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It is well documented that the primary limits to power scaling in fiber amplifiers are Stimulated Brillouin Scattering (SBS), Stimulated Raman Scattering (SRS), Thermal Lensing (TL), Transverse Modal Instability (TMI), and Diode Pump Brightness (DPB). These effects are well known in glass host fiber amplifiers and still garner active research in mitigating techniques for higher power scaling. In this paper, we present power thresholds for these limitations in crystalline host fiber amplifiers. We have leveraged a Coupled Mode Theory (CMT) model to simulate and analyze crystalline YAG fiber lasers for multiple dopants and with variation in step-index fiber core diameters and lengths. The dopants of interest are Ytterbium (Yb), Holmium (Ho), Thulium (Tm), and Erbium (Er). We have generated Power Scalability Maps (PSM) with varying fiber lengths and diameters which depicts the influence of the aforementioned limitations. We have leveraged a higher fidelity CMT-based model to develop comprehensive PSMs for crystalline fibers and for Yb, Ho, Tm, and Er dopants. To produce the PSMs for Tm and Er, additional considerations are required. Both Tm and Er have nonlinear energy transfer processes that make predicting the population concentration, given pump and signal intensities, challenging. We applied a specialized fit function based on a sigmoidal structure to allow analytic interpolation within the CMT-TMI model to accommodate for the complicated energy transfer effects that occur in Tm and Er. The PSMs serve as references for determining limits and potential of crystalline fibers.
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