# Two Polarization Comb Dynamics in VCSELs Subject to Optical Injection

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Polarization Dynamics

#### 2.1. Experimental Setup

#### 2.2. Impact of the Injected Comb Spacing

#### 2.3. Influence of the Injection Current

#### 2.4. Tailoring Comb Properties

## 3. Theoretical Bifurcation Analysis

#### 3.1. Y-PM Comb Dynamics

#### 3.2. Influence of Spin-Flip Relaxation Rate

## 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.**(

**a**) Setup for frequency comb injection into a single-mode VCSEL. TL: Tunable Laser, EDFA: amplifier, P.C: Polarization Controller, AWG: Arbitrary Waveform Generator, MZM: Mach–Zehnder Modulator, VOA: Variable Optical Attenuator, OSA: Optical Spectrum Analyser, PD: photodiode, ESA: Electrical spectrum analyzer. (

**b**–

**d**) correspond to the optical spectra of the injected comb for comb spacing of $\mathsf{\Omega}=1$ GHz, $\mathsf{\Omega}=2$ GHz and $\mathsf{\Omega}=4$ GHz, respectively. (

**e**) shows the optical spectrum of the VCSEL in free running.

**Figure 2.**Bifurcation scenarios resulting in the excitation of the depressed polarization mode. These optical spectra are obtained for detuning $\Delta \nu =1.6$ GHz and injected comb spacing $\mathsf{\Omega}=1$ GHz when increasing the injected power, ${P}_{inj}$. (

**a**) Stable output at ${P}_{inj}=3$ µW, (

**b**,

**c**) wave mixing at ${P}_{inj}=16$ µW and ${P}_{inj}=32$ µW, respectively, (

**d**) two polarization comb at ${P}_{inj}=48$ µW, (

**e**,

**f**) two polarization harmonics comb at ${P}_{inj}=80$ µW and ${P}_{inj}=96$ µW, respectively, (

**g**) two polarization complex dynamics at ${P}_{inj}=128$ µW and (

**h**,

**i**) X-polarization comb at ${P}_{inj}=144$ µW and ${P}_{inj}=240$ µW, respectively.

**Figure 3.**Polarization resolved-optical spectra corresponding to an example of two polarization comb dynamics similar to Figure 2d–f for detuning $\Delta \nu =1.6$ GHz and injected power ${P}_{inj}=20$ µW. (

**a**–

**c**) correspond to the optical spectra of Y-PM, X-PM and the superposition of Y-PM and X-PM, respectively.

**Figure 4.**Bifurcation scenarios resulting in the excitation of the depressed polarization mode. These optical spectra are obtained for detuning $\Delta \nu =1.6$ GHz and injected comb spacing $\mathsf{\Omega}=2$ GHz. (

**a**) Stable output at ${P}_{inj}=3$ µW, (

**b**) wave mixing at ${P}_{inj}=16$ µW, (

**c**) two polarizations comb at ${P}_{inj}=48$ µW, (

**d**) two polarization harmonics comb at ${P}_{inj}=112$ µW, (

**e**) two polarization complex dynamics at ${P}_{inj}=208$ µW and (

**f**) X-polarization comb at ${P}_{inj}=240$ µW.

**Figure 5.**Polarization resolved-optical spectra corresponding to an example of two polarization comb dynamics in Figure 4c. (

**a**–

**c**) are obtained for detuning $\Delta \nu =1.6$ GHz and injected power ${P}_{inj}=20$ µW. (

**a**–

**c**) correspond to the optical spectra of Y-PM, X-PM and the superposition of Y-PM and X-PM, respectively.

**Figure 6.**Bifurcation scenarios resulting in the excitation of the depressed polarization mode. These optical spectra are obtained for detuning $\Delta \nu =-0.9$ GHz and injected comb spacing $\mathsf{\Omega}=4$ GHz. (

**a**,

**b**) Wave mixing at ${P}_{inj}=3$ µW and ${P}_{inj}=32$ µW, respectively, (

**c**,

**d**) single polarization comb at ${P}_{inj}=48$ µW and ${P}_{inj}=228$ µW, respectively, (

**e**,

**h**,

**i**) two polarizations comb at ${P}_{inj}=304$ µW, ${P}_{inj}=560$ µW and ${P}_{inj}=704$ µW, respectively, (

**f**) two polarization harmonics comb at ${P}_{inj}=376$ µW and (

**g**) two polarization complex dynamics at ${P}_{inj}=448$ µW.

**Figure 7.**Polarization resolved-optical spectra corresponding to an example of two polarization comb dynamics in Figure 6e–i. (

