Semiconductor lasers (SLs) show relaxation oscillation (RO) due to the cavity damping rate being higher than the carrier damping rate. The presence of RO in SLs contributes to abundant complex dynamics when the laser is perturbed by external optical feedback (EOF). In this work, the influence of feedback optical phase on the relaxation oscillation frequency (ROF) in an SL is investigated both theoretically and experimentally. By numerically solving the well-known Lang Kobayashi equations, the relationship between the ROF and feedback optical phase was obtained, which shows ROF is in a sinusoidal manner with respect to the feedback optical phase under weak feedback strength. A simplified mathematic expression for ROF was derived to describe such a sinusoidal relationship. Potential sensing applications can be developed based on the relationship. As an example, a new method of measuring linewidth enhancement factor of an SL was presented. Finally, an experimental setup was built and experiments were carried out to verify the relationship and the measurement method for linewidth enhancement factor.

中文翻译：

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反馈光学相位对半导体激光器弛豫振荡频率的影响及其应用

半导体激光器（SLs）由于腔阻尼率高于载流子阻尼率而显示出弛豫振荡（RO）。当激光受到外部光反馈（EOF）干扰时，SL中RO的存在会导致丰富的复杂动态。在这项工作中，从理论上和实验上研究了反馈光相位对SL中弛豫振荡频率（ROF）的影响。通过数值求解著名的Lang Kobayashi方程，获得ROF与反馈光学相位之间的关系，这表明ROF在弱反馈强度下相对于反馈光学相位呈正弦形式。推导了ROF的简化数学表达式来描述这种正弦关系。可以基于该关系开发潜在的传感应用程序。作为示例，提出了一种测量SL的线宽增强因子的新方法。最后，建立了一个实验装置，并进行了实验以验证关系和线宽增强因子的测量方法。