[en] In this work we investigated crystal growth procedures aiming the development of single crystal fiber (SCF) for laser applications. For quality optimization in the fabrication of fluorides SCF a new growth chamber for a micro-pulling down furnace (μ-PD) was constructed targeting the fibers fabrication with strict atmosphere control (high vacuum, gas flux and static atmospheres). Simultaneously, the SCF growth process of rare earth double molybdates was studied. The growth of pure and Nd³⁺-doped SCF of LiLa(MoO₄)₂ (LLM) was studied in the range of 0,5 - 10mol% doping. The designed furnace growth chamber with controlled atmosphere was successfully constructed and tested under different conditions. Specially, it was tested with the growth of LiF SFC under CF₄ atmosphere showing the expected results. Transparent and homogeneous SCF of Nd:LLM were grown. In the pure fibers was observed facets formation, however, these defects were minimized after tuning of the growth parameters and additionally with the fibers doping. X-ray analysis showed the crystallization of a single phase (space group I4₁/a); the optical coherence tomography showed the presence of scattering centers only in regions were some growth stability occurred due to the manual process control. The measured Nd³⁺ distribution showed uniform incorporation, indicative of a segregation coefficient close to unity in LLM. The potential laser gain of the system was determined using a numerical solution of the rate equations system for the 805nm, CW pumping regime, showing the maximum laser emission gain at 1.064 μm for a Nd³⁺-doping of 5mol%. (author)