**a**–

**c**) are obtained for detuning $\Delta \nu =-0.9$ GHz and injected power ${P}_{inj}=432.8$ µW. (

**a**–

**c**) correspond to the optical spectra of Y-PM, X-PM and the superposition of Y-PM and X-PM, respectively.

**Figure 8.**Control of comb properties using the injection parameters and polarization of the injected light. (

**a**,

**b**) are obtained for fixed detuning and comb spacing $\Delta \nu =1.6$ GHz and $\mathsf{\Omega}=2$ GHz, respectively. (

**c**,

**d**) are obtained for fixed comb spacing ($\mathsf{\Omega}=4$ GHz) and injection current $I=8$ mA. The blue and red curves correspond to the parallel and orthogonal optical injection, respectively. The comb dynamics in parallel and orthogonal optical injection are obtained for fixed detuning $\Delta \nu =-0.9$ GHz and $\Delta \nu =-11.6$ GHz, respectively.

**Figure 9.**Bifurcation diagrams for fixed injected comb spacing $\mathsf{\Omega}=2$ GHz and detuning $\Delta {\nu}_{x}=-9$ GHz. The left and right panels correspond to X-polarization mode (X-PM) and Y-polarization mode (Y-PM). (

**a**${}_{\mathbf{1}}$,

**b**${}_{\mathbf{1}}$), (

**a**${}_{\mathbf{2}}$,

**b**${}_{\mathbf{2}}$), (

**a**${}_{\mathbf{3}}$,

**b**${}_{\mathbf{3}}$) and (

**a**${}_{\mathbf{4}}$,

**b**${}_{\mathbf{4}}$) are obtained for ${\gamma}_{a}=-0.1$ ns${}^{-1}$, ${\gamma}_{a}=-0.2$ ns${}^{-1}$, ${\gamma}_{a}=-0.6$ ns${}^{-1}$ and ${\gamma}_{a}=-0.8$ ns${}^{-1}$.

**Figure 10.**Optical spectra for fixed $\mathsf{\Omega}=2$ GHz, $\Delta {\nu}_{x}=-9$ GHz and ${\gamma}_{a}=-0.6$ ns${}^{-1}$. The left (

**a**) and right (

**b**) panels correspond to X-PM and Y-PM, respectively. The top figures (

**a**${}_{\mathbf{1}}$,

**b**${}_{\mathbf{1}}$) are obtained for $\mathbf{\kappa}=\mathbf{0}.\mathbf{525}$ and the bottom figures (

**a**${}_{\mathbf{2}}$,

**b**${}_{\mathbf{2}}$) are obtained for $\mathbf{\kappa}=\mathbf{0}.\mathbf{6}$.

**Figure 11.**Bifurcation diagrams for fixed injected comb spacing $\mathsf{\Omega}=2$ GHz and ${\gamma}_{a}=-0.8$ ns${}^{-1}$. The left and right panels correspond to X-PM and Y-PM, respectively. (

**a**,

**b**) are obtained for $\mu =4.2$ and (

**c**,

**d**) for $\mu =5.29$.

**Figure 12.**Bifurcation diagrams for fixed injected comb spacing $\mathsf{\Omega}=2$ GHz and detuning $\Delta {\nu}_{x}=-9$ GHz when varying ${\gamma}_{s}$. (

**a**–

**d**) are obtained for ${\gamma}_{s}=50$ ns${}^{-1}$, ${\gamma}_{s}=200$ ns${}^{-1}$, ${\gamma}_{s}=1000$ ns${}^{-1}$ and ${\gamma}_{s}=2300$ ns${}^{-1}$, respectively.

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**MDPI and ACS Style**

Doumbia, Y.; Wolfersberger, D.; Panajotov, K.; Sciamanna, M.
Two Polarization Comb Dynamics in VCSELs Subject to Optical Injection. *Photonics* **2022**, *9*, 115.
https://doi.org/10.3390/photonics9020115

**AMA Style**

Doumbia Y, Wolfersberger D, Panajotov K, Sciamanna M.
Two Polarization Comb Dynamics in VCSELs Subject to Optical Injection. *Photonics*. 2022; 9(2):115.
https://doi.org/10.3390/photonics9020115

**Chicago/Turabian Style**

Doumbia, Yaya, Delphine Wolfersberger, Krassimir Panajotov, and Marc Sciamanna.
2022. "Two Polarization Comb Dynamics in VCSELs Subject to Optical Injection" *Photonics* 9, no. 2: 115.
https://doi.org/10.3390/photonics9020115