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Transparent Multilayer Electromagnetic Structures Based on Metal Metamaterials

  • ELECTRODYNAMICS AND WAVE PROPAGATION
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Abstract—Layered isotropic structures including layers of metamaterial are considered. Two-layer and multilayer symmetric structures, as well as a structure with a continuous change in material parameters, have been investigated. For the first time, the conditions of transparency of such structures and structures derived from them are presented. It is shown that the boundaries of the regions of no passage of the wave correspond to the conditions of transparency of such structures. It is shown that for transparency parity-time (PT) symmetric structures in electrodynamics and optics, additional conditions are required, in contrast to the structures presented.

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Funding

The study was supported by the Russian Foundation for Basic Research (project no. 19-29-06043).

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Authors and Affiliations

  1. Institute for Management Problems, Russian Academy of Sciences, 117342, Moscow, Russia

    K. A. Vytovtov, E. A. Barabanova & V. M. Vishnevsky

Authors
  1. K. A. Vytovtov
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  2. E. A. Barabanova
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  3. V. M. Vishnevsky
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Corresponding author

Correspondence to K. A. Vytovtov.

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This study was reported at the Fourth International Youth Conference “Information and Communication Technologies: Modern Achievements” (Astrakhan, October 5–7, 2020).

APPENDIX

APPENDIX

The condition for the transparency of an isotropic structure is the equality of the field components at its output to the field components at its input:

$$\left| {\begin{array}{*{20}{c}} {{{E}_{x}}} \\ {{{H}_{y}}} \end{array}} \right| = \left| {\begin{array}{*{20}{c}} {{{E}_{{x0}}}} \\ {{{H}_{{y0}}}} \end{array}} \right|.$$
(A.1)

Further, given that the components of the fields at the output of the structure can be obtained using the transformation operator matrix as

$$\left| {\begin{array}{*{20}{c}} {{{E}_{x}}} \\ {{{H}_{y}}} \end{array}} \right| = \left| {\begin{array}{*{20}{c}} {{{L}_{{11}}}}&{{{L}_{{12}}}} \\ {{{L}_{{21}}}}&{{{L}_{{22}}}} \end{array}} \right|\left| {\begin{array}{*{20}{c}} {{{E}_{{x0}}}} \\ {{{H}_{{y0}}}} \end{array}} \right|,$$
(A.2)

we obtain equation

$$\left| {\begin{array}{*{20}{c}} {{{E}_{{x0}}}} \\ {{{H}_{{y0}}}} \end{array}} \right| = \left| {\begin{array}{*{20}{c}} {{{L}_{{11}}}}&{{{L}_{{12}}}} \\ {{{L}_{{21}}}}&{{{L}_{{22}}}} \end{array}} \right|\left| {\begin{array}{*{20}{c}} {{{E}_{{x0}}}} \\ {{{H}_{{y0}}}} \end{array}} \right|.$$
(A.3)

Let us write (A.3) in scalar form

$$\left\{ {\begin{array}{*{20}{c}} {{{E}_{{x0}}} = {{L}_{{11}}}{{E}_{{x0}}} + {{L}_{{12}}}{{H}_{{y0}}}} \\ {{{H}_{{y0}}} = {{L}_{{21}}}{{E}_{{x0}}} + {{L}_{{22}}}{{H}_{{y0}}}} \end{array}} \right..$$
(A.4)

Expressing from second equation (A.4)\({{H}_{{y0}}},\) substituting it into the first equation in (A.4) and performing simple algebraic transformations, we obtain

$${{L}_{{11}}} + {{L}_{{22}}} = 1 + {{L}_{{11}}}{{L}_{{22}}} - {{L}_{{12}}}{{L}_{{21}}}.$$
(A.5)

Taking into account that the transformation matrix of an isotropic structure is always unimodular [1, 3], that is, \({{L}_{{11}}}{{L}_{{22}}} - {{L}_{{12}}}{{L}_{{21}}} = 1,\) we obtain the final expression that determines the transparency condition for the layered isotropic structure:

$${\text{tr}}{\mathbf{L}} = {{L}_{{11}}} + {{L}_{{22}}} = 2.$$
(A.6)

In this case, any phase shift, even with equal field amplitudes at the input and output, indicates the opacity of the structure, since the phase shift will lead to a rotation of the polarization plane.

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Vytovtov, K.A., Barabanova, E.A. & Vishnevsky, V.M. Transparent Multilayer Electromagnetic Structures Based on Metal Metamaterials. J. Commun. Technol. Electron. 66, 1221–1228 (2021). https://doi.org/10.1134/S1064226921110115

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