# A Monte-Carlo/FDTD Study of High-Efficiency Optical Antennas for LED-Based Visible Light Communication

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}/Si nanoparticles. In our structure, we used this nanoparticle due to its significant characteristics, such as low relaxation times, which made it possible to use a high switching rate compared to fluorescent materials, high stability, and adjustable absorption spectra with its size, a considerable extinction cross-section, and its low cost. All of these factors attracted our attention, so we decided to use them as a luminescent material in our structure.

_{2}/Si nanoparticle and eventually reach the desired structure for an optical antenna.

## 2. Materials and Methods

#### 2.1. Antenna Structure and Underlying Physics

_{2}/Si nanoparticles absorb the incident light from the cylinder’s lateral surface and then emit it respectively. The photons emitted by the nanoparticles (through the TIR phenomenon) will be able to reach the edges of the cylinder where the photodetectors are located due to their change in the mean free path length of the incident photons. Finally, the absorbed photons by photodetectors are converted into an electrical signal (Figure 2).

_{2}/Si QDs is in the nanosecond range, which could provide the bandwidth required for VLCs.

- (1)
- The photon passes through the cylinder without being absorbed by the nanoparticles (transmission losses).
- (2)
- The photon is absorbed by the nanoparticle and then is emitted and escapes from the cylinder because its incident angle with the surface is smaller than the critical angle (transmission losses).
- (3)
- The photon is absorbed by the nanoparticle and is emitted and then absorbed by another nanoparticle (re-absorption), and (3, 6) is not emitted (absorption losses). To be more precise, each photon’s absorption loss can be calculated using Equation (10).
- (4)
- The photon is absorbed by the nanoparticles and emitted and then reaches the photodetector by the TIR phenomenon.
- (5)
- The photon is reflected from the surface of the cylinder without entering it.

#### 2.2. Simulation

#### 2.2.1. FDTD Simulation

_{2}/Si nanoparticle in a medium with a background refractive index of SiO

_{2}(1.46) and exposed it to planar source radiation ranging from 300 to 800 nanometers. Then, we obtained the nanoparticle absorption and emission spectra for its different dimensions employing the FDTD (finite-difference time-domain) method. Figure 4 and Table 1 represent the FDTD region and its related parameters, respectively.

- Boundary conditions of the FDTD region,
- Background medium,
- Scattering calculation region,
- Planar light source,
- Absorption calculation region,
- Shell material, and
- Core material.

#### 2.2.2. Monte Carlo Simulation

_{T}is the maximum range where photons can travel.

_{T}are considered 100 and 10 cm, respectively. Thus, according to Equation (2), θ

_{T}is equal to 2.86°. In addition, we changed the antenna’s length from 2 to 10 cm and the antenna’s radius from 1 to 5 cm with a step of 2 cm.

_{j}is the wavelength of the jth photon, and k is its last term of the series [37].

_{2}) is considered constant and equal to the refractive index of SiO

_{2}since n

_{1}= n

_{Air}= 1, and the concentration of the nanoparticles is not high enough to change it considerably. The θ

_{i}is the angle of the incident photon on the structure, and θ

_{t}is its transmission angle. In the case of p-polarized light, the reflectance is as follows:

_{t}), and distance traveled. θ

_{t}is determined using Snell’s law (Equation (8)) [42]. Earlier, we introduced n

_{1}and n

_{2}.

_{2}/Si nanoparticles, c is the concentration of the so-called material, and ΔL is the path length traveled by the photon before being absorbed. Please refer to Figure 8 for ε(λ).

_{2}or F

_{3}) (Figure 5), it is harvested by the photodetector; second, the photon escapes from face one, which is known as transmission loss.

_{opt}) is defined as the ratio of photons collected from F

_{2}and F

_{3}to all photons emitted by the LED (Equation (15)).

## 3. Results

_{2}/Si nanoparticles are shown for the core thickness of 6 nanometers and the shell thickness of 75 to 95 nanometers, respectively.

_{2}/Si nanoparticles of different sizes. In these figures, the peaks represent the local surface plasmon resonances (LSPRs) that occur between SiO

_{2}and Si.

_{2}/Si nanoparticle with a radius of 85 nm because the peak of the extinction cross-section occurs in the two places (450 and approximately 550 nm), matching the emission spectrum of the white LED (Figure 1). The absorption cross-section of the nanoparticle with a radius of 85 nm is shown in Figure 13.

