# Double-Resolved Beam Steering by Metagrating-Based Tamm Plasmon Polariton

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## Abstract

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## 1. Introduction

## 2. Model

#### 2.1. Electrostatic Simulation

#### 2.2. Full-Wave Simulation

## 3. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Sketch view of the structure; (

**b**,

**c**) electron concentration N and real part of the dielectric permittivity $\mathrm{Re}{\epsilon}_{\mathrm{ITO}}$ of the ITO layer for different applied bias voltage. The DBR layers’ thicknesses are ${d}_{a}=165$ nm and ${d}_{b}=135$ nm, for silica and titanium dioxide, correspondingly. The number of DBR layers are equal to 15. The 2D array with thickness $h=95$ nm and width $L=470$ nm has infinite length along the y axis. The pitch of the array $p=500$ nm. The ITO and Al${}_{2}$O${}_{3}$ layer thicknesses are 20 nm and 5 nm, respectively. The structure in the inset of Figure 1b is presented schematically to demonstrate the non-uniform distribution of charges in the ITO in the case of applying a bias voltage between Ag nanostripes and monolayer graphene.

**Figure 2.**(

**a**,

**b**) Reflectance spectra of the structure presented in Figure 1a,b simulated phase shift as a function of applied bias voltage between Ag nanostripes and monolayer graphene; (

**c**) schematic of the diffraction grating for a different number of nanostrip pairs; dark gray and orange nanostrips depict nanostrips without bias voltage and with bias voltage of 3.5 V, respectively; an increase in the number of nanostripes with bias voltage and without it leads to an increase in the grating period; (

**d**) Simulated far-field reflected intensity from the metagrating as a function of the diffraction angles for a different grating period.

**Figure 3.**(

**a**) Schematic representation of the structure for control over the angle of the first diffraction order; (

**b**) three types of the phase distribution along the metagrating; (

**c**) simulated far-field reflected intensity from the metagrating based on phase distribution presented in (

**b**) in the case of asymmetric phase distribution.

**Table 1.**The dependence of the ± first order diffraction angle on number of nanostrips. Half-integer n corresponds to double resolution.

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**MDPI and ACS Style**

Bikbaev, R.G.; Maksimov, D.N.; Chen, K.-P.; Timofeev, I.V.
Double-Resolved Beam Steering by Metagrating-Based Tamm Plasmon Polariton. *Materials* **2022**, *15*, 6014.
https://doi.org/10.3390/ma15176014

**AMA Style**

Bikbaev RG, Maksimov DN, Chen K-P, Timofeev IV.
Double-Resolved Beam Steering by Metagrating-Based Tamm Plasmon Polariton. *Materials*. 2022; 15(17):6014.
https://doi.org/10.3390/ma15176014

**Chicago/Turabian Style**

Bikbaev, Rashid G., Dmitrii N. Maksimov, Kuo-Ping Chen, and Ivan V. Timofeev.
2022. "Double-Resolved Beam Steering by Metagrating-Based Tamm Plasmon Polariton" *Materials* 15, no. 17: 6014.
https://doi.org/10.3390/ma15176014