Evaporation characteristics of Er$^{3+}$ doped silica fiber and its application in the preparation of whispering gallery mode lasers

The fabrication of whispering gallery lasers (WGL) is used to experimentally evaluate the evaporation rate (mol/$\mu$m) and ratio (mol/mol) of erbium and silica lost from a doped fiber during heating. Fixed lengths of doped silica fiber are spliced to different lengths of undoped fiber and then evaporated by feeding into the focus of a CO$_{2}$ laser. During evaporation, erbium ions are precipitated in the doped silica fiber to control the erbium concentration in the remaining SiO$_2$, which is melted into a microsphere. By increasing the length of the undoped section, a critical point is reached where effectively no ions remain in the glass microsphere. The critical point is found using the lasing spectra of the whispering gallery modes in microspheres with equal sizes. From the critical point, it is estimated that, for a given CO$_{2}$ laser power, $6.36 \times 10^{-21}$~mol of Er$^{3+}$ is lost during the evaporation process for every cubic micron of silica fiber. This is equivalent to $1.74 \times 10^{-7}$~mol of Er$^{3+}$ lost per mol of SiO$_{2}$ evaporated. This result facilitates the control of the doping concentration in WGLs and provides insight into the kinetics of laser-induced evaporation of doped silica.