#### 3.1. CIE Colorspace Comparison between LED Illumination and SiO_{2}/Si QD Scattering

_{2}/Si Quantum Dot with a radius of 85 nm. It is evident in Figure 15 that both the transmitter (white LED) and the receiver (SiO

_{2}/Si QDs inside glass substrate) have similar color representations, and this can aid in constructing an optical antenna with greater efficiency.

#### 3.2. Results for Monte-Carlo Ray Tracing

_{2}/Si nanoparticles was considered, at values of 0.3, 0.6, and 0.95, to be as comprehensive as possible.

## 4. Conclusions

_{2}/Si. An FDTD analysis was conducted on SiO

_{2}/Si quantum dots to determine their optimum size to be used as dopants inside the cylindrical substrate. An analysis of the absorption, scattering, and extinction cross sections of SiO

_{2}/Si QDs was carried out using the FDTD method. An optimal radius of 79 nm was determined for SiO

_{2}/Si nanoparticles that match the spectrum of source white LEDs. The SiO

_{2}/Si nanoparticle with this size shows absorption, scattering, and extinction cross sections of 6.65 × 10

^{−14}m

^{−2}, 4.4 × 10

^{−13}m

^{−2}, and 5.05 × 10

^{−13}m

^{−2}. We numerically modeled the proposed optical antenna using the Monte-Carlo ray-tracing approach, and we reported the optical efficiency for a variety of substrate sizes and dopant concentrations inside the substrate.

_{2}/Si Quantum dots, which have a low relaxation time compared to phosphorescence-based LSCs, so that it could be applied to VLC applications demanding fast response times. A cylindrical surface and a wide field of view make it an excellent light-collecting antenna, liberating a VLC system from active light-tracking systems.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The emission spectrum of a commercially available white light LED. Adapted from Ref [36].

**Figure 7.**The probability density function (

**A**) and cumulative distribution function (

**B**) for commercially available white light LED emission spectrums.

**Figure 9.**Probability density function (PDF) and cumulative distribution function (CDF) for emission spectrum of core-shell SiO

_{2}-silicon nanoparticle (

**A**,

**B**), respectively.

**Figure 15.**CIE 1931 representations for (

**a**) white LED from Figure 1 and (

**b**) proposed SiO

_{2}/Si nano-particle with R = 85 nm.

**Figure 16.**Optical efficiency concerning concentrations of nanoparticles in radii of 1, 3, and 5 cm with lengths of 2, 4, 6, 8, and 10 cm (

**A**–

**E**), respectively.

**Figure 17.**Structures with optical efficiencies over 20 (%). (

**a**) L = 10 cm, R = 5 cm, QY = 0.95, Concentration = 3.88 × 10

^{8}(1/cm

^{3}), η

_{opt}= 29.0990 (%). (

**b**) L = 8 cm, R = 5 cm, QY = 0.95, Concentration = 3.88 × 10

^{8}(1/cm

^{3}), η

_{opt}= 25.7964 (%).(

**c**) L = 6 cm, R = 5 cm, QY = 0.95, Concentration =3.88 × 10

^{8}(1/cm

^{3}), η

_{opt}= 22.0142 (%). (

**d**) L = 10 cm, R = 3 cm, QY = 0.95, Concentration = 3.88 × 10

^{8}(1/cm

^{3}), η

_{opt}= 20.1008 (%).

**Figure 18.**Structures with optical efficiencies lower than 1 (%). (

**a**) L = 2 cm, R = 1 cm, QY = 0.3, Concentration = 3.88 × 10

^{10}(1/cm

^{3}), η

_{opt}= 0.1700 (%). (

**b**) L = 2 cm, R = 3 cm, QY = 0.3, Concentration = 3.88 × 10

^{10}(1/cm

^{3}), η

_{opt}= 0.1852 (%).(

**c**) L = 2 cm, R = 1 cm, QY = 0.3, Concentration = 3.88 × 10

^{7}(1/cm

^{3}), η

_{opt}= 0.1160 (%). (

**d**) L = 4 cm, R = 1 cm, QY = 0.3, Concentration = 3.88 × 10

^{7}(1/cm

^{3}), η

_{opt}= 0.2084 (%).

