Advanced Matrix-Based Model for Doped Fiber Devices: from Yellow Dysprosium Fiber Lasers to Broadband Bismuth Fiber Amplifiers

Fiber lasers (FLs) and fiber amplifiers (FAs) have become enabling technologies across scientific and industrial fields, including optical communications, sensing, spectroscopy, medicine, and high-precision photonics. Their success stems from the unique properties of optical fibers, such as excellent heat dissipation, long interaction lengths, compactness, and compatibility with integrated optical architectures. As active fiber devices evolve toward increasingly complex configurations — multi-level energy schemes, multiple active centers, broadband amplification, and nonlinear interactions — accurate, physically consistent numerical modelling becomes essential for device understanding and performance optimization. This PhD Thesis presents a general matrix-based rate-equation model for the simulation and optimization of doped FLs and FAs. The approach relies on a scalable formalism describing arbitrary energy-level systems, multiple dopant species, and optional nonlinear processes within a unified MATLAB framework. The model is dopant-independent and integrates an automated parameter optimization routine enabling systematic calibration against experimental data — valuable when spectroscopic parameters are uncertain or only partially characterized. The model has been validated against several experimental and literature datasets, showing strong predictive capability across different classes of active fiber devices. The framework is applied to two main research directions. The first focuses on dysprosium-doped ZBLAN FLs for direct yellow emission near 573 nm. Yellow FLs are of strong interest for biomedical applications, ophthalmology, spectroscopy, and precision processing, yet their development is limited by efficiency degradation mechanisms tied to excited state absorption (ESA) and lower-level population saturation. After calibration, the model investigates the influence of pump power, fiber length, cavity reflectivity, and emission wavelength on laser performance. Particular attention is devoted to ESA effects and to mid-infrared (MIR) cascade lasing as a mitigation strategy based on depopulation of the lower laser level. Results show that cascade lasing yields substantial improvements in slope efficiency and tunability bandwidth, while providing practical cavity design guidelines in terms of fiber length, mirror reflectivities, and optimal MIR wavelength. The second direction addresses bismuth-doped fiber amplifiers (BDFAs) for broadband optical communication. In future multi-band optical networks, BDFAs are promising candidates for signal amplification within the O-, E-, and extended near-infrared bands, where erbium-doped amplifiers are ineffective. The spectroscopic complexity of bismuth active centers and incomplete understanding of their physical nature make accurate modelling challenging. The proposed framework treats distinct bismuth active centers as independent dopants with different spectroscopic properties, and introduces an automatic optimization procedure to reconstruct unknown absorption and emission characteristics from experimental gain and noise figure data. The model is validated against multiple phosphosilicate and germanosilicate BDFA configurations from the literature, accurately reproducing gain spectra and noise figure behavior under different pumping conditions. The framework is then used to investigate how the relative concentration of silica-related (BAC-Si) and phosphorus-related (BAC-P) bismuth active centers affects bandwidth extension, gain uniformity, efficiency, and gain–noise trade-offs in ultra-wideband amplification.