# Nanoscale Waveguide Beam Splitter in Quantum Technologies

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

## 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.**3D representation of the waveguide BS. Photons (in the general case nonmonochromatic) fall on the input ports BS. At the output ports of the BS are detectors ${D}_{1},{D}_{2}$ registering photons. The figure highlights the coupling region of the waveguide, where the electromagnetic fields from ports 1 and 2 overlap.

**Figure 2.**The calculation is presented: (

**a**) probabilities ${P}_{0,2}$ of detecting 2 photons at the second detector and 0 of photons at 1 detector (with ${P}_{0,2}={P}_{2,0}$ ) at different parameters $\sigma /\Omega $={0,1/2,3/2,3,5,10} (respectively, the color of the graphs in the figure: {black, yellow, green, red, blue, brown}) depending on the dimensionless BS length $L/{L}_{BS}$; (

**b**) the same but with larger dimensions of the beamsplitter, i.e., at $L/{L}_{BS}\to \infty $; (

**c**) the same as in (

**a**) but only for the probability ${P}_{1,1}$ of one photon detected at each detector; (

**d**) the same as in (

**b**) but only for the probability ${P}_{1,1}$.

**Figure 3.**The calculation is presented: (

**a**) quantum entanglement ${S}_{N}$ at different parameters $\sigma /\mathrm{\Omega}$={0,1/2,3/2,3,5,10} (respectively, the color of the graphs in the figure: {black, yellow, green, red, blue, brown}) depending on the dimensionless BS length $L/{L}_{BS}$; (

**b**) the same but with larger dimensions of the BS, i.e., at $L/{L}_{BS}\to \infty $.

**Figure 4.**The calculation for the initial state $|4,4\rangle $ is presented: (

**a**) quantum entanglement ${S}_{N}$ at different parameters $\sigma /\mathrm{\Omega}$={0,1/2,3/2,3,5,10} (respectively, the color of the graphs in the figure: {black, yellow, green, red, blue, brown}) depending on the dimensionless BS length $L/{L}_{BS}$; (

**b**) same but at larger BS size, i.e., at $L/{L}_{BS}\to \infty $.

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## Share and Cite

**MDPI and ACS Style**

Makarov, D.; Makarova, K.; Tsykareva, Y.; Kapustin, S.; Kharlamova, A.; Gusarevich, E.; Goshev, A.
Nanoscale Waveguide Beam Splitter in Quantum Technologies. *Nanomaterials* **2022**, *12*, 4030.
https://doi.org/10.3390/nano12224030

**AMA Style**

Makarov D, Makarova K, Tsykareva Y, Kapustin S, Kharlamova A, Gusarevich E, Goshev A.
Nanoscale Waveguide Beam Splitter in Quantum Technologies. *Nanomaterials*. 2022; 12(22):4030.
https://doi.org/10.3390/nano12224030

**Chicago/Turabian Style**

Makarov, Dmitry, Ksenia Makarova, Yuliana Tsykareva, Sergey Kapustin, Anastasia Kharlamova, Eugeny Gusarevich, and Andrey Goshev.
2022. "Nanoscale Waveguide Beam Splitter in Quantum Technologies" *Nanomaterials* 12, no. 22: 4030.
https://doi.org/10.3390/nano12224030