# Switchable Ultra-Wideband All-Optical Quantum Dot Reflective Semiconductor Optical Amplifier

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## Abstract

**:**

## 1. Introduction

## 2. Concept and Modeling

#### 2.1. Proposed Structure

_{p}to pump the carriers to the ES in the conduction band. Otherwise, we will not have enough carriers, and the system will not work.

#### 2.2. Selective Amplification

_{p}must be adjusted for each of these groups to be activated. Figure 7 depicts the energy difference between the ESs in the conduction and the valence band versus the QD’s radius. We know that without enough carriers in the conduction band, the QDs cannot perform their task as an amplifier. This fact is used to have selective amplification for any desired group with its specified radius. In other words, by applying a pump with the energy of E

_{p1}, only the QDs with the corresponding radii R1 are activated, and the other two groups are deactivated. In addition, pumps with the energy E

_{p2}and E

_{p3}can activate QDs groups with radii R2 and R3, respectively.

#### 2.3. Homogenous and Inhomogeneous Broadenings

_{1}= E

_{1,n}, E

_{2}= E

_{2,n}, and E

_{3}= E

_{3,n}. Homogenous Broadening (HB) and Inhomogeneous Broadening (IHB) can be derived by [2]:

_{h}denotes the Full Width Half Maximum (FWHM) of the Lorentzian profile, and ξ the coverage of the channel. If we use N groups of QDs with distinct radii, the total Gaussian profile can be obtained by:

#### 2.4. Numerical Algorithm

_{g}∆t. To figure out the optimum step size, several quantities were assessed. Finally, we derived enough accuracy and stability by implementing ∆t = 50 fs. Furthermore, at each spatial step, pulses are delayed by ∆t. To derive the dynamic results, static simulation outcomes are utilized [35,36]. Figure 9 demonstrates how the solutions are extracted using this numerical approach.

## 3. Results and Discussion

#### 3.1. Coupled Differential Rate and Signal Propagation Equations

_{w}. τ

_{w−e}and τ

_{e−w}are the electron relaxation lifetime from the wetting layer to the excited state and the electron escape lifetime from the excited state to the wetting layer, respectively. τ

_{w−r}, τ

_{g−r}, and τ

_{e−r}are the spontaneous radiative lifetimes in the WL, GS, and ES. In addition, the electron relaxation lifetime from the ES to the GS is denoted by τ

_{e−g}. The electron escape lifetime from the GS to the ES is shown by τ

_{g−e}. N

_{Q}and V

_{g}are the volume density of the QDs, and the group velocity of light, respectively. α

_{max}identifies the maximum modal absorption coefficient. As can be seen, the term (1 − 2h) defines ES carrier dynamics. When 2h > 1, we have optical gain. However, when it is less than one, absorption is the dominant mechanism. Due to the optical pump power (last term in Equation (7)), h escalates toward 0.5. As a result, the term 1 − 2h vanishes. In this case, a transient decrease in the h value makes the term 1 − 2h positive. Hence, absorption is achieved using optical pumping [39]. g

_{i,mn}denotes the linear gain for a specified group of QDs (n) and a particular photon mode (m) [19,40].

_{0}and q, respectively. ε

_{0}is the vacuum permittivity. The refractive index is denoted by n

_{r}. D is the degeneracy rate, and N

_{Q}is the QD volume density. |M

_{env}|

^{2}and <|e.p

_{cv}|

^{2}> are the envelope function and the momentum matrix element.

^{+}, P

^{−}, P

_{p}

^{+}, and P

_{p}

^{−}represent the backward and forward signal and pump powers. α

_{int}denotes the material absorption coefficient. The modal absorption coefficient of the pump can be derived from α

_{abs}= −α

_{max}(1 − 2h) − α

_{int}. Material gain is denoted by ${g}_{{w}_{s}}$, which can be calculated by:

#### 3.2. Stimulation Parameters

#### 3.3. Ultra-Wideband Optical Gain

_{Q}is increased. This leads to higher optical gain. This is why the optical gain is about 32 dB for nine groups of QDs; whereas this number is about 18 dB for seven groups. Furthermore, a smoother surface is achieved by using more QD groups. However, increasing the QDs results in a more sophisticated model, therefore increasing the cost of fabrication. Hence, there is a trade-off between the device’s performance and the cost of fabrication. One can engineer the desired model based on one’s needs, using the appropriate number of groups with distinct radii. In addition, one can alter the materials of the QDs and the cladding layers to cover a different wavelength spectrum. The only thing that must be taken care of is the procedure, which is described in the concept and modeling section. First, the energy levels for the corresponding materials must be calculated. Then, by sweeping the QD’s radius, energy differences between the conduction and valence band for each eigenstate versus the QD’s radius must be derived. Figure 2 and Figure 6 depict these profiles for QD mode from InGaAs with AlAs claddings.

