On the Independence of the Excitation of Complex Modes in Isotropic Structures

Islam, R.; Eleftheriades, George V.

doi:10.1109/tap.2010.2044341

Cited by 20 publications

(8 citation statements)

References 27 publications

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“…In section B2, we discuss some of the distinguishing features of fast and slow waves. A good source for early references on the subject of complex waves on isotropic structures plus a treatment that in some ways complements ours is given by Islam and Eleftheriades [2010]. Also see the treatment of traveling waves by A. Hessel in the work by Collin and Zucker [1969, chapter 10], and the treatment of leaky waves by T. Tamir and A. Oliner in the work by Collin and Zucker [1969, chapter 11] and in the work by Jackson and Oliner [2008, section IV].…”

Section: Appendix B: Properties Of Complex Waves On Uniform or Periodmentioning

confidence: 98%

Complex waves on periodic arrays of lossy and lossless permeable spheres: 1. Theory

Shore¹,

Yaghjian²

2012

Radio Science

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[1] This is the first part of a two-part series dealing with complex dipolar waves propagating along the axes of 1D, 2D, and 3D infinite periodic arrays of small lossless and lossy permeable spheres. The theory is presented in this paper and numerical results are presented by Shore and Yaghjian (2012). The focus is on the dispersion (k-b) equations relating the array propagation constant, b, to the free-space wave number, k, for dipolar complex waves. The k-b equation for the complex propagation constants of a given array is obtained from the corresponding equation previously obtained for the real propagation constants by rewriting the real propagation dispersion equation in a form that can be analytically continued into the complex b plane. This equation reduces correctly to the real b dispersion equation and enables complex values of b to be found as a function of the array element parameters. By allowing for all the possible branches of the multivalued homogeneous dispersion equation analytically continued into the complex b plane, the propagation constants of all the improper as well as proper complex waves supported by the 1D, 2D, and 3D arrays are found from the homogeneous solutions for these arrays. Green's functions for external sources are not required to find the propagation constants of the complex waves supported by the arrays. For 3D arrays, in certain frequency ranges, it is possible to regard the arrays as media characterized by bulk or effective permittivities and permeabilities. Expressions for these bulk parameters, more accurate than the Clausius-Mossotti expressions, are obtained from quantities readily available in the solutions of the dispersion equations.Citation: Shore, R. A., and A. D. Yaghjian (2012), Complex waves on periodic arrays of lossy and lossless permeable spheres: 1. Theory, Radio Sci., 47, RS2014,

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Section: Appendix B: Properties Of Complex Waves On Uniform or Periodmentioning

confidence: 98%

Complex waves on periodic arrays of lossy and lossless permeable spheres: 1. Theory

Shore¹,

Yaghjian²

2012

Radio Science

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“…These complex modes exist in complex conjugate pairs, and the two conjugate modes transport power in opposite directions. Only if the conjugate modes are excited unequally can they transport real power [14]. Using Muller's method to determine the roots in the complex-γ plane, it is possible to numerically arrive at a set of continuous dispersion curves.…”

Section: Theorymentioning

confidence: 99%

Below-Cutoff Propagation in Metamaterial-Lined Circular Waveguides

Pollock

Iyer

2013

IEEE Trans. Microwave Theory Techn.

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This paper investigates the propagation characteristics of circular waveguides whose interior surface is coated with a thin metamaterial liner possessing dispersive, negative, and near-zero permittivity. A field analysis of this system produces the dispersion of complex modes, and reveals in detail intriguing phenomena such as backward-wave propagation below the unlined waveguide's fundamental-mode cutoff, resonant tunneling of power, field collimation, and miniaturization. It is shown how the waveguide geometry and metamaterial parameters may be selected to engineer the lined waveguide's spectral response. Theoretical dispersion and transmission results are closely validated by full-wave simulations.Comment: 8 pages, 8 figure

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“…. A physical example of this situation is the bifurcation of a mode into two complex modes [10]. However, the bifurcation of β 2 (ω) at ω 0 is not possible, as it would violate Theorem III.2.…”

Section: Properties Of the Discretized Systemmentioning

confidence: 99%

Analytic properties of dispersion curves for efficient eigenmode analysis of isotropic waveguides using a boundary element method

Dobbelaere

Rogier

Zutter

2014

2014 International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applicati

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Abstract-Recent developments in high-speed interconnects show a clear tendency towards higher bitrates, emphasizing the need for a reliable prediction of the waveguide behavior. We present a frequency domain eigenmode analysis of isotropic waveguides using a boundary element method. Some properties of the dispersion curves can be beneficially leveraged into the numerical framework for calculating the waveguide characteristics as a function of frequency. The method allows the incorporation of highly conductive materials, which is demonstrated in a numerical example.

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On the Independence of the Excitation of Complex Modes in Isotropic Structures

Cited by 20 publications

References 27 publications

Complex waves on periodic arrays of lossy and lossless permeable spheres: 1. Theory

Complex waves on periodic arrays of lossy and lossless permeable spheres: 1. Theory

Below-Cutoff Propagation in Metamaterial-Lined Circular Waveguides

Analytic properties of dispersion curves for efficient eigenmode analysis of isotropic waveguides using a boundary element method

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