## 5 Conclusions  
We presented a numerical investigation of the dynamics, states, and RIN of LDs operating under a double OFB by providing our previous model of a single OFB external cavity. The dynamics of the LD were studied within two regions: the short double external cavity (3.5 \(\times\) 10\({}^{-2}\) m) and the long double cavity (10\({}^{-1}\) m). In the single OFB cavity, the first reflector has been set at 3 \(\times\) 10\({}^{-2}\) m far from the LD front facet, which agrees with a PD route-to-chaos. The simulations show that the LD turns its state into POs, PD, and then a chaotic state. In the regime of a short double external cavity, the LD is taken from each of the states with a single OFB to a route-to-CW state. This route-to-CW is a reflection of the identical route-from-chaos to the identical state with a single OFB. In long double OFB, the rise in double OFB strength takes the LD to a route-to-chaos. In comparison with a single OFB case, the double OFB external cavity produces smoother chaotic RIN with two broad and weak peaks at frequencies = 3.6, 3.8, and 6.5, 6.3 GHz, as \(\psi_{2}\) = 0.0 and \(\omega(\tau_{1}+\tau_{2})\), respectively. These frequencies have no relation to the resonance frequencies of the external cavities. This kind of chaos can be used in a secure communication system. By considering the optical phase due to OFB in single OFB and double OFB cavities, it causes significant intensity suppression and phase shift in the LD output temporal changes. This intensity suppression and phase shift induced RIN suppression and a frequency shift in the RIN spectrum. These simulation results on the impacts of the optical phase due to double OFB on the lasing frequency shift in the RIN spectra are new contributions and have not been investigated before. The RIN is reduced near the solitary noise level as LD operates in the CW and PO regimes. Considering the double OFB and optical phase due to OFB, it causes a change in the dynamic states of the LD from a chaotic state to a more stable CW or PO. The dynamic states of LDs can get better by considering the effects of double OFB and optical phase due to OFB, which leads to a better drawing and a best-performance LD.  
Conceptualization, S.A.; methodology, S.A., A.M.A. and A.Y.M.; software, S.A.; validation, S.A.; formal analysis, S.A.; investigation, S.A., A.M.A. and A.Y.M.; resources, S.A., A.M.A. and A.Y.M.; data curation, S.A., A.M.A. and A.Y.M.; writing--original draft preparation, S.A.; writing--review and editing, S.A., A.M.A. and A.Y.M.; visualization, S.A., A.M.A. and A.Y.M.; supervision, S.A.; project administration, S.A. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Jazan University, Deanship of Scientific Research, Research Units Support Program, Support Number: RUP2-0, Jazan University, Jazan, Saudi Arabia.  
The data presented in this study are available in the article.  
The authors extend their appreciation to Deanship of Scientific Research, Jazan University, for supporting this research work through the Research Units Support Program, Support Number: RUP2-02.  
The authors declare no conflict of interest.