#### 3.4. Selective Amplification

_{Q}(volume density of QDs) is distinct for each of these channels, which explains the difference in the amplification quantities between them.

#### 3.5. Gain Versus Length

_{max}≈ 6 mm). After this length, the device saturates, and the gain drops. This is because, in this region, the gain is dominated by material loss. As a result, the device attenuates the signal instead of amplifying it. In this paper, a 2 mm length has been selected for the amplifier. Hence, it is guaranteed that we are not in the saturation regime.

#### 3.6. Dynamic Characteristics

_{ew}. Since more carriers are absorbed to the ES in the case of higher optical pumping power, more of them move to the wetting layer with the time rate of τ

_{ew}. Figure 18 depicts the time evolution of f and h for different input powers. Higher input powers engage more carriers in the amplification process. As a result, the transient drops in f and h values are higher when high input power is utilized. This can be somehow recompensated by using higher optical pump power. As a result, more carriers are absorbed. Hence, the decrease in f and h values will be lower.

#### 3.7. Gain Versus Input Power

#### 3.8. Optical Bandwidth Comparison

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**The energy difference between the ground states in the conduction band and the valence band (radiated energy) as a function of the QD’s radius. Three groups have been chosen (R1, R2, and R3).

**Figure 7.**The energy difference between the excited states in the conduction band and the valence band (pump energies) as a function of the radii of the QDs. Three groups of QDs have been chosen (R1, R2, and R3).

**Figure 16.**Occupation probability in the ground and excited states versus time for distinct pump powers (input signal power = 1 μW). f and h can vary between 0 to 1.

**Figure 17.**The electron concentration in the wetting layer for distinct optical pump power (input signal power = 1 μW).

**Figure 18.**Occupation probability in the ground and excited states versus time for distinct input signal powers (Pump power = 80 mW).

Symbol | Value | Description |
---|---|---|

L | 2 mm | RSOA length |

H | 0.25 µm | Height of the RSOA |

W | 4 µm | Width of the RSOA |

α_{max} | 1000 m^{−1} | The maximum modal absorption coefficient |

α_{int} | 200 m^{−1} | Material absorption coefficient |

τ_{w−r} | 1.4 ns | Recombination lifetime for WL |

τ_{g−r} | 2.8 ns | Recombination lifetime for GS |

τ_{e−r} | 2.8 ns | Recombination lifetime for ES |

τ_{w−e} | 2 ps | Relaxation lifetime from WL to ES |

τ_{e−w} | 1 ns | Escape lifetime from ES to WL |

τ_{e−g} | 3 ps | Relaxation lifetime from ES to GS |

τ_{g−e} | 20 ps | Escape lifetime from GS to ES |

D_{e(g)} | 4 (2) | Degeneracy rate of ES (GS) |

n_{r} | 3.5 | Refractive index |

R | 0.8 | Reflection of the mirror |

**Table 2.**Reported broadband optical amplifiers with their corresponding optical bandwidth and operation region.

Paper’s Title | Optical Bandwidth | Operation Regime |
---|---|---|

Wideband Gain MQW-SOA Modeling and Saturation Power Improvement in a Tri-Electrode Configuration [44] | 76 nm | 1470–1546 nm |

A broad-band MQW semiconductor optical amplifier with high saturation output power and low noise figure [45] | 120 nm | 1450–1570 nm |

C- and L-Band External Cavity Wavelength Tunable Lasers Utilizing a Wideband SOA With Coupled Quantum Well Active Layer [46] | 77 nm | C-band and L-band |

Ultrabroadband reflective semiconductor optical amplifier using superimposed quantum dots [16] | 270 nm | 460–730 nm |

Switchable Ultra-wideband All-optical Quantum Dot Reflective Semiconductor Optical Amplifier | 1000 nm | 800–1800 nm |

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**MDPI and ACS Style**

Nahaei, F.S.; Rostami, A.; Mirtagioglu, H.; Maghoul, A.; Simonsen, I. Switchable Ultra-Wideband All-Optical Quantum Dot Reflective Semiconductor Optical Amplifier. *Nanomaterials* **2023**, *13*, 685.
https://doi.org/10.3390/nano13040685

**AMA Style**

Nahaei FS, Rostami A, Mirtagioglu H, Maghoul A, Simonsen I. Switchable Ultra-Wideband All-Optical Quantum Dot Reflective Semiconductor Optical Amplifier. *Nanomaterials*. 2023; 13(4):685.
https://doi.org/10.3390/nano13040685

**Chicago/Turabian Style**

Nahaei, Farshad Serat, Ali Rostami, Hamit Mirtagioglu, Amir Maghoul, and Ingve Simonsen. 2023. "Switchable Ultra-Wideband All-Optical Quantum Dot Reflective Semiconductor Optical Amplifier" *Nanomaterials* 13, no. 4: 685.
https://doi.org/10.3390/nano13040685