Numerically Efficient Technique for Metamaterial Modeling (Invited Paper)
TL;DR: Two simulation techniques for modeling periodic structures with three-dimensional elements in general are presented, one based on the Method of Moments (MoM) and the other a Finite Difierence Time Domain (FDTD)-based approach, which is well suited for handling arbitrary, inhomogeneous, three- dimensional periodic structures.
Abstract: In this paper we present two simulation techniques for modeling periodic structures with three-dimensional elements in general. The flrst of these is based on the Method of Moments (MoM) and is suitable for thin-wire structures, which could be either PEC or plasmonic, e.g., nanowires at optical wavelengths. The second is a Finite Difierence Time Domain (FDTD)-based approach, which is well suited for handling arbitrary, inhomogeneous, three-dimensional periodic structures. Neither of the two approaches make use of the traditional Periodic Boundary Conditions (PBCs), and are free from the di-culties encountered in the application of the PBC, as for instance slowness in convergence (MoM) and instabilities (FDTD).
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TL;DR: A beam-steering antenna based on non-uniform metasurface superstrate and artificial magnetic conductor (AMC) operating at 3.5 GHz was proposed in this article .
Abstract: A beam-steering antenna based on non-uniform metasurface superstrate and artificial magnetic conductor (AMC), operating at 3.5 GHz, is proposed. The antenna can steer the beam along θ = −18° and 18° with the superstrate and along θ = 0° in the absence of the superstrate with almost zero scan loss. The proposed antenna structure consists of a top layer of non-uniform metasurface superstrate made of a 20 × 20 grid of electrically-small square-shaped metallic pixels while the bottom part consists of AMC with a grid of 5 × 5 pixels. The radiating element, CPW-fed monopole antenna, is placed between AMC and superstrate. The fabricated prototype shows desired beam steering in directions of θ = −18°, 0°, and 18° while maintaining uniform realized gain of 5.5 dBi and matching well with simulations.
4 citations
TL;DR: In this article , the authors proposed an alternative periodic boundary condition (APBC) algorithm according to the unconditionally stable SIDS algorithm to analyze the periodic structures, which can not only maintain the calculation stability with the enlargement of time steps but also tighten the finite-difference time domain (FDTD) implementation.
2 citations
01 Jan 1989
TL;DR: In this article, a variational formulation for anisotropic, dielectric waveguides using only the (E/sub x/, E/sub y/) or (H/sub X/, H/sub Y/) components of the electromagnetic field was derived.
Abstract: The authors derive a variational formulation for anisotropic, dielectric waveguides using only the (E/sub x/, E/sub y/) or (H/sub x/, H/sub y/) components of the electromagnetic field. They show that the (E/sub x/, E/sub y/) formulation is completely equivalent to the (H/sub x/, H/sub y/) formulation. In fact, they are the transpose problems of each other. Given the variational formulation, one can derive the finite-element solution quite easily. The authors also show how to derive a variational expression where the natural boundary conditions are incorporated as an optimal solution of the variational expression. The theory is illustrated with a simple implementation of a finite-element solution. The solutions agree with previous results, and there is no occurrence of spurious modes. >
1 citations
References
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Book•
31 May 1995
TL;DR: This paper presents background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology, and the proposed three-dimensional Yee algorithm for solving these equations.
Abstract: Part 1 Reinventing electromagnetics: background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology. Part 2 The one-dimensional scalar wave equation: propagating wave solutions finite-difference approximation of the scalar wave equation dispersion relations for the one-dimensional wave equation numerical group velocity numerical stability. Part 3 Introduction to Maxwell's equations and the Yee algorithm: Maxwell's equations in three dimensions reduction to two dimensions equivalence to the wave equation in one dimension. Part 4 Numerical stability: TM mode time eigenvalue problem space eigenvalue problem extension to the full three-dimensional Yee algorithm. Part 5 Numerical dispersion: comparison with the ideal dispersion case reduction to the ideal dispersion case for special grid conditions dispersion-optimized basic Yee algorithm dispersion-optimized Yee algorithm with fourth-order accurate spatial differences. Part 6 Incident wave source conditions for free space and waveguides: requirements for the plane wave source condition the hard source total-field/scattered field formulation pure scattered field formulation choice of incident plane wave formulation. Part 7 Absorbing boundary conditions for free space and waveguides: Bayliss-Turkel scattered-wave annihilating operators Engquist-Majda one-way wave equations Higdon operator Liao extrapolation Mei-Fang superabsorption Berenger perfectly-matched layer (PML) absorbing boundary conditions for waveguides. Part 8 Near-to-far field transformation: obtaining phasor quantities via discrete fourier transformation surface equivalence theorem extension to three dimensions phasor domain. Part 9 Dispersive, nonlinear, and gain materials: linear isotropic case recursive convolution method linear gyrontropic case linear isotropic case auxiliary differential equation method, Lorentz gain media. Part 10 Local subcell models of the fine geometrical features: basis of contour-path FD-TD modelling the simplest contour-path subcell models the thin wire conformal modelling of curved surfaces the thin material sheet relativistic motion of PEC boundaries. Part 11 Explicit time-domain solution of Maxwell's equations using non-orthogonal and unstructured grids, Stephen Gedney and Faiza Lansing: nonuniform, orthogonal grids globally orthogonal global curvilinear co-ordinates irregular non-orthogonal unstructured grids analysis of printed circuit devices using the planar generalized Yee algorithm. Part 12 The body of revolution FD-TD algorithm, Thomas Jurgens and Gregory Saewert: field expansion difference equations for on-axis cells numerical stability PML absorbing boundary condition. Part 13 Modelling of electromagnetic fields in high-speed electronic circuits, Piket-May and Taflove. (part contents).
11,194 citations
"Numerically Efficient Technique for..." refers methods in this paper
...The method described herein not only circumvents these difficulties with the instabilities and time-step reduction, but it also does not require the introduction of auxiliary functions [15] in the FDTD update equations....
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Book•
01 Jan 1968
TL;DR: This first book to explore the computation of electromagnetic fields by the most popular method for the numerical solution to electromagnetic field problems presents a unified approach to moment methods by employing the concepts of linear spaces and functional analysis.
Abstract: From the Publisher:
"An IEEE reprinting of this classic 1968 edition, FIELD COMPUTATION BY MOMENT METHODS is the first book to explore the computation of electromagnetic fields by the most popular method for the numerical solution to electromagnetic field problems. It presents a unified approach to moment methods by employing the concepts of linear spaces and functional analysis. Written especially for those who have a minimal amount of experience in electromagnetic theory, this book illustrates theoretical and mathematical concepts to prepare all readers with the skills they need to apply the method of moments to new, engineering-related problems.Written especially for those who have a minimal amount of experience in electromagnetic theory, theoretical and mathematical concepts are illustrated by examples that prepare all readers with the skills they need to apply the method of moments to new, engineering-related problems."
6,593 citations
"Numerically Efficient Technique for..." refers background in this paper
...The conventional Method of Moments (MoM) [4, 5] is often the algorithm of choice for electromagnetic scattering problems....
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Book•
01 Jan 1989
TL;DR: In this article, the authors introduce the notion of circular cross-section waveguides and cavities, and the moment method is used to compute the wave propagation and polarization.
Abstract: Time--Varying and Time--Harmonic Electromagnetic Fields. Electrical Properties of Matter. Wave Equation and Its Solutions. Wave Propagation and Polarization. Reflection and Transmission. Auxiliary Vector Potentials, Contruction of Solutions, and Radiation and Scattering Equations. Electromagnetic Theorems and Principles. Rectangular Cross--Section Waveguides and Cavities. Circular Cross--Section Waveguides and Cavities. Spherical Transmission Lines and Cavities. Scattering. Integral Equations and the Moment Method. Geometrical Theory of Diffraction. Greena s Functions. Appendices. Index.
5,693 citations
Book•
26 Apr 2000
TL;DR: In this article, the authors present a comparison of band-pass and Dichroic filter designs for one and two-dimensional periodic structures, and present an overview of the current state-of-the-art.
Abstract: General Overview. Element Types: A Comparison. Evaluating Periodic Structures: An Overview. Spectral Expansion of One- and Two-Dimensional Periodic Structures. Dipole Arrays in a Stratified Medium. Slot Arrays in a Stratified Medium. Band-Pass Filter Designs: The Hybrid Radome. Band-Stop and Dichroic Filter Designs. Jaumann and Circuit Analog Absorbers. Power Handling of Periodic Surfaces. Concluding Remarks and Future Trends. Appendices. References. Index.
3,896 citations
"Numerically Efficient Technique for..." refers background in this paper
...The periodic structures are typically modeled as infinite doublyperiodic arrays of scatterers, and are commonly analyzed by imposing periodic boundary conditions to a unit cell to reduce the original problem to a manageable size [3]....
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TL;DR: The mathematical justification of the theory on the basis of electromagnetic theory is described, and the applicability of this theory, or a modification of it, to other branches of physics is explained.
Abstract: The geometrical theory of diffraction is an extension of geometrical optics which accounts for diffraction. It introduces diffracted rays in addition to the usual rays of geometrical optics. These rays are produced by incident rays which hit edges, corners, or vertices of boundary surfaces, or which graze such surfaces. Various laws of diffraction, analogous to the laws of reflection and refraction, are employed to characterize the diffracted rays. A modified form of Fermat’s principle, equivalent to these laws, can also be used. Diffracted wave fronts are defined, which can be found by a Huygens wavelet construction. There is an associated phase or eikonal function which satisfies the eikonal equation. In addition complex or imaginary rays are introduced. A field is associated with each ray and the total field at a point is the sum of the fields on all rays through the point. The phase of the field on a ray is proportional to the optical length of the ray from some reference point. The amplitude varies in accordance with the principle of conservation of energy in a narrow tube of rays. The initial value of the field on a diffracted ray is determined from the incident field with the aid of an appropriate diffraction coefficient. These diffraction coefficients are determined from certain canonical problems. They all vanish as the wavelength tends to zero. The theory is applied to diffraction by an aperture in a thin screen diffraction by a disk, etc., to illustrate it. Agreement is shown between the predictions of the theory and various other theoretical analyses of some of these problems. Experimental confirmation of the theory is also presented. The mathematical justification of the theory on the basis of electromagnetic theory is described. Finally, the applicability of this theory, or a modification of it, to other branches of physics is explained.
3,032 citations