Derivation of relaxation oscillation frequency of a semiconductor laser with dual optical feedback based on linear stability analysis

Semiconductor lasers (SLs) are subject to external optical feedback (EOF), which can disturb their output power and optical frequency, leading to rich dynamics. Relaxation oscillation (RO) is a key phenomenon in this process. While the influence of EOF on RO in SLs with single feedback has been widely studied, recent applications have focused on dual feedback lasers. Hence, it is crucial to investigate RO in SLs with dual EOFs. This paper presents a novel approach to deriving the RO frequency in a SL with dual EOFs, using linear stability analysis and modified Lang-Kobayashi equations. The results obtained provide insight into the behavior of these systems and can facilitate the development of corresponding applications.