# Epsilon-Near-Zero Absorber by Tamm Plasmon Polariton

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## Abstract

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## 1. Introduction

## 2. Model Description

## 3. Temporal Coupled-Mode Theory

## 4. Study of the Spectral Properties of the TPP Using the Temporal Coupled-Mode Theory

## 5. Numerical Calculation

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of a one-dimensional photonic crystal (PhC) coupled with a nanocomposite (NC) layer with the near-zero permittivity.

**Figure 2.**Dependences of the real $Re\phantom{\rule{3.33333pt}{0ex}}{\epsilon}_{\mathit{eff}}$ (purple line) and imaginary $Im\phantom{\rule{3.33333pt}{0ex}}{\epsilon}_{\mathit{eff}}$ (green line) parts of the effective permittivity ${\epsilon}_{\mathit{eff}}$ on the incident light wavelength. The filling factor is $f=0.11$.

**Figure 3.**Schematic of the Tamm plasmon polariton (TPP) excitation from the side of (

**a**) an NC film and (

**b**) a PhC.

**Figure 4.**(

**a**) Transmission and (

**b**) absorption spectra of the NC film at different film thicknesses and incident radiation wavelengths. The filling factor is $f=0.11$.

**Figure 5.**The dependence of absorptance of the NC film on its transmittance at different film thicknesses (blue line) and the dependence of the absorptance of an opaque NC film on the PhC transmittance at different numbers of PhC periods (red line). The point of intersection between the black and blue lines corresponds to the critical coupling condition (12), and the point of intersection between the black and red lines corresponds to Condition (13). The wavelength is $\lambda =407.1$ nm.

**Figure 6.**(

**a**) NC-PhC and (

**b**) PhC-NC reflectance spectra of the structure at different NC layer thicknesses ${d}_{\mathit{eff}}$ and a constant filling factor of $f=0.11$. The green dashed line shows the reflectance spectra of the structures under critical coupling conditions.

**Figure 7.**Transmittance (red line), reflectance (blue line), and absorptance (black line) spectra of the structure under the critical coupling conditions upon TPP excitation from (

**a**) the NC and (

**b**) PhC side. The NC layer thickness and number of PhC periods are ${d}_{\mathit{eff}}=201$ nm, $N=25$ and ${d}_{\mathit{eff}}=700$ nm, $N=3$, respectively.

**Figure 8.**TPP in the region of positive ${\epsilon}_{\mathit{eff}}$. Spatial distribution of the refractive index of the structure (green line) and local field intensity at the TPP wavelength (red line) for the TPP excitation from (

**a**) the NC and (

**b**) PhC side.

**Figure 9.**(

**a**) TPP in the metal-like NC region ${\epsilon}_{\mathit{eff}}<0$. Transmittance (black line), reflectance (blue line), and absorptance (red line) spectra of the structure under the critical coupling conditions for the scheme of TPP excitation from the PhC side at a thickness of ${d}_{\mathit{first}}=78$ nm of the layer adjacent to the PhC and (

**b**) the spatial distribution of the local field intensity at the TPP wavelength.

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**MDPI and ACS Style**

Bikbaev, R.G.; Vetrov, S.Y.; Timofeev, I.V.
Epsilon-Near-Zero Absorber by Tamm Plasmon Polariton. *Photonics* **2019**, *6*, 28.
https://doi.org/10.3390/photonics6010028

**AMA Style**

Bikbaev RG, Vetrov SY, Timofeev IV.
Epsilon-Near-Zero Absorber by Tamm Plasmon Polariton. *Photonics*. 2019; 6(1):28.
https://doi.org/10.3390/photonics6010028

**Chicago/Turabian Style**

Bikbaev, Rashid G., Stepan Ya. Vetrov, and Ivan V. Timofeev.
2019. "Epsilon-Near-Zero Absorber by Tamm Plasmon Polariton" *Photonics* 6, no. 1: 28.
https://doi.org/10.3390/photonics6010028