Synchronization Properties of Multi-Layer Photonic Spiking Neural Networks Based on VCSEL-SA

Jianhao Zhou; Wei Pan; Lianshan Yan; Bin Luo; Xihua Zou; Songsui Li; Liyue Zhang

doi:10.3788/LOP250740

Laser & Optoelectronics Progress, Volume. 62, Issue 17, 1739024(2025)

Synchronization Properties of Multi-Layer Photonic Spiking Neural Networks Based on VCSEL-SA

Jianhao Zhou, Wei Pan^**, Lianshan Yan, Bin Luo, Xihua Zou, Songsui Li, and Liyue Zhang^*

Author Affiliations

The Center for Information Photonics and Communications, Southwest Jiaotong University, Chengdu 611756, Sichuan , China

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Figures & Tables(11)

Fig. 1. Schematic structure of VCSEL-SA

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Fig. 2. Schematic of the network model, an external neuron is unidirectionally connected to 100 neurons in the SW network via synapses with coupling strength $k_{c} = 8 \times 10^{4} m W^{- 1}$ , and connection probability $p = 50 %$ , neurons within the SW network are interconnected with different time delays. (a) Single-layer network structure with uniform time delay $τ$ ; (b) bilayer network structure with intralayer coupling delays $τ_{α}$ , $τ_{β}$ and interlayer coupling delay $τ_{γ}$ ; (c) three-layer network structure based on the bilayer network with an additional intralayer coupling delay $τ_{δ}$

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Fig. 3. Synchronization measure $R$ curves, pulse pattern diagrams, and phase distribution diagrams. (a) Synchronization measure variation with coupling delay, where (a1)‒(a4) show carrier density time series for delays of 0.8 ns, 1 ns, 2 ns, and 4 ns; (b1)‒(b4) pulse patterns for Fig. 3 (a1)‒(a4); (c1)‒(c4) phase distributions under conditions of 70 ns, 1 ns; 100 ns, 1 ns; 70 ns, 2 ns; and 100 ns, 2 ns

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Fig. 4. The distribution pattern of synchronization measure $R$ under different time delay conditions. (a) $τ =$ 2 ns; (b) $τ =$ 3 ns

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Fig. 5. Neuronal dynamics during the transition from stage Ⅱ to stage Ⅲ. (a1)‒(a4) The pulse mode diagrams when the time delay τ is 2.1 ns, 2.2 ns, 2.3 ns, and 3 ns respectively (from top to bottom); (b1)‒(b4) phase distribution plots corresponding to Figs. 5 (a1)‒(a4)

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Fig. 6. The distribution pattern of synchronization measure R. (a) $R_{α}$ ; (b) $R_{β}$ ; (c) $R_{α β}$

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Fig. 7. Synchronization patterns of the network under different $D_{α γ}$ . (a1)‒(a3) When the coupling time-delay $τ_{α}$ of layer $α$ is $4 n s$ , the pulse-mode diagrams for $D_{α γ}$ of 1 ns, 2 ns, 4 ns; (b1)‒(b3) the phase-distribution diagrams corresponding to Figs.7 (a1)‒(a3); (c) the number of pulse-triggering clusters under different $D_{α γ}$

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Fig. 8. The distribution patterns of synchronization measure R

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Fig. 9. The distribution patterns of synchronization measure R

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Fig. 10. Synchronization measure $R$ as a function of $τ_{δ}$ in a three-layer spiking neural network with different $τ_{β}$

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Table 1. Internal parameters and values of VCSEL-SA

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Table 1. Internal parameters and values of VCSEL-SA

Parameter	Symbol and value
Gain region cavity volume	$V_{a} = 2.4 \times 10^{- 18} m^{3}$
SA region cavity volume	$V_{s} = 2.4 \times 10^{- 18} m^{3}$
Gain region confinement factor	$Γ_{a} = 0.06$
SA region confinement factor	$Γ_{s} = 0.05$
Gain region carrier lifetime	$τ_{a} = 1 n s$
SA region carrier lifetime	$τ_{s} = 100 p s$
Gain region differential gain/loss	$g_{a} = 2.9 \times 10^{- 12} m^{3} s^{- 1}$
SA region differential gain/loss	$g_{s} = 14.5 \times 10^{- 12} m^{3} s^{- 1}$
Gain region transparency carrier density	$n_{0, a} = 1.1 \times 10^{24} m^{- 3}$
SA region transparency carrier density	$n_{0, s} = 0.89 \times 10^{24} m^{- 3}$
Lasing wavelength	$λ = 850 n m$
Bimolecular recombination term	$B_{r} = 10 \times 10^{- 16} m^{- 3} s^{- 1}$
Spontaneous emission coupling factor	$β = 1 \times 10^{- 4}$
Output power coupling coefficient	$η_{c} = 0.4$
Photon lifetime	$τ_{p h} = 4.8 \times 10^{- 12} s$
Velocity of light	$c = 3 \times 10^{8} m s^{- 1}$
Planck constant	$h = 6.63 \times 10^{- 34} J s$

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Jianhao Zhou, Wei Pan, Lianshan Yan, Bin Luo, Xihua Zou, Songsui Li, Liyue Zhang. Synchronization Properties of Multi-Layer Photonic Spiking Neural Networks Based on VCSEL-SA[J]. Laser & Optoelectronics Progress, 2025, 62(17): 1739024

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Paper Information

Category: AI for Optics

Received: Mar. 3, 2025

Accepted: Apr. 24, 2025

Published Online: Sep. 12, 2025

The Author Email: Wei Pan (wpan@home.swjtu.edu.cn), Liyue Zhang (lyzhang@swjtu.edu.cn)

DOI:10.3788/LOP250740

CSTR:32186.14.LOP250740

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology