# Frequency-Selective Surface Based on Negative-Group-Delay Bismuth–Mica Medium

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Sample Preparation

#### 2.2. Measurements, Numerical Simulation, and Material Parameter Extraction

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**THz TDS setup. The sample consisting of 120 nm Bi film on 21 $\mathsf{\mu}$m mica substrate (inset) is placed between two central lenses. The bismuth film has an area of 15 × 15 mm. The electrodes on both sides of the sample are used for dynamic tuning.

**Figure 2.**Amplitude transmission (

**a**) and phase delay (

**b**) spectra of a THz wave transmitted through the mica and the bismuth–mica structure (rationed as $|{\widehat{E}}_{mica}\left(f\right)|/|{\widehat{E}}_{air}\left(f\right)|$, $|{\widehat{E}}_{Bi+mica}\left(f\right)|/|{\widehat{E}}_{air}\left(f\right)|$ and ${\varphi}_{mica}\left(f\right)-{\varphi}_{air}\left(f\right)$, ${\varphi}_{Bi+mica}\left(f\right)-{\varphi}_{air}\left(f\right)$, respectively).

**Figure 4.**Complex effective permittivity dispersion (${\widehat{\epsilon}}_{eff}\left(f\right)$) of the bismuth–mica structure extracted from THz TDS (direct measurement) and numerical simulation or calculation based on the transfer matrix method (simulation).

**Figure 5.**(

**a**) Schematic view of the FSS. The configuration is defined by the square unit cell size (G) and by the length (L) and width (K) of a slot in the bismuth film. (

**b**) Photo of the laser engraving process.

**Figure 6.**Amplitude transmission (

**a**) and phase delay (

**b**) spectra of a THz wave passed through the bismuth-based FSS at $G=280$ $\mathsf{\mu}$m, $L=250$ $\mathsf{\mu}$m, and $K=80$ $\mathsf{\mu}$m.

**Figure 7.**Real (

**a**) and imaginary (

**b**) parts of the complex effective permittivity dispersion of the bismuth-based FSS at $G=280$ $\mathsf{\mu}$m, $L=250$ $\mathsf{\mu}$m, and $K=80$ $\mathsf{\mu}$m.

**Figure 8.**THz waveforms for radiation transmitted through the air, the mica substrate, and the substrate-film medium in the cases of solid Bi film (

**a**) and Bi-based FSS (

**b**). Vertical lines indicate peak positions of wave packets.

**Figure 9.**Amplitude transmission (

**a**) and phase delay (

**b**) spectra of a THz wave passed through the bismuth-based FSS at different values of the square unit cell size (G).

**Figure 10.**Real (

**a**) and imaginary (

**b**) parts of the complex effective permittivity dispersion of the bismuth-based FSS at different values of the square unit cell size (G).

**Figure 11.**Frequency-dependent group delay (

**a**) and group velocity (

**b**) normalized to c at different values of the square unit cell size (G).

**Figure 12.**Amplitude transmission (

**a**) and phase delay (

**b**) spectra of a THz wave passed through the bismuth-based FSS at different values of the cross-like slot side length (L).

**Figure 13.**Real (

**a**) and imaginary (

**b**) parts of the complex effective permittivity dispersion of the bismuth-based FSS at different values of the cross-like slot side length (L).

**Figure 14.**Frequency-dependent group delay (

**a**) and group velocity (

**b**) normalized to c at different values of the cross-like slot side length (L).

**Figure 15.**Amplitude transmission (

**a**) and phase delay (

**b**) spectra of a THz wave passed through the bismuth-based FSS at different values of the cross-like slot side width (K).

**Figure 16.**Real (

**a**) and imaginary (

**b**) parts of the complex effective permittivity dispersion of the bismuth-based FSS at different values of the cross-like slot side width (K).

**Figure 17.**Frequency-dependent group delay (

**a**) and group velocity (

**b**) normalized to c at different values of the cross-like slot side width (K).

**Figure 18.**Shift of the complex effective permittivity dispersion real (

**a**) and imaginary (

**b**) parts for the bismuth-based FSS with $G=280$ $\mathsf{\mu}$m, $L=250$ $\mathsf{\mu}$m, and $K=80$ $\mathsf{\mu}$m under the influence of external voltage applied between two opposite electrodes (up to 10 V).

**Figure 19.**Shift of the group delay spectrum for the bismuth-based FSS with $G=280$ $\mathsf{\mu}$m, $L=250$ $\mathsf{\mu}$m, and $K=80$ $\mathsf{\mu}$m under the influence of external voltage.

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**MDPI and ACS Style**

Zaitsev, A.D.; Demchenko, P.S.; Kablukova, N.S.; Vozianova, A.V.; Khodzitsky, M.K.
Frequency-Selective Surface Based on Negative-Group-Delay Bismuth–Mica Medium. *Photonics* **2023**, *10*, 501.
https://doi.org/10.3390/photonics10050501

**AMA Style**

Zaitsev AD, Demchenko PS, Kablukova NS, Vozianova AV, Khodzitsky MK.
Frequency-Selective Surface Based on Negative-Group-Delay Bismuth–Mica Medium. *Photonics*. 2023; 10(5):501.
https://doi.org/10.3390/photonics10050501

**Chicago/Turabian Style**

Zaitsev, Anton D., Petr S. Demchenko, Natallya S. Kablukova, Anna V. Vozianova, and Mikhail K. Khodzitsky.
2023. "Frequency-Selective Surface Based on Negative-Group-Delay Bismuth–Mica Medium" *Photonics* 10, no. 5: 501.
https://doi.org/10.3390/photonics10050501