# Evaluation of Performance Enhancement of Optical Multi-Level Modulation Based on Direct Modulation of Optically Injection-Locked Semiconductor Lasers

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Principle and Theoretical Model

## 3. Simulation and Result

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Winzer, P.J.; Essiambre, R.J. Advanced Optical Modulation Formats. Proc. IEEE
**2006**, 94, 952–985. [Google Scholar] [CrossRef] - Karinou, F.; Borkowski, R.; Zibar, D.; Roudas, I.; Vlachos, K.G.; Monroy, I.T. Advanced Modulation Techniques for High-Performance Computing Optical Interconnects. IEEE J. Sel. Top. Quantum Electron.
**2013**, 19, 3700614. [Google Scholar] [CrossRef] - Olmedo, M.I.; Zuo, T.; Jensen, J.B.; Zhong, Q.; Xu, X.; Popov, S.; Monroy, I.T. Multiband Carrierless Amplitude Phase Modulation for High Capacity Optical Data Links. J. Lightwave Technol.
**2014**, 32, 798–804. [Google Scholar] [CrossRef][Green Version] - Dong, P.; Liu, X.; Chandrasekhar, S.; Buhl, L.L.; Aroca, R.; Chen, Y. Monolithic Silicon Photonic Integrated Circuits for Compact 100 +Gb/s Coherent Optical Receivers and Transmitters. IEEE J. Sel. Top. Quantum Electron.
**2014**, 20, 150–157. [Google Scholar] [CrossRef] - Cheng, Q.; Bahadori, M.; Glick, M.; Rumley, S.; Bergman, K. Recent advances in optical technologies for data centers: A review. Optica
**2018**, 5, 1354–1370. [Google Scholar] [CrossRef] - Lau, K.S.; Wong, K.H.; Chan, T.L.; Yeung, S.K. An Economical Piezoelectric Phase Modulator for Fiber Optic Sensors. Appl. Opt.
**1996**, 35, 6836–6838. [Google Scholar] [CrossRef] [PubMed][Green Version] - Saleh, B.E.A.; Teich, M.C. Fundamentals of Photonics, 2nd ed.; John Wiley & Sons, Inc.: New York, NY, USA, 1991; pp. 819–856. [Google Scholar]
- Liu, Z.; Kakande, J.; Kelly, B.; O’Carroll, J.; Phelan, R.; Richardson, D.J.; Slavík, R. Modulator-free quadrature amplitude modulation signal synthesis. Nat. Commun.
**2014**, 5, 5911. [Google Scholar] [CrossRef][Green Version] - Sung, H.K.; Lau, E.K.; Wu, M.C. Optical Properties and Modulation Characteristics of Ultra-Strong Injection-Locked Distributed Feedback Lasers. IEEE J. Sel. Top. Quantum Electron.
**2007**, 13, 1215–1221. [Google Scholar] [CrossRef][Green Version] - Simpson, T.B.; Liu, J.M.; Huang, K.F.; Tai, K.; Clayton, C.M.; Gavrielides, A.; Kovanis, V. Cavity enhancement of resonant frequencies in semiconductor lasers subject to optical injection. Phys. Rev. A
**1995**, 52, R4348–R4351. [Google Scholar] [CrossRef] [PubMed][Green Version] - Lee, H.L.T.; Ram, R.J.; Kjebon, O.; Schatz, R. Bandwidth enhancement and chirp reduction in DBR lasers by strong optical injection. In Proceedings of the Conference on Lasers and Electro-Optics (CLEO 2000), San Francisco, CA, USA, 7–12 May 2000. [Google Scholar]
- Murakami, A.; Kawashima, K.; Atsuki, K. Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection. IEEE J. Quantum Electron.
**2003**, 39, 1196–1204. [Google Scholar] [CrossRef] - Chrostowski, L.; Zhao, X.; Chang-Hasnain, C.J.; Shau, R.; Ortsiefer, M.; Amann, M. 50 GHz Directly-Modulated Injection-Locked 1.55 μm VCSELs. In Proceedings of the Optical Fiber Communication Conference, Anaheim, CA, USA, 6 March 2005. [Google Scholar]
- Iwashita, K.; Nakagawa, K. Suppression of mode partition noise by laser diode light injection. IEEE J. Quantum Electron.
**1985**, 18, 1669–1674. [Google Scholar] [CrossRef] - Lin, C.; Mengel, F. Reduction of frequency chirping and dynamic linewidth in high-speed directly modulated semiconductor lasers by injection locking. Electron. Lett.
**1984**, 20, 1073–1075. [Google Scholar] [CrossRef] - Olsson, N.; Temkin, H.; Logan, R.; Johnson, L.; Dolan, G.; van der Ziel, J.; Campbell, J. Chirp-free transmission over 82.5 km of single mode fibers at 2 Gbit/s with injection locked DFB semiconductor lasers. J. Lightwave Technol.
**1985**, 3, 63–67. [Google Scholar] [CrossRef] - Mohrdiek, S.; Burkhard, H.; Walter, H. Chirp reduction of directly modulated semiconductor lasers at 10 Gb/s by strong CW light injection. J. Lightwave Technol.
**1994**, 12, 418–424. [Google Scholar] [CrossRef] - Meng, X.J.; Chau, T.; Wu, M.C. Improved intrinsic dynamic distortions in directly modulated semiconductor lasers by optical injection locking. IEEE Trans. Microw. Theory Tech.
**1999**, 47, 1172–1176. [Google Scholar] [CrossRef][Green Version] - Meng, X.J.; Chau, T.; Tong, D.T.K.; Wu, M.C. Suppression of second harmonic distortion in directly modulated distributed feedback lasers by external light injection. Electron. Lett.
**1998**, 34, 2040–2041. [Google Scholar] [CrossRef][Green Version] - Yamaoka, S.; Diamantopoulos, N.-P.; Nishi, H.; Nakao, R.; Fujii, T.; Takeda, K.; Hiraki, T.; Tsurugaya, T.; Kanazawa, S.; Tanobe, H.; et al. Directly modulated membrane lasers with 108 GHz bandwidth on a high-thermal-conductivity silicon carbide substrate. Nat. Photon.
**2021**, 15, 28–35. [Google Scholar] [CrossRef] - Matsui, Y.; Schatz, R.; Che, D.; Khan, F.; Kwakernaak, M.; Tsurugi, S. Low-chirp isolator-free 65-GHz-bandwidth directly modulated lasers. Nat. Photonics
**2021**, 15, 59–63. [Google Scholar] [CrossRef] - Kobayashi, W.; Ito, T.; Yamanaka, T.; Fujisawa, T.; Shibata, Y.; Kurosaki, T.; Kohtoku, M.; Tadokoro, T.; Sanjoh, H. 50-Gb/s Direct Modulation of a 1.3-μm InGaAlAs-Based DFB Laser With a Ridge Waveguide Structure. IEEE J. Sel. Top. Quantum Electron.
**2013**, 19, 1500908. [Google Scholar] [CrossRef] - Nguyen, A.H.; Cho, J.H.; Bae, H.J.; Sung, H.K. Side-lobe Level Reduction of an Optical Phased Array Using Amplitude and Phase Modulation of Array Elements Based on Optically Injection-Locked Semiconductor Lasers. Photonics
**2020**, 7, 20. [Google Scholar] [CrossRef][Green Version] - Cho, J.H.; Cho, C.H.; Sung, H.K. Theoretical performance evaluation of optical complex signals based on optically injection-locked semiconductor lasers. IEEE J. Sel. Top. Quantum Electron.
**2019**, 25, 1–9. [Google Scholar] [CrossRef] - Lau, E.K.; Wong, L.J.; Wu, M.C. Enhanced Modulation Characteristics of Optical Injection-Locked Lasers: A Tutorial. IEEE J. Sel. Top. Quantum Electron.
**2009**, 15, 618–633. [Google Scholar] [CrossRef] - Lee, H.; Cho, J.H.; Sung, H.K. Enhancement of the phase-modulation range by using cascaded injection-locked semiconductor lasers. J. Korean Phys. Soc.
**2016**, 68, 756–761. [Google Scholar] [CrossRef] - Lee, H.; Cho, J.H.; Sung, H.K. Theoretical analysis of a method for extracting the phase of a phase-amplitude modulated signal generated by a direct-modulated optical injection-locked semiconductor laser. Opt. Eng.
**2017**, 56, 056112. [Google Scholar] [CrossRef][Green Version] - Abdullah, M.F.L.; Talib, R. Multilevel signal analyzer tool for optical communication system. Int. J. Electr. Comput. Eng.
**2012**, 2, 529. [Google Scholar] [CrossRef]

**Figure 1.**Schematic for the generation of the multi-level (M-level) amplitude shift keying (ASK) optical signals based on the optically injection-locked (OIL) semiconductor lasers.

