Short-term prediction for chaotic time series based on photonic reservoir computing using VCSEL with a feedback loop

Xingxing Guo; Hanxu Zhou; Shuiying Xiang; Qian Yu; Yahui Zhang; Yanan Han; Tao Wang; Yue Hao

doi:10.1364/PRJ.517275

Photonics Research, Volume. 12, Issue 6, 1222(2024)

Short-term prediction for chaotic time series based on photonic reservoir computing using VCSEL with a feedback loop

Xingxing Guo¹, Hanxu Zhou¹, Shuiying Xiang^1,2、*, Qian Yu¹, Yahui Zhang^1,2, Yanan Han¹, Tao Wang¹, and Yue Hao²

Author Affiliations

¹State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China

²State Key Discipline Laboratory of Wide Bandgap Semiconductor Technology, School of Microelectronics, Xidian University, Xi'an 710071, China

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Figures & Tables(11)

Fig. 1. (a) Chaotic system of a multi-delay mutual coupling VCSEL ring network structure for chaotic signal generation: PC1, PC2, and PC3, polarization controllers; EDFA, erbium-doped optical fiber amplifier; VOA, variable optical attenuator; OC1 and OC2, optical circulators; FC, fiber coupler; LAC, higher-stability and low-noise diode controller; VCSEL1, VCSEL2, and VCSEL3, vertical-cavity surface-emitting lasers. (b) Conceptual diagram of the RC. (c) Photonic RC system based on VCSEL for chaos time series prediction: PC4, PC5, and PC6, polarization controllers; EDFA, erbium-doped optical fiber amplifier; VOA, variable optical attenuator; OC3, optical circulator; FC2, FC3, and FC4, fiber couplers; PD1 and PD2, photodetectors; OSC, oscilloscope; DL, delay line; TL, tunable laser; RF, RF amplifier; MZM, Mach–Zehnder modulator; VCSEL, vertical-cavity surface-emitting laser.

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Fig. 2. Chaotic time series obtained in experiment. (a1)–(d1) Time-domain signal. (a2)–(d2) Power spectrum. (a3)–(d3) PE as a function of lag time. (a4)–(d4) ACF as a function of lag time.

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Fig. 3. Time-domain chaotic signal (first column), power spectrum (second column), permutation entropy (third column), and autocorrelation curve function (fourth column) obtained by simulation.

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Fig. 4. NMSE of the system as a function of the injection strength for (a) different MPEs and (b) approximate MPE.

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Fig. 5. NMSE of the system as a function of the (a) injection strength kinj and (b) feedback strength kd. The black (red, blue, or green) line represents the result of 1- (2, 3, or 4) step-ahead prediction.

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Fig. 6. (a) Optical spectrum of the free running VCSEL. (b) Optical spectrum of the VCSEL with the external optical injection. (c) Power-current curve of the VCSEL when the temperature is stabilized at 25°C.

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Fig. 7. NMSE as a function of attenuation coefficient.

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Fig. 8. Time domain prediction results for (a) 1-step-ahead task, (b) 2-steps-ahead task, (c) 3-steps-ahead task, and (d) 4-steps-ahead task. The red (blue) line is for the target (prediction) sequences.

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Table 1. Parameter Values for Three VCSELs in the Numerical Simulation

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Table 1. Parameter Values for Three VCSELs in the Numerical Simulation

Descriptions	Parameters	Values
Field decay rate	$k$	$300 {ns}^{- 1}$
Linewidth enhancement factor	$α$	3
Decay rate of $N$	$γ_{N}$	$1 {ns}^{- 1}$
Spin-flip rate	$γ_{S}$	$50 {ns}^{- 1}$
Linear dichroism	$γ_{α}$	$0.1 {ns}^{- 1}$
Linear birefringence	$γ_{p}$	$10 {ns}^{- 1}$
Normalized injection current	$μ$	2.7
Optical wavelength	$λ$	1550 nm
Frequency detuning	$Δ f_{21}$	−15 GHz to 15 GHz
Frequency detuning	$Δ f_{23}$	−15 GHz to 15 GHz
Coupling strength	$k_{r}$	$5 {ns}^{- 1}$ to $50 {ns}^{- 1}$

Table 2. Parameter Values for the Photonic RC System in Our Numerical Simulation^a

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Table 2. Parameter Values for the Photonic RC System in Our Numerical Simulation^a

Descriptions	Parameters	Values
Field decay rate	$k_{r}$	$300 {ns}^{- 1}$
Linewidth enhancement factor	$α_{r}$	3
Decay rate of $N$	$γ_{r n}$	$1 {ns}^{- 1}$
Spin-flip rate	$γ_{r s}$	$50 {ns}^{- 1}$
Linear dichroism	$γ_{r α}$	$0.1 {ns}^{- 1}$
Linear birefringence	$γ_{r p}$	$10 {ns}^{- 1}$
Injection field amplitude	$\| ε_{0} \|$	1
Frequency detuning	$Δ f$	0 GHz

Table 3. Impact of Dataset Size on the System
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Table 3. Impact of Dataset Size on the System
Training Set Testing Set NMSE
3000 2000 0.1159
4000 2000 0.0940
5000 2000 0.0786
7000 2000 0.0678

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Xingxing Guo, Hanxu Zhou, Shuiying Xiang, Qian Yu, Yahui Zhang, Yanan Han, Tao Wang, Yue Hao, "Short-term prediction for chaotic time series based on photonic reservoir computing using VCSEL with a feedback loop," Photonics Res. 12, 1222 (2024)

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Paper Information

Category: Lasers and Laser Optics

Received: Jan. 3, 2024

Accepted: Mar. 18, 2024

Published Online: May. 30, 2024

The Author Email: Shuiying Xiang (syxiang@xidian.edu.cn)

DOI:10.1364/PRJ.517275

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Parameter Values for Three VCSELs in the Numerical Simulation

Table 1. Parameter Values for Three VCSELs in the Numerical Simulation

Table 2. Parameter Values for the Photonic RC System in Our Numerical Simulationa

Table 2. Parameter Values for the Photonic RC System in Our Numerical Simulationa

Table 3. Impact of Dataset Size on the System

Table 3. Impact of Dataset Size on the System

Table 2. Parameter Values for the Photonic RC System in Our Numerical Simulation^a

Table 2. Parameter Values for the Photonic RC System in Our Numerical Simulation^a