Period-one (P1) oscillations in a semiconductor laser under optical feedback from a narrowband fiber Bragg grating (FBG) are numerically investigated. FBG feedback enhances the stability of P1 oscillations compared to the conventional mirror feedback in the form of P1 microwave linewidth and phase noise reduction and residual noise peaks suppression. In the proposed scheme, the FBG has a narrow bandwidth smaller than the laser relaxation oscillation frequency. Then it effectively suppresses the coherence collapse of the laser by filtered feedback. Hence it can keep the laser in P1 operation even under relatively strong feedback. Besides, a uniform FBG has a comb-filtered reflectivity spectrum with a main lobe surrounded by several side lobes. Hence it can limit the external cavity modes by each lobe. As a result, FBG feedback can reduce microwave linewidth and phase noise by sustaining stronger feedback power and improve side-peak suppression ratio (SPSR) by filtering external cavity modes. The effects of stabilization are enhanced by properly increasing grating bandwidth. By fine-tuning the feedback delay time, the microwave linewidth can be reduced to a local minimum which reveals the optimal locking between P1 frequency and one of the external cavity modes. Increasing the feedback delay time, the local minimum linewidth can be further reduced. FBG feedback reduces the microwave linewidth by up to more than an order of magnitude and improves the SPSR by up to more than two orders of magnitude than mirror feedback using the same delay time.

中文翻译：

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半导体激光器在窄带光纤布拉格光栅的光反馈下稳定的周期一振荡。

数值研究了半导体激光器在窄带光纤布拉格光栅（FBG）的光反馈下的周期一（P1）振荡。与传统的镜面反馈相比，FBG反馈以P1微波线宽和相位噪声降低以及残余噪声峰值抑制的形式增强了P1振荡的稳定性。在所提出的方案中，FBG具有比激光弛豫振荡频率小的窄带宽。然后通过滤波后的反馈有效地抑制了激光器的相干塌陷。因此，即使在相对强的反馈下，也可以使激光器保持P1操作。此外，均匀的FBG具有梳状滤波的反射光谱，其主瓣被多个旁瓣围绕。因此，它可以通过每个瓣来限制外腔模式。结果是，FBG反馈可通过保持更强的反馈功率来减少微波线宽和相位噪声，并通过对外部腔模式进行滤波来改善侧峰抑制比（SPSR）。通过适当增加光栅带宽可以增强稳定效果。通过微调反馈延迟时间，可以将微波线宽减小到局部最小值，从而显示出P1频率与外腔模式之一之间的最佳锁定。增加反馈延迟时间，可以进一步减小局部最小线宽。与使用相同延迟时间的镜面反馈相比，FBG反馈最多可将微波线宽减小一个数量级以上，并且将SPSR最多提高两个数量级以上。