the direct problem with FEM for given current waveforms.Findings – The improvement in reconstruction accuracy of the new time domain BIE formulation employing high order SIBCs has been demonstrated numerically in a simple test case. The range of validity of the technique has been extended to current pulses of longer duration and the computational burden has shown to increase only by a factor of 4.Research limitations/implications – The proposed ...

Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications

An extended surface impedance boundary condition algorithm is developed that allows for the optical properties of a wide variety of complex one-dimensional periodic grating structures to be modeled. Wood-Rayleigh anomalies, diffraction, and electromagnetic resonance modes including horizontally oriented surface plasmons and vertical surface resonances are identified and described as well as analyzing their structural and geometrical dependencies. Methods to combine these modes to produce hybrid modes that channel and localize light are described. Application of these modes to metal-semiconductor-metal photodetectors (MSM-PD) is discussed and an example silicon-based MSM-PD with over 30 GHz bandwidth and 0.3 A/W responsivity is described.

Numerical modeling of surface plasmon enhanced silicon on insulator avalanche photodiodes

We report an atypical device structure for a silicon-on-insulator (SOI) avalanche photodiode (APD) that uses vertically oriented surface plasmons to enable high device performance including high bandwidth and high responsivity. This device structure would allow for high bandwidth (>10 GHz) read out integrated circuitry to be fabricated alongside the photodetector. A detailed numerical simulation of the device is performed that includes the use of the surface impedance boundary condition (SIBC) algorithm to calculate the optical resonance modes of the structure. The SIBC algorithm is integrated with a Poisson’s equation solver and a Monte Carlo algorithm to model many aspects of the SOI APD device including bandwidth and responsivity as a function of applied bias. A brief discussion of surface plasmon modes and other optical modes in the APD and similar structures is also given.

Time domain surface impedance concept for low frequency electromagnetic problems—Part II: Application to transient skin and proximity effect problems in cylindrical conductors

A time domain boundary element formulation employing the surface impedance boundary conditions (SIBCs) is developed for the 3-dimensional transient eddy current problem of cylindrical conductors. SIBCs of different orders of approximation are implemented using the perturbation technique in the small parameter proportional to the ratio of the skin depth and characteristic size of the conductor cross-section. The formulation consists of a set of time domain surface integral equations that have identical left-hand sides and can be solved using the same program procedure. The number of equations is determined by the order of approximation of the SIBC, namely: solutions in the perfect electrical conductor (PEC) limit (lowest order) and in the so-called Rytov approximation (highest order) are given by one and four equations, respectively. It is demonstrated that each equation admits separation of variables into space and time components, a property that significantly reduces computational costs compared with traditional time domain formulations that require the integral equations to be solved at each time step. For the purpose of validation, a test problem is solved by the proposed formulation and by the ‘original’ BEM based on the time-dependent fundamental solution. Conditions of applicability are discussed and the effect of such factors as the shape of the incident current pulse and proximity effect are considered.

Time domain surface impedance concept for low frequency electromagnetic problems—Part I: Derivation of high order surface impedance boundary conditions in the time domain

The surface impedance boundary conditions (SIBCs) for the tangential component of the electric field and normal component of the magnetic field on the smooth curved surface of a homogeneous non-magnetic conductor are derived in time- and frequency-domain. Scale factors for the basic variables are introduced in such a way that, a small parameter, equal to the ratio of the penetration depth and the body's characteristic size, appears in the dimensionless Maxwell's equations for the conducting region. The perturbation method is then used to represent the SIBCs in the form of power series in this small parameter and the first four terms of the expansions are derived. The zero-order, first-order, second-order and third-order terms of the expansions are the solution of the problem in the perfect electrical conductor limit, the Leontovich approximation, the Mitzner approximation and in the high order approximation (referred to as Rytov's approximation), respectively. Therefore, the accuracy of the proposed conditions exceeds the accuracy of the SIBC for planar surfaces (Leontovich's approximation) that are usually used in the time-domain analysis, by two orders of magnitude. In Part II of this paper, the formulation of the SIBCs developed here in conjunction with a boundary element method is demonstrated and applied to the problem of transient skin and proximity effect problems in cylindrical conductors.

