# A Multichannel Superconductor-Based Photonic Crystal Optical Filter Tunable in the Visible and Telecom Windows at Cryogenic Temperature

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Framework

## 3. Results and Discussion

**k**, where

**E**and

**B**represent the electric and magnetic fields, respectively (see Figure 1). To compute the transmittance spectra, we first consider a ${\mathrm{BaTiO}}_{3}$ layer thickness ${\mathit{d}}_{a}=160$ nm, and ${\mathit{d}}_{a}=62$ nm for estimations in the infrared and visible regions, respectively. Here, we consider an operation temperature that varies from 20 K to 80 K; hence, the ${\mathrm{BaTiO}}_{3}$-dielectric function can be considered constant, $\u03f5=5.8$ [46,47,48]. In turn, the ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ layer thickness ${\mathit{d}}_{b}=201$ nm, and ${\mathit{d}}_{b}=78$ nm, for the corresponding calculations in the infrared and visible regions, respectively; the ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ dielectric constant $\u03f5=3.76$ [49]. The considered superconductor defect layer ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ exhibits $p=2$, ${T}_{c}=92$ K, ${\lambda}_{0}=145$ nm at $T=0$ K, and a dielectric function ${\u03f5}_{2}$, as described above.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematics of the ${(\mathrm{BTO}/{\mathrm{Y}}_{2}{\mathrm{O}}_{3})}_{\mathrm{N}}/\mathrm{YBCO}/{({\mathrm{Y}}_{2}{\mathrm{O}}_{3}/\mathrm{BTO})}_{\mathrm{N}}$ 1D tunable photonic filter, composed of alternating layers of ${\mathrm{BaTiO}}_{3}$ and ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$, with a ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7-\mathrm{x}}$ superconductor defect layer, with corresponding widths ${d}_{a}$, ${d}_{b}$ and ${d}_{s}$, respectively. One period, $N=1$, ${(\mathrm{BTO}/{\mathrm{Y}}_{2}{\mathrm{O}}_{3})}_{1}/\mathrm{YBCO}/{({\mathrm{Y}}_{2}{\mathrm{O}}_{3}/\mathrm{BTO})}_{1}$ corresponds to one bilayer of BaTiO

_{3}and Y

_{2}O

_{3}saving a mirror symmetry respect to the YBCO superconductor defect layer. Thus, N periods refer to the number of repetitions of BaTiO

_{3}and Y

_{2}O

_{3}bilayers.

**k**is the incident wave vector that fixes the direction of $\mathbf{E}\times \mathbf{B}$, and

**E**and

**B**denote the electric and magnetic fields, respectively. The light propagation is defined by ${\theta}_{i}$, the angle with the z-axis, and xz is the plane of light incidence. ${M}_{bab}$, ${M}_{bs}$ and ${M}_{sb}$ indicate the transfer matrices in the intermediate layers (${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$, ${\mathrm{BaTiO}}_{3}$ or ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7-\mathrm{x}}$).

**Figure 2.**(

**a**) Photonic crystal optical filter response for TE polarization in the whole range of incident angles at $T=80$ K in the NIR range. The dark areas correspond to the high-reflectance ranges, and yellow regions indicate high transmission bands. White vertical lines in the figure are a guide to the eye, and correspond to the results for 40°, 70° and 85°, respectively. Panels (

**b**–

**d**) display the calculated transmittance of a ${(\mathrm{BTO}/{\mathrm{Y}}_{2}{\mathrm{O}}_{3})}_{2}/\mathrm{YBCO}/{({\mathrm{Y}}_{2}{\mathrm{O}}_{3}/\mathrm{BTO})}_{2}$ nanostructure, at $T=80$ K and incidence angles of 40°, 70° and 85°, for TE polarization, respectively.

