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In this article, we report a theoretical study concerning some statistical parameters which characterize the single-and double-pass Er 3C -doped Ti:LiNbO 3 M-mode straight waveguides. For the derivation and the evaluation of the Fano factor, the statistical fluctuation and the spontaneous emission factor we used a quasi two-level model in the small gain approximation and the unsaturated regime. The simulation results show the evolution of these parameters under various pump regimes and waveguide lengths. The obtained results can be used for the design of complex rare earth-doped integrated circuits.

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