# Broad Tunable and High-Purity Photonic Microwave Generation Based on an Optically Pumped QD Spin-VCSEL with Optical Feedback

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## Abstract

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## 1. Introduction

## 2. Theoretical Model

## 3. Results and Discussion

#### 3.1. P1 Oscillation in a Solitary Optically Pumped QD Spin-VCSEL

#### 3.2. The Effect of Intrinsic Parameters on the Microwave Characteristics

#### 3.3. P1 Oscillation in the Optically Pumped QD Spin-VCSEL with Optical Feedback

## 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.**(

**a1**–

**a3**) Optical spectra and (

**b1**–

**b3**) RF spectra of the solitary optically pumped QD spin-VCSEL. (

**a1**,

**b1**) ${\gamma}_{p}=30\mathsf{\pi}{\mathrm{ns}}^{-1}$, (

**a2**,

**b2**) ${\gamma}_{p}=60\mathsf{\pi}{\mathrm{ns}}^{-1}$, and (

**a3**,

**b3**)${\gamma}_{p}=90\mathsf{\pi}{\mathrm{ns}}^{-1}$. Other parameters are set as ${\gamma}_{j}=10{\mathrm{ns}}^{-1}$, ${\gamma}_{a}=0{\mathrm{ns}}^{-1}$, ${\gamma}_{n}=1{\mathrm{ns}}^{-1}$, ${\gamma}_{o}=400{\mathrm{ns}}^{-1}$, $\mathsf{\kappa}=250{\mathrm{ns}}^{-1}$, $\alpha =3$, $h=1.1995$, $\eta =4$, and $p=0.7$.

**Figure 2.**Calculated color maps for the microwave power in the $({\gamma}_{j},{\gamma}_{p})$ plane. (

**a1**,

**b1**) $\alpha =2$, (

**a2**,

**b2**) $\alpha =3$, (

**a3**,

**b3**) $\alpha =4$, where $h=1.1995$ in the column (

**a**), and $h=2$ in the column (

**b**). The color bars on the right represent microwave power.

**Figure 3.**Calculated color maps for the microwave power in the $({\gamma}_{o},{\gamma}_{j})$ plane (left column) and $({\gamma}_{o},{\gamma}_{p})$ plane (right column). (

**a1**) ${\gamma}_{p}=10\mathsf{\pi}{\mathrm{ns}}^{-1}$, (

**a2**) ${\gamma}_{p}=20\mathsf{\pi}{\mathrm{ns}}^{-1}$, and (

**a3**) ${\gamma}_{p}=30\mathsf{\pi}{\mathrm{ns}}^{-1}$. (

**b1**) ${\gamma}_{j}=10{\mathrm{ns}}^{-1}$, (

**b2**) ${\gamma}_{j}=15{\mathrm{ns}}^{-1}$, and (

**b3**) ${\gamma}_{j}=20{\mathrm{ns}}^{-1}$. The colored regions indicate the P1 dynamics, while the CW and other complex dynamics, including chaos, are marked as white. The color bars on the right represent microwave power.

**Figure 4.**(

**a1**,

**a2**) Optical spectra and (

**b1**,

**b2**) RF spectra of the solitary optically pumped QD spin-VCSEL with (

**a1**,

**b1**) ${\gamma}_{o}=400{\mathrm{ns}}^{-1}$ and (

**a2**,

**b2**) ${\gamma}_{o}=7000{\mathrm{ns}}^{-1}$. The spin relaxation rate is ${\gamma}_{j}=10{\mathrm{ns}}^{-1}$, and other parameters are the same as those in Figure 1.

**Figure 5.**(

**a**) Microwave linewidth, (

**b**) phase noise variance (blue curve), power (crimson curve), and inset (

**c1**,

**c2**) microwave frequency of the solitary optically pumped QD spin-VCSEL versus the carrier capture rate, ${\gamma}_{o}$. The solid dots indicate ${\gamma}_{j}=10{\mathrm{ns}}^{-1}$ and the birefringence, ${\gamma}_{p}=10\mathsf{\pi}{\mathrm{ns}}^{-1}$, and the empty circles represent ${\gamma}_{j}=15{\mathrm{ns}}^{-1}$ and ${\gamma}_{p}=30\mathsf{\pi}{\mathrm{ns}}^{-1}$. (

**c**) Microwave linewidth at ${\gamma}_{o}=400{\mathrm{ns}}^{-1}$ (dashed line), ${\gamma}_{o}=600{\mathrm{ns}}^{-1}$ (dotted line) and ${\gamma}_{o}=7000{\mathrm{ns}}^{-1}$ (solid line).

**Figure 6.**(

**a1**,

**a2**) Optical spectra and (

**b1**,

**b2**) RF spectra of the optically pumped QD spin-VCSEL subject to (

**a1**,

**b1**) single-loop feedback and (

**a2**,

**b2**) dual-loop feedback. The feedback strengths are fixed at ${k}_{\mathrm{f}}=2.5{\mathrm{ns}}^{-1}$ and (${k}_{\mathrm{f}1}$

_{,}${k}_{\mathrm{f}2}$ ) = ($1.5{\mathrm{ns}}^{-1}$, $1.5{\mathrm{ns}}^{-1}$ ). The feedback delay times are set as $\tau =4\mathrm{ns}$ and (${\tau}_{1}$, ${\tau}_{2}$ ) = ($4\mathrm{ns},6.5\mathrm{ns}$ ) in (

**b**). Other parameters are the same as those in Figure 1 (

**a1**,

**b1**).

**Figure 7.**The bifurcation of an optically pumped QD spin-VCSEL subject to (

**a**) single-loop feedback and (

**b**) dual-loop feedback. The delay times are fixed at $\tau =4\mathrm{ns}$ for single-loop feedback and (${\tau}_{1}$, ${\tau}_{2}$) = ($4\mathrm{ns},6.5\mathrm{ns}$) for dual-loop feedback.

**Figure 8.**(

**a1**,

**b1**) Microwave linewidth, (

**a2**,

**b2**) the SPSC, and (

**a3**,

**b3**) phase noise variance as a function of the total feedback strength in the left column and feedback delay time in the right column. The feedback strength is set to ${k}_{\mathrm{f}}=3{\mathrm{ns}}^{-1}$ when the delay time varies. The other parameters are the same as those in Figure 7.

**Figure 9.**(

**a**) Microwave linewidth and (

**b**) phase noise variance as a function of P1 oscillation frequencies, where the optically pumped QD spin-VCSEL is subject to no feedback (hollow circles), single-loop feedback (black dots), and dual-loop feedback (red dots). These dots represent relatively optimized results with varying feedback parameters.

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## Share and Cite

**MDPI and ACS Style**

Shen, Z.; Huang, Y.; Zhu, X.; Zhou, P.; Mu, P.; Li, N.
Broad Tunable and High-Purity Photonic Microwave Generation Based on an Optically Pumped QD Spin-VCSEL with Optical Feedback. *Photonics* **2023**, *10*, 326.
https://doi.org/10.3390/photonics10030326

**AMA Style**

Shen Z, Huang Y, Zhu X, Zhou P, Mu P, Li N.
Broad Tunable and High-Purity Photonic Microwave Generation Based on an Optically Pumped QD Spin-VCSEL with Optical Feedback. *Photonics*. 2023; 10(3):326.
https://doi.org/10.3390/photonics10030326

**Chicago/Turabian Style**

Shen, Zhenye, Yu Huang, Xin Zhu, Pei Zhou, Penghua Mu, and Nianqiang Li.
2023. "Broad Tunable and High-Purity Photonic Microwave Generation Based on an Optically Pumped QD Spin-VCSEL with Optical Feedback" *Photonics* 10, no. 3: 326.
https://doi.org/10.3390/photonics10030326