# Stability Analysis of Quantum-Dot Spin-VCSELs

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model and Analysis

## 3. Results

#### 3.1. Results for VCSEL1

#### 3.2. Results for VCSEL2

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Output ellipticity vs. pump ellipticity for vertical-cavity surface-emitting laser 1 (VCSEL1) with (

**a**) $\mathsf{\eta}=1.2$; and (

**b**) $\mathsf{\eta}=1.7$.

**Figure 2.**Real parts of the critical eigenvalues vs. pump ellipticity for VCSEL1 with (

**a**) $\mathsf{\eta}=1.2$; and (

**b**) $\mathsf{\eta}=1.7$.

**Figure 3.**Circularly polarized intensity components vs. time for VCSEL1 with (

**a**) $\mathsf{\eta}=1.2$, $P=0.35$; and (

**b**) $\mathsf{\eta}=1.7$, $P=0.5$.

**Figure 4.**Output ellipticity vs. pump ellipticity for VCSEL2 with (

**a**) $\mathsf{\eta}=1.1$; and (

**b**) $\mathsf{\eta}=1.9$.

**Figure 5.**Real parts of eigenvalues vs. pump ellipticity for VCSEL2 with (

**a**) $\mathsf{\eta}=1.1$; and (

**b**) $\mathsf{\eta}=1.9$.

**Table 1.**Values of parameters for two examples of quantum dot spin-vertical-cavity surface-emitting lasers (QD spin-VCSELs).

Parameter | Symbol | VCSEL1 Value | VCSEL2 Value |
---|---|---|---|

Photon decay rate | κ | 250 ns^{−1} | 250 ns^{−1} |

Carrier recombination rate | γ_{n} | 1 ns^{−1} | 1 ns^{−1} |

Capture rate into from WL into QD | γ_{o} | 400 ns^{−1} | 400 ns^{−1} |

Spin relaxation rate | γ_{j} | 10 ns^{−1} | 10 ns^{−1} |

Birefringence rate | γ_{p} | 20 ns^{−1} | 20 ns^{−1} |

Dichroism rate | γ_{a} | 0 | 0 |

Linewidth enhancement factor | α | 3 | 4 |

Normalized gain coefficient | h | 1.1995 | 1.05 |

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**MDPI and ACS Style**

Li, N.; Alexandropoulos, D.; Susanto, H.; Henning, I.; Adams, M. Stability Analysis of Quantum-Dot Spin-VCSELs. *Electronics* **2016**, *5*, 83.
https://doi.org/10.3390/electronics5040083

**AMA Style**

Li N, Alexandropoulos D, Susanto H, Henning I, Adams M. Stability Analysis of Quantum-Dot Spin-VCSELs. *Electronics*. 2016; 5(4):83.
https://doi.org/10.3390/electronics5040083

**Chicago/Turabian Style**

Li, Nianqiang, Dimitris Alexandropoulos, Hadi Susanto, Ian Henning, and Michael Adams. 2016. "Stability Analysis of Quantum-Dot Spin-VCSELs" *Electronics* 5, no. 4: 83.
https://doi.org/10.3390/electronics5040083