## 1 Introduction  
The optical properties of trivalent chromium (Cr) ions in bulk alumina (Al\({}_{2}\)O\({}_{3}\)) have been extensively studied in the past and resulted in the development of the ruby laser, as reported by [PERSON] et al. [1, 2], which emits in the red region of the electromagnetic spectrum. [PERSON] and [PERSON] [3, 4, 5, 6] studied the electronic energy levels of Cr\({}^{3+}\) in Al\({}_{2}\)O\({}_{3}\) both from the theoretical and experimental points of view. Under diluted doping conditions, Cr\({}^{3+}\) ions are known to substitute Al\({}^{3+}\) in the Al\({}_{2}\)O\({}_{3}\) lattice forming a trigonal distorted octahedron [3, 4, 5, 6]. As such, the levels of the ion in the cubic field are further split by the interplay of the trigonal field strength and the spin-orbit interaction [3, 4, 5, 6]. Accordingly, in octahedral symmetry, and for a measured crystal field and Racah parameters of D\({}_{4}\)/B = 2.8 (obtained from absorption spectroscopy measurements), the electronic states of the ion correspond to the \({}^{4}\)A\({}_{2}\)(\(\frac{\mathrm{e}}{\mathrm{e}}^{\mathrm{i}}_{2}\)) ground state and \({}^{2}\)E (\(\frac{\mathrm{e}}{\mathrm{e}}^{\mathrm{i}}_{2}\)), \({}^{2}\)T\({}_{1}\)(\(\frac{\mathrm{e}}{\mathrm{e}}^{\mathrm{i}}_{2}\)), \({}^{4}\)T\({}_{2}\)(\(\frac{\mathrm{e}}{\mathrm{e}}^{\mathrm{i}}_{2}\)), \({}^{2}\)T\({}_{2}\)(\(\frac{\mathrm{e}}{\mathrm{e}}^{\mathrm{i}}_{2}\)), \({or fluorescent probes for biological applications [20], among others. In addition, doped polycrystalline alumina is a material of excellence in high-power phosphor color converters or laser gain media [21; 22]. The doping is typically attained during the growth [17; 21; 23] but there are some works reporting on ex situ doping, for instance by ion implantation [24]. Particularly, micrometer-sized crystalline spheres are known to be suitable for application in non-linear optical devices, quantum optics, sensing, and lasing [25; 26; 27]. Indeed, microspheres are amongst the most common microresonators that sustain whispering gallery modes (WGM), providing the highest quality factor (Q factor) values when compared with structures like microdisks and Fabry-Perot cavities [25; 26]. The use of WGM microresonators as microlasers is one of the most interesting possibilities, given the high Q factor and small volumes of the modes, which allow for obtaining an ultralow lasing threshold [26; 27]. Additionally, biosensors based on microcavities are especially valuable for exploiting the effects generated by the evanescