Semiconductor laser (SL) with optical feedback presents rich nonlinear dynamics, e.g., period-one oscillation (POO), quasi-periodic oscillation, and chaotic states. It is of significance to study the state boundary between different dynamic states for an SL with optical feedback from the perspective of both suppressing and using these dynamics, especially the boundary of POO state. This paper reveals the POO boundary of an SL with dual optical feedback (DOF). The modified Lang-Kobayashi equations were first numerically solved to develop a bifurcation diagram to determine the boundary between POO and other states. Then the POO-DOF boundary was compared with that of an SL with single optical feedback. Moreover, the effect of system parameters on the POO-DOF boundaries is researched. The results obtained are helpful to promote the development of the applications of POO dynamics.

Self-mixing interferometry (SMI) is superior to other laser interferometry methods due to its simplicity and compactness. However, SMI signals are often complex and difficult to process due to interference in the form of variations in the effective reflectivity of the target, noisy signals, complex signal shapes, and other dependencies. Deep neural networks have been a very popular area of research in computer artificial intelligence in recent years, allowing more implicit features to be uncovered than traditional shallow machine learning. It has been shown that convolutional and back-propagation neural networks can be used for SMI signal processing. There are also studies that have used machine learning genetic algorithms for absolute distance measurement. Based on the above, this study used convolutional neural networks to form a deep neural network for absolute distance measurement based on SMI technology. We first trained the deep convolutional neural network at different feedback strengths. The results of the Convolutional Neural Network (CNN) model showed a coefficient of determination of 0.9987. which is consistent with the required model. The trained network was then used to estimate absolute distances with and without the addition of noise. The comparison proves that the proposed method is noise-proof and has high adaptability for measurements under different conditions.