_applied_  
_sciences_  
_Article_  
Dynamics of Semiconductor Laser Coupled with Two  
External Cavities  
[PERSON],*(r), [PERSON],+(r) and [PERSON] 1  
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accounting for multiple round-trips and optical phases due to OFB, has been presented in Ref. [5], which was applied in investigating the dynamics and noise of pumping LDs used in fiber amplifier systems [5; 6]. Moreover, the impacts of nonlinear gain, radiative and non-radiative lifetime, linewidth enhancement factor (LEF), and combined optical phase on the operation states and relative intensity noise (RIN) of 0.1550 \(\upmu\)m InGaAsP/InP time-delayed LD have been studied [7; 8; 9]. To address more complex scenarios where LDs encounter external OFB from two reflectors, such as in fiber-optic communication systems, additional research is needed. This double OFB, typically a result of reflections on both facets of an optical fiber, has applications in encrypted systems of data, generating secured signals that do not reveal any data about the system itself [10]. [PERSON] et al. investigated experimentally and theoretically the dynamics of the LD subjected to two filtered OFBs from two separate external cavities. They found that a second filtered OFB allows versatile manipulation of the LD frequency and provides an extra set of control parameters to get a stable laser [11]. In this paper, we extended a model in Ref. [5] based on the existing time-delay rate equation model from single OFB to encompass double OFB scenarios. This is completed using a traveling-wave approach to propagate the laser in the double cavities and their reflections between the laser front facet and the external reflectors [12]. After that, we propose a modified time delay term to describe double OFB and include it in the LD rate equation. This expansion represents a novel work in the investigations of OFB in LDs and their implementations in communication systems and other applications. LDs are, for instance, widely used in optical communication systems, including fiber-optic communication networks, where they serve as optical transmitters for data transmission. Another example is Optical Data Storage where LDs are used in devices such as CD and DVD players, as well as in Blu-ray technology, for reading and writing data on optical discs. The common issue for all these applications is the distortion of the signal as a result of OFB-induced signal distortion. OFB can, for instance, introduce timing errors and jitters in the laser output, which can lead to issues with data synchronization and the precise writing or reading of data on optical storage media. This can result in difficulty in accurately positioning the laser spot on the storage medium. Excessive OFB can cause data integrity problems. When writing data to optical storage media, any fluctuations in the laser power or position due to feedback can result in data being written incorrectly or with errors. Similarly, during data retrieval, the feedback-induced noise can lead to difficulty in accurately reading the stored data. In extreme cases, OFB-induced power fluctuations can lead to excessive heating of the media or optical components, potentially causing physical damage to the storage medium or laser diode.