Parameter | Value or Type | Unit |
---|---|---|

FDTD simulation type | 3D | - |

Simulation time | 800 | fs |

Temperature | 300 | K |

FDTD region x, y, z span | 3200 | nm |

FDTD background material index | 1.46 | - |

FDTD mesh type | Custom non-uniform | - |

Mesh spacing | 1 | nm |

Boundary condition in all directions | Perfectly Matched Layer (PML) | - |

Source type | Planar TFSF source | - |

Source x, y, z span | 1600 | nm |

Source direction | Forward | - |

Source amplitude | 1 | - |

Source wavelength range | 300–800 | nm |

Scattering calculation x, y, z span | 1800 | nm |

Absorption calculation x, y, z span | 300 | nm |

Shell material | Si | - |

Core material | SiO_{2} | - |

Shell radius (R2) | Sweeping dimensions (85–95) | nm |

Core radius (R1) | 6 | nm |

**Table 2.**Optimal efficiencies for different lengths and optimal concentrations in a radius of 1 cm and quantum yields of 0.3, 0.6, and 0.95.

Length (cm) | 2 | 4 | 6 | 8 | 10 | |
---|---|---|---|---|---|---|

QY = 0.3 | Optimal concentration (cm^{−3}) | 3.88 × 10^{9} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} |

Efficiency η_{opt} (%) | 1.0180 | 1.2034 | 1.5200 | 1.7832 | 1.9844 | |

QY = 0.6 | Optimal concentration (cm^{−3}) | 3.88 × 10^{9} | 3.88 × 10^{9} | 3.88 × 10^{9} | 3.88 × 10^{8} | 3.88 × 10^{8} |

Efficiency η_{opt} (%) | 2.5738 | 3.1016 | 3.3340 | 3.8666 | 4.3932 | |

QY = 0.95 | Optimal concentration (cm^{−3}) | 3.88 × 10^{9} | 3.88 × 10^{9} | 3.88 × 10^{9} | 3.88 × 10^{9} | 3.88 × 10^{9} |

Efficiency η_{opt} (%) | 6.1952 | 7.8912 | 8.4874 | 8.8340 | 8.9946 |

**Table 3.**Optimal efficiencies for different lengths and optimal concentrations in a radius of 3 cm and quantum yields of 0.3, 0.6, and 0.95.

Length (cm) | 2 | 4 | 6 | 8 | 10 | |
---|---|---|---|---|---|---|

QY = 0.3 | Optimal concentration (cm^{−3}) | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} |

Efficiency η_{opt} (%) | 2.0432 | 2.9740 | 3.5698 | 4.0784 | 4.5104 | |

QY = 0.6 | Optimal concentration (cm^{−3}) | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} |

Efficiency η_{opt} (%) | 4.3908 | 6.5162 | 8.0778 | 9.4004 | 10.4696 | |

QY = 0.95 | Optimal concentration (cm^{−3}) | 3.88 × 10^{9} | 3.88 × 10^{9} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} |

Efficiency η_{opt} (%) | 9.4390 | 13.1292 | 15.1644 | 17.7336 | 20.1008 |

**Table 4.**Optimal efficiencies for different lengths and optimal concentrations in a radius of 5 cm and quantum yields of 0.3, 0.6, and 0.95.

Length(cm) | 2 | 4 | 6 | 8 | 10 | |
---|---|---|---|---|---|---|

QY = 0.3 | Optimal concentration (cm^{−3}) | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} |

Efficiency η_{opt} (%) | 2.6706 | 4.0234 | 4.9420 | 5.5804 | 6.1712 | |

QY = 0.6 | Optimal concentration (cm^{−3}) | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} |

Efficiency η_{opt} (%) | 5.9408 | 9.1848 | 11.3164 | 13.0406 | 14.4636 | |

QY = 0.95 | Optimal concentration (m^{−3}) | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} | 3.88 × 10^{8} |

Efficiency η_{opt} (%) | 10.6198 | 17.2854 | 22.0142 | 25.7964 | 29.0990 |

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**MDPI and ACS Style**

Fakhri, D.; Alidoust, F.; Rostami, A.; Mirtaheri, P. A Monte-Carlo/FDTD Study of High-Efficiency Optical Antennas for LED-Based Visible Light Communication. *Nanomaterials* **2022**, *12*, 3594.
https://doi.org/10.3390/nano12203594

**AMA Style**

Fakhri D, Alidoust F, Rostami A, Mirtaheri P. A Monte-Carlo/FDTD Study of High-Efficiency Optical Antennas for LED-Based Visible Light Communication. *Nanomaterials*. 2022; 12(20):3594.
https://doi.org/10.3390/nano12203594

**Chicago/Turabian Style**

Fakhri, Darya, Farid Alidoust, Ali Rostami, and Peyman Mirtaheri. 2022. "A Monte-Carlo/FDTD Study of High-Efficiency Optical Antennas for LED-Based Visible Light Communication" *Nanomaterials* 12, no. 20: 3594.
https://doi.org/10.3390/nano12203594