###### Abstract  
To increase the spectral efficiency of coherent communication systems, lasers with ever-narrower linewidths are required as they enable higher-order modulation formats with lower bit-error rates. In particular, semiconductor lasers are a key component due to their compactness, low power consumption, and potential for mass production. In field-testing scenarios their output is coupled to a fiber, making them susceptible to external optical feedback (EOF). This has a detrimental effect on its stability, thus it is traditionally countered by employing, for example, optical isolators and angled output waveguides. In this work, EOF is explored in a novel way with the aim to reduce and stabilize the laser linewidth. EOF has been traditionally studied in the case where it is applied to only one side of the laser cavity. In contrast, this work gives a generalization to the case of feedback on both sides. It is implemented using photonic components available via generic foundry platforms, thus creating a path towards devices with high technology-readiness level. Numerical results shows an improvement in performance of the double-feedback case with respect to the single-feedback case. In particularly, by appropriately selecting the phase of the feedback from both sides, a broad stability regime is discovered. This work paves the way towards low-cost, integrated and stable narrow-linewidth integrated lasers.  
laser dynamics; optical feedback; narrow-linewidth lasers; semiconductor lasers; laser stability +
Footnote †: journal: _Photonics_  
of self-mixing interferometers for sensing applications [29; 30; 31]. These studies focus on improving the interferometric signal in terms of output power characteristics, yet they do not study the effect EOF has on linewidth, which is crucial for other applications such as coherent communications [32] or frequency metrology [33]. Furthermore, in all works exploring dual external cavities, both external reflections return to the same side of the laser cavity and thus have the same propagation direction. Moreover, phase shifts in the external phase cavity are not accounted for, thus ignoring, e.g., possible phase shifts at the mirrors.  
The established line of thought relies on the key assumption that feedback is introduced from only one side of the laser cavity. Current integration technologies make this assumption obsolete, as they allow for arbitrarily complex design geometries with a variety of functionalities, such as tunability and modulation, while maintaining narrow-linewidth performance [34; 35; 36; 37; 38]. Consequently, this work aims to extend the theoretical foundations of EOF to the case of feedback coupling into the laser cavity from both sides. This system is studied to obtain and analyze its dynamic rate equations. Furthermore, the frequency noise power spectral density and subsequently the intrinsic linewidth's dependence on feedback is computed. The Lang-Kobayashi approach is used [39], where an additional term to account for the extra feedback term is included. In a similar fashion, to obtain analytical solutions both small-signal and weak feedback conditions are assumed. The obtained equations are then numerically solved. Results show that feedback-insensitivity can be achieved by tuning the feedback parameters. In contrast with previous works, this can be accomplished in a monolithic platform by including a single active component in a straightforward geometric configuration. As such, design complexity is reduced which enables devices with a compact form factor. Furthermore, existing methods for laser fabrication are suitable for realizing the proposed device. In particular, the proposed laser system can be made with mature photonic integrated components available in generic foundry platforms [40; 41], thus creating a path towards devices with high technology-readiness level while maintaining low cost and size.