Emissvity of metallic microcontoured surfaces

In this paper, we study the diffraction of electromagnetic radiation by a periodic micro-rough surface separating vacuum from a metal with a finite conductivity. We submit the integral method to the surface impedance boundary condition. Thus the numerical implementation is greatly reduced. We compare the numerical emissivities obtained by this approach to those we have calculated through the rigorous multilayer modal method. This enables us to show that the mentioned approximate method has two regions of validity: one corresponding to fairly flat surfaces and the other to very deep surfaces. It is well known that both the Kirchhoff approximation and the constant flat boundary impedance approximation are also valid for fairly flat surfaces. Our investigation aims also to establish whether these two approximate methods lead to the same results, and whether the integral method submitted to the surface impedance condition has a larger domain of validity. Concerning deep surfaces with a period smaller than the wavelength, we introduce the homogenization process in order to study its accuracy. Finally, this work permitted to identify three different regimes depending on the surface slopes: the simple scattering regime, the homogenization regime and the intermediate regime. For the latter, if the period is in the order of the wavelength, then we will show that the emissivity can be exalted.

FDTD model of electrically thick frequency-dispersive coatings on metals and semiconductors based on surface impedance boundary conditions

A new finite-difference time-domain (FDTD) model for conductors coated with electrically thick frequency-dispersive coatings is developed. The model is based on first-order impedance boundary conditions. As the most important original feature of the model, the frequency dependence of the material parameters of the coating is very general: dispersive coatings of Lorentz-, Debye-, or Drude-type with multiple pole pairs and a fixed electrical conductivity can be modeled with the proposed technique. Another new property of the model is the use of rational approximation in a way that enables accurate approximation of the impedance function in a wide range, corresponding to several thickness resonances of the coating. The conductor losses in the metal backing that are neglected in many earlier models are accounted for in the proposed model. The model is formulated for planar interfaces in the general three-dimensional situation for the Yee algorithm and verified against analytical reference results with numerical examples in one-dimensional and two-dimensional problems.

An Efficient Surface-Impedance Boundary Condition for Thin Wires of Finite Conductivity

To include dispersive loss into a sub-cell thin-wire model, a new implementation of a surface-impedance boundary condition (SIBC) is proposed. The surface-impedance function is approximated in the frequency domain by a series of first-order rational functions allowing straightforward transform into time domain. The contribution of the wire radius is included in the surface-impedance function extending the model to very thin or poorly conducting metal wires. Further, the SIBC includes the direct-current (dc) resistance. The approximation for the SIBC is chosen such that the dependence on the wire radius and conductivity can be removed prior to the computation of the approximation coefficients. Consequently, the wire radius and conductivity can be varied without re-computing the coefficients. The proposed model is compared with an existing SIBC wire model based on the high-frequency approximation and Prony's method, NEC-2 generated reference data, and analytical results. The results indicate enhanced accuracy at a reduced computational cost as compared with an existing model.

2D full‐wave finite‐difference frequency‐domain method for lossy metal waveguide

AbstractThe 2D finite‐difference frequency‐domain method combined with the surface‐impedance boundary condition is applied for the analysis of dispersion characteristics of lossy metal waveguides. Six electromagnetic field components are involved in the final eigen equation. By solving the eigen equation, the method finds the propagation constants for a given frequency. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 158–161, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20238

Broadband lossy conductor wall processing using lumped constant circuit on FDTD method

AbstractA practical conductor boundary processing technique in the FDTD method based on the surface impedance boundary condition is proposed. The surface impedance of the conductor is approximated by the input impedance of a lumped element circuit. It is shown that this approximation is highly accurate in a broad bandwidth. The effectiveness of this method is numerically confirmed. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 87(6): 1–9, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20068

FDTD Surface Impedance Model for Coated Conductors

A new finite-difference time-domain (FDTD) model of dielectric and conductive layers on conductive surfaces is developed. The model is based on surface impedance boundary condition, allowing the coating and the conductive backing to be removed from the computational space. The proposed model extends the previous FDTD models, which are formulated for coatings on perfect electric conductors (PEC), to coatings on more general dielectric and conductive materials. On the other hand, the model can also be regarded as a generalization of models designed for conductors without coatings. The present model accounts for the first thickness resonance of the layer by modeling the singularity of the tangent function appearing in the impedance function. The proposed model is numerically verified for normal incidence in the frequency domain and for varying oblique angles of incidence in the time domain by comparison with analytical results.

Finite-difference time-domain model of interfaces with metals and semiconductors based on a higher order surface impedance boundary condition

A new numerical finite-difference time-domain (FDTD) model of interfaces with metals and semiconductors is developed. The model uses a higher order impedance boundary condition to simulate the fields in conductive media. The approach has been found to be considerably more accurate than the known models based on the simple Leontovich impedance boundary condition. This is because the new model takes the incidence angle of the incident waves into account, and it is valid for all values of conductivity. The derivation of the method is presented in the two-dimensional (2D) case, and the performance is studied over a wide range of conductivity. The validation of the method is made by comparing with the exact results in a 2D example problem. The proposed method is also compared with some other methods available in the literature.