# Key Space Enhancement of Chaos Communication Using Semiconductor Lasers with Spectrum-Programmable Optoelectronic Feedback

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## Abstract

**:**

^{100}at a data rate of 10 Gbit/s, and it can be further enhanced by increasing the number of feedback loops. These results suggest an alternative approach for security-enhanced optical chaos communication.

## 1. Introduction

^{48}by adding a frequency-dependent group delay module with high-frequency tuning resolution in chaotic optoelectronic oscillation [18]. Wang et al. demonstrated that the key space is enhanced by 2

^{44}compared to conventional mirror feedback using external chirped fibre Bragg grating feedback. This is because they time delay signature is suppressed, and new dimensions of the key space are introduced [17,19]. A vertical-cavity surface-emitting laser with common phase-modulated electro-optic feedback has been proposed by Wang et al. to eliminate the time-delay signature and enhance the dimensions of the key space [20]. Gao et al. demonstrated that the key space can be enhanced by 2

^{34}by introducing an electro-optic nonlinear transformation hardware module [21]. Wang et al. proposed a key-space-enhanced optical chaos secure communication scheme using a pair of monolithically integrated multi-section semiconductor lasers as transceivers and numerically demonstrated the key space reaches 2

^{48}with a data rate of 2.5 Gbit/s [22].

^{100}at a communication rate of 10 Gbit/s.

## 2. Theoretical Model

^{TM}commercial simulation software. The time delay of the optoelectronic filtered feedback is fixed at 2.55 ns in each feedback loop. The bias currents of the two lasers are both 30 mA, which is 1.5 times the threshold current. In order to provide a certain initial feedback strength, the amplifier gain (G

_{0}) in the optoelectronic feedback loop is fixed at 2 dB. The injection strength, k

_{inj}, is defined as the ratio of the optical power of the injection to the laser output power. In the simulation, the optical coupling strength of different devices is considered 100%. The two lasers have the same internal parameters, which are listed in Table 1.

## 3. Simulation Results

#### 3.1. Chaos Generation and Synchronization

_{0}= 3 GHz. The laser operates in a steady state for G = 0.4 dB (Figure 2(a1–a3)). The time series shows only minor fluctuations, and the power spectrum almost coincides with the noise floor except for a slight bulge around 2 GHz, which is the characteristic relaxation–oscillation frequency. In addition, an extended dot is observed in the phase portrait. A period-one state is observed at G = 1.5 dB (Figure 2(b1–b3)). The time series shows regular fluctuations, and the fundamental frequency is around the relaxation–oscillation frequency and its harmonics in the corresponding power spectrum. The trajectories of the phase portrait show clear limit cycle features. The laser enters a quasiperiodic state at G = 3.2 dB (Figure 2(c1–c3)). The time series shows irregular fluctuations. The trajectories of the phase portrait are dispersed within a certain range. The laser enters the chaos state at G = 5.6 dB (Figure 2(d1–d3)). The time series shows strong fluctuations, and the corresponding power spectrum continuously covers an extremely broad frequency range. The phase portrait shows a widely scattered distribution over a large area.

_{inj}= 0.16 and an amplifier gain of G = 20 dB. The chaotic waveforms generated by the response lasers exhibit almost the same profiles. A correlation coefficient of 0.98 is achieved between the output chaotic signals from the two lasers, as shown in Figure 3d, indicating high-quality synchronization. In contrast, the chaotic waveforms output by the response lasers are evidently distinct from the temporal intensity fluctuation of the driving source, and a correlation coefficient of 0.21 is obtained between them, as shown in Figure 3e. Such a low correlation coefficient implies that it is difficult for an eavesdropper to extract the private chaotic encryption signal by tapping the public driving signal.

_{inj}= 0.16, and the filtered feedback strength is constant. At centre frequencies of 1–12 GHz, the correlation coefficient is constant at approximately 0.98, with only minor fluctuations. These results show that the response lasers exhibit similar synchronization characteristics when the filtered feedback strength is fixed, even though the filter width or centre frequency of the BPF may be different.

_{a}and DFB

_{b}is sensitive to the centre frequency detuning. The mismatch tolerance to the centre frequency of the BPF is in the order of tens of MHz, and the tolerance reduces with the centre frequency (Figure 5a). This is because the detuning of the centre frequency result in a large variation in the filtered feedback strength when it is close to the relaxation–oscillation frequency of the DFB laser. Nevertheless, with the frequency increasing, the chaotic spectrum becomes flatter. Thus, the effects of centre frequency mismatch on feedback strength are limited. However, the tolerances for different filter widths are similar (Figure 5b). Figure 5c shows the effect of the mismatch of the amplifier gain on the correlation for different filter widths. The synchronization performance decreases as the mismatch increases, and a similar trend is observed for different filter widths.

#### 3.2. Physical Key Space Analysis

_{0i}= 1.6 + 0.2 × (i − 1) GHz (i = 1–12).