**Figure 3.**Optical filter response in the whole range of incident angles, for period numbers (

**a**) $N=2$, (

**b**) $N=5$, and (

**c**) $N=8$; $T=80$ K and ${d}_{s}=30$ nm. The resonant peak becomes thinner with increasing N and angle of incidence, which act as key parameters in the quantification of the filtered signal quality. Panels (

**d**–

**f**) present the transmission spectra of the 1D tunable resonant filter ${(\mathrm{BTO}/{\mathrm{Y}}_{2}{\mathrm{O}}_{3})}_{\mathrm{N}}/\mathrm{YBCO}/{({\mathrm{Y}}_{2}{\mathrm{O}}_{3}/\mathrm{BTO})}_{\mathrm{N}}$ at normal incidence, as a function of the wavelength and the filter’s period number. The graphs show a 100% peak at defect resonance wavelength ${\lambda}_{c}$ = 1550 nm for (

**d**) $N=2$, $Q\sim 10$, (

**e**) $N=5$, $Q\sim 66$, and (

**f**) $N=8$, $Q\sim 470$. The gray shaded regions indicate the FWHM transmission characterized by $\Delta \lambda $. The quality factor $Q\equiv {\lambda}_{c}/\Delta \lambda $ scales exponentially with N.

**Figure 4.**(

**a**) Simulated photonic band structure of the ${(\mathrm{BTO}/{\mathrm{Y}}_{2}{\mathrm{O}}_{3})}_{5}/\mathrm{YBCO}/{({\mathrm{Y}}_{2}{\mathrm{O}}_{3}/\mathrm{BTO})}_{5}$ filter ($N=5$) as a function of wavelength and temperature T, in the region $T=20$ K to 80 K, with ${d}_{s}=30$ nm, at normal incidence. The dark areas correspond to the high-reflectance ranges, and yellow regions indicate high transmission bands where radiation passes through the structure. (

**b**) Optical response amplification of the $N=5$ PhC filter to a wavelength range between 1520 nm and 1570 nm. (

**c**) Transmission light behavior of the $N=5$ filter as a function of temperature for $T=30$ K (purple line), $T=50$ K (red line) and $T=70$ K (orange line), respectively.

**Figure 5.**(

**a**) Simulated photonic band structure of the ${(\mathrm{BTO}/{\mathrm{Y}}_{2}{\mathrm{O}}_{3})}_{5}/\mathrm{YBCO}/{({\mathrm{Y}}_{2}{\mathrm{O}}_{3}/\mathrm{BTO})}_{5}$ filter as a function of wavelength and superconductor layer thickness for $T=80$ K at normal incidence. (

**b**) Filter optical response amplification in the range 1530 nm–1580 nm.

**Figure 6.**(

**a**) Optical response of the ${(\mathrm{BTO}/{\mathrm{Y}}_{2}{\mathrm{O}}_{3})}_{2}/\mathrm{YBCO}/{({\mathrm{Y}}_{2}{\mathrm{O}}_{3}/\mathrm{BTO})}_{2}$ filter in the visible spectral region, for TE polarization in the whole range of incident angles at $T=80$ K. The dark areas correspond to the high-reflectance ranges, and yellow regions indicate high transmission bands where radiation passes through the structure. Panels (

**b**–

**d**) display the measured transmittance at incident angles of 40°, 70° and 85° (marked by the white vertical lines in (

**a**), respectively.

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**MDPI and ACS Style**

González, L.E.; Segura-Gutierrez, L.M.; Ordoñez, J.E.; Zambrano, G.; Reina, J.H.
A Multichannel Superconductor-Based Photonic Crystal Optical Filter Tunable in the Visible and Telecom Windows at Cryogenic Temperature. *Photonics* **2022**, *9*, 485.
https://doi.org/10.3390/photonics9070485

**AMA Style**

González LE, Segura-Gutierrez LM, Ordoñez JE, Zambrano G, Reina JH.
A Multichannel Superconductor-Based Photonic Crystal Optical Filter Tunable in the Visible and Telecom Windows at Cryogenic Temperature. *Photonics*. 2022; 9(7):485.
https://doi.org/10.3390/photonics9070485

**Chicago/Turabian Style**

González, Luz E., Lina M. Segura-Gutierrez, John E. Ordoñez, Gustavo Zambrano, and John H. Reina.
2022. "A Multichannel Superconductor-Based Photonic Crystal Optical Filter Tunable in the Visible and Telecom Windows at Cryogenic Temperature" *Photonics* 9, no. 7: 485.
https://doi.org/10.3390/photonics9070485