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Tunable Microwave Metamaterial Structures pp 7–34Cite as

Wave Propagation in Periodic Structures

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Abstract

Wave propagation in periodic structures is closely related to propagation of waves in continuous media. Thus, dispersion parameters such as wavenumber and wave impedance or permeability and permittivity, can be used to describe the propagation of waves in one-dimensional periodic structures like loaded or artificial transmission lines and waveguides, and in two- and three-dimensional structures like artificial lenses, transmit arrays and meta surfaces. In this chapter, the connection between transmission line theory and effective material parameters, that can be used to describe the propagation of waves in periodic lattices, is investigated. Furthermore, based on a general form of a transmission line model and effective material parameters, a physical limitation for dispersion characteristics and corresponding equivalent circuit are derived. Finally, the effect of discretization and finite unit cell size in periodic structures on effective material parameters is considered.

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Notes

  1. 1.

    Losses can be taken into account by adding a resistance to each necessary reactive element, yielding \(\delta >0\).

  2. 2.

    In a two- or three-dimensonal anisotropic material, the angle between the Poynting vector and wave vector can have arbitrary values [7].

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Authors and Affiliations

  1. Terahertz Sensors Group, Department of Electrical Engineering and Information Technology, Technische Universität Darmstadt, Darmstadt, Germany

    Matthias Maasch

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  1. Matthias Maasch
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Correspondence to Matthias Maasch .

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Maasch, M. (2016). Wave Propagation in Periodic Structures. In: Tunable Microwave Metamaterial Structures . Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-28179-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-28179-7_2

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  • Print ISBN: 978-3-319-28178-0

  • Online ISBN: 978-3-319-28179-7

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