# Controlling Surface Plasmon Polaritons Propagating at the Boundary of Low-Dimensional Acoustic Metamaterials

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Approach

_{n}. Semiconductor nanoparticles with permittivity ε

_{m}are regularly distributed in its host material. The dielectric function of the TCO based nanoparticles is of special importance to r the academic community. The topic has become one of significance due to the metal being opaque to light. The parameters of the Drude–Lorentz approach for AZO, GZO, and ITO are obtained from experimental data [2].

## 3. Results and Discussions

_{||0}the semiconductor-dielectric metamaterial possesses hyperbolic properties. It can be seen from Figure 2, that the propagation of DSW is possible in the case of ${\epsilon}_{n}=2.25$, ${\epsilon}_{d}=11.8$. It is worthwhile to note that the regime of DSW propagation is possible in the case of ${\epsilon}_{\left|\right|},\text{\hspace{0.17em}}{\epsilon}_{nc}>0$. Moreover, it is possible to increase the frequency range of DSW existence by changing the nature of inclusions, i.e., by replacing AZO with ITO.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic design under consideration, comprising a semi-infinite hypercrystal (x > 0) and a nanocomposite with semiconductor inclusions (x < 0) (

**a**), metamaterial (hypercrystal) unit cell (

**b**).

**Figure 2.**Relative permittivity components of the nanocomposite and hypercrystal versus frequency. Herein, f = 0.3. (

**a**,

**b**) ${\epsilon}_{n}=11.8$, ${\epsilon}_{d}=2.25$; (

**c**,

**d**) ${\epsilon}_{n}=2.25$, ${\epsilon}_{d}=11.8$. Herein AZO (

**a**,

**c**) and ITO (

**b**,

**d**) inclusions are employed in nanocomposite and hypercrystal.

**Figure 3.**Solution of the wave equation for different filling ratio f: (

**a**,

**b**)—${\epsilon}_{n}=2.25$, ${\epsilon}_{d}=11.8$; (

**c**,

**d**)—${\epsilon}_{n}=11.8$, ${\epsilon}_{d}=2.25$. Herein AZO (

**a**,

**c**) and ITO (

**b**,

**d**) inclusions are employed in nanocomposite and hypercrystal.

**Figure 4.**Dependence of transmission characteristics versus frequency for different filling factors: (

**a**,

**c**) the imaginary part of β; (

**b**,

**d**) the propagation length L

_{p}. The case ${\epsilon}_{n}=2.25$, ${\epsilon}_{d}=11.8$.is presented in (

**a**,

**b**); ${\epsilon}_{n}=11.8$, ${\epsilon}_{d}=2.25$—(

**c**,

**d**). All of the presented results were obtained for the AZO inclusions.

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**MDPI and ACS Style**

Ioannidis, T.; Gric, T.; Rafailov, E.
Controlling Surface Plasmon Polaritons Propagating at the Boundary of Low-Dimensional Acoustic Metamaterials. *Appl. Sci.* **2021**, *11*, 6302.
https://doi.org/10.3390/app11146302

**AMA Style**

Ioannidis T, Gric T, Rafailov E.
Controlling Surface Plasmon Polaritons Propagating at the Boundary of Low-Dimensional Acoustic Metamaterials. *Applied Sciences*. 2021; 11(14):6302.
https://doi.org/10.3390/app11146302

**Chicago/Turabian Style**

Ioannidis, Thanos, Tatjana Gric, and Edik Rafailov.
2021. "Controlling Surface Plasmon Polaritons Propagating at the Boundary of Low-Dimensional Acoustic Metamaterials" *Applied Sciences* 11, no. 14: 6302.
https://doi.org/10.3390/app11146302