This paper numerically studies the long-haul chaotic synchronization scheme of semiconductor lasers driven by a common signal based on erbium-doped fiber amplifier (EDFA) relay and periodic dispersion compensation. By optimizing the injection conditions of the driving light and the mismatch of the relaxation oscillation frequency between driving and response lasers, the response laser achieves synchronization with a synchronization coefficient of 0.98 in back-to-back situations. At the same time, the correlation between the driving and response lasers is reduced to 0.32, ensuring the security of the co-drive synchronization system. Furthermore, considering the damage factors such as fiber dispersion, nonlinear effects, and EDFA noise, the optimal conditions for fiber input power and single-span fiber length are numerically studied. It is expected that under the condition of dispersion compensation deviation of 5 ps/nm per 100 km fiber, a high-quality chaotic synchronization with a synchronization coefficient of 0.90 can be achieved after 700 km of fiber transmission. This research result has reference significance for long-distance chaotic laser carrier communication and key distribution.
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