^{−4}, which is below the hard-decision forward-error correction (FEC) threshold of 3.8 × 10

^{−3}[23]. Figure 6f shows the effects of the synchronization coefficient on the BER of the decoded message. As the synchronization coefficient decreases to 0.9, the BER increases to a limit of 3.8 × 10

^{−3}, below which the decoded message can still be recovered by the FEC processing technique. The message cannot be recovered as the synchronization coefficient decreases further. Therefore, we adopt 0.9 as the synchronization threshold to calculate the critical mismatch of each parameter.

^{100}is expected from the use of 12 parallel optoelectronic filtered feedback loops.

## 4. Discussion

## 5. Conclusions

^{100}at a communication rate of 10 Gbit/s using 12 filtered feedback loops, and it can be further enhanced by increasing the parallel number.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic of key-space-enhanced secure optical communication using spectrum-programmable optoelectronic feedback. ASE: amplified spontaneous emission; OI: optical isolator; TF: tuneable filter; EDFA: erbium-doped fibre amplifier; OC: optical coupler; VOA: variable optical attenuator; PD: photodetector; BPF: bandpass filter; Amp: amplifier.

**Figure 2.**Time series, power spectrum, and corresponding phase portraits of dynamic states under optoelectronic filtered feedback. (

**a1**–

**a3**) Steady state at G = 0.4 dB; (

**b1**–

**b3**) Regular pulse at G = 1.5 dB; (

**c1**–

**c3**) Quasiperiodic state at G = 3.2 dB; (

**d1**–

**d3**) Chaotic pulsing at G = 5.6 dB.

**Figure 3.**Time series of (

**a**) drive signal, (

**b**) DFB

_{a}, and (

**c**) DFB

_{b}; (

**d**) correlation plots of the transceiver; (

**e**) correlation plots of DFB

_{a}and drive signal.

**Figure 4.**Correlation coefficient versus injection strength for different (

**a**) amplifier gains and (

**b**) filter widths; (

**c**) correlation coefficient versus centre frequency of filter.

**Figure 5.**Correlation coefficient versus (

**a**) centre frequency detuning mismatch for different centre frequencies, (

**b**) centre frequency detuning mismatch for different BPF widths, and (

**c**) amplifier gain detuning for different BPF widths.

**Figure 6.**Time series for (

**a**) original message, (

**b**) chaotic carrier, (

**c**) chaotic carrier with message, and (

**d**) decrypted message. (

**e**) Eye diagrams for decrypted message; (

**f**) BER of decoded message as a function of synchronization coefficient. The message rate is 10 Gbit/s with a modulation amplitude of 0.2.

**Figure 7.**Effects of mismatch of centre frequency of BPFs on correlation coefficient. The centre frequency of BPFs is (

**a**) 1.6 GHz, (

**b**) 1.8 GHz, (

**c**) 2.0 GHz, (

**d**) 2.2 GHz, (

**e**) 2.4 GHz, (

**f**) 2.6 GHz, (

**g**) 2.8 GHz, (

**h**) 3.0 GHz, (

**i**) 3.2 GHz, (

**j**) 3.4 GHz, (

**k**) 3.6 GHz, (

**l**) 3.8 GHz.

**Figure 8.**Effects of mismatch of amplifier gain on correlation coefficient. (

**a**–

**l**) The gain of amplifier is 20 dB.

Parameters | Values | Units | |
---|---|---|---|

ASE noise | Noise frequency of ASE | 193.1 | THz |

Noise bin spacing of ASE | 3.0 × 10^{11} | Hz | |

Filter width of TF | 100 | GHz | |

DFB laser | Linewidth enhancement factor | 3.0 | -- |

Group index | 3.7 | -- | |

Internal loss factor | 3000 | m^{−1} | |

Linear gain coefficient | 3.0 × 10^{−20} | m^{2} | |

Nonlinear gain coefficient | 1.0 × 10^{−23} | m^{3} | |

Carrier density at transparency | 1.5 × 10^{24} | m^{−3} | |

Initial carrier density | 1.0 × 10^{24} | m^{−3} | |

Linear recombination coefficient | 3.0 × 10^{8} | s^{−1} |

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**MDPI and ACS Style**

Guo, Y.; Wang, D.; Wang, L.; Jia, Z.; Zhao, T.; Chang, P.; Wang, Y.; Wang, A. Key Space Enhancement of Chaos Communication Using Semiconductor Lasers with Spectrum-Programmable Optoelectronic Feedback. *Photonics* **2023**, *10*, 370.
https://doi.org/10.3390/photonics10040370

**AMA Style**

Guo Y, Wang D, Wang L, Jia Z, Zhao T, Chang P, Wang Y, Wang A. Key Space Enhancement of Chaos Communication Using Semiconductor Lasers with Spectrum-Programmable Optoelectronic Feedback. *Photonics*. 2023; 10(4):370.
https://doi.org/10.3390/photonics10040370

**Chicago/Turabian Style**

Guo, Yuanyuan, Dongsheng Wang, Longsheng Wang, Zhiwei Jia, Tong Zhao, Pengfa Chang, Yuncai Wang, and Anbang Wang. 2023. "Key Space Enhancement of Chaos Communication Using Semiconductor Lasers with Spectrum-Programmable Optoelectronic Feedback" *Photonics* 10, no. 4: 370.
https://doi.org/10.3390/photonics10040370