**Figure 2.**Eye patterns of the free-running lasers. (

**a**) 2-level amplitude-shift keying (ASK) signal at 1-Gbaud data modulation. (

**b**) 4-level ASK signal at 1-Gbaud data modulation. (

**c**) 8-level ASK signal at 1-Gbaud data modulation. (

**d**) 2-level ASK signal at 5-Gbaud data modulation. (

**e**) 4-level ASK signal at 5-Gbaud data modulation. (

**f**) 8-level ASK signal at 5-Gbaud data modulation.

**Figure 3.**Eye pattern of the OIL semiconductor lasers. (

**a**) 2-level amplitude-shift keying (ASK) signal at 1-Gbaud data modulation. (

**b**) 4-level ASK signal at 1-Gbaud data modulation. (

**c**) 8-level ASK signal at 1-Gbaud data modulation. (

**d**) 2-level ASK signal at 5-Gbaud data modulation. (

**e**) 4-level ASK signal at 5-Gbaud data modulation. (

**f**) 8-level ASK signal at 5-Gbaud data modulation.

**Figure 4.**Averaged Q-factors of the free-running and the OIL semiconductor lasers as a function of various M-levels for 10-Gbaud and 20-Gbaud modulation. Q-factor: quality-factor; M-level: multi-level; OIL: optically injection locked.

**Figure 5.**Averaged Q-factors of the free-running and the OIL semiconductor lasers as a function of various data rates for 2 and 4-level ASK signals. Q-factor: quality-factor; ASK: amplitude-shift keying; OIL: optically injection-locked.

**Figure 6.**Q-factor dependence on the injection-locking parameters for two-level ASK signals at 10-Gbaud data modulation. The locking range is represented as a gray-scaled range that shows the Q-factor value. Q-factor: quality-factor; n.s.: unstable locking range.

Symbol | Quantity | Value | Unit |
---|---|---|---|

${\lambda}_{0}$ | Wavelength | $1550$ | nm |

$g$ | Net stimulated gain | $4.7\times {10}^{4}$ | $1/\mathrm{s}$ |

${N}_{tr}$ | Transparency carrier number | $9.36\times {10}^{6}$ | No unit |

${J}_{th}$ | Threshold current | $2\times {10}^{16}$ | $1/\mathrm{s}$ |

${J}_{bias}$ | Bias current | $5\times {J}_{th}$ | $1/\mathrm{s}$ |

${\gamma}_{p}$ | Photon decay rate | $5\times {10}^{11}$ | $1/\mathrm{s}$ |

${\gamma}_{n}$ | Carrier decay rate | $1\times {10}^{9}$ | $1/\mathrm{s}$ |

$\alpha $ | Linewidth enhancement factor | $5$ | No unit |

$\kappa $ | Coupling ratio | $225$ | $1/\mathrm{s}$ |

${R}_{inj}$ | Injection power ratio | $10$ | dB |

$\Delta {\omega}_{inj}$ | Detuning frequency | $-10$ | GHz |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jeong, H.-S.; Cho, J.-H.; Sung, H.-K. Evaluation of Performance Enhancement of Optical Multi-Level Modulation Based on Direct Modulation of Optically Injection-Locked Semiconductor Lasers. *Photonics* **2021**, *8*, 130.
https://doi.org/10.3390/photonics8040130

**AMA Style**

Jeong H-S, Cho J-H, Sung H-K. Evaluation of Performance Enhancement of Optical Multi-Level Modulation Based on Direct Modulation of Optically Injection-Locked Semiconductor Lasers. *Photonics*. 2021; 8(4):130.
https://doi.org/10.3390/photonics8040130

**Chicago/Turabian Style**

Jeong, Hyo-Sang, Jun-Hyung Cho, and Hyuk-Kee Sung. 2021. "Evaluation of Performance Enhancement of Optical Multi-Level Modulation Based on Direct Modulation of Optically Injection-Locked Semiconductor Lasers" *Photonics* 8, no. 4: 130.
https://doi.org/10.3390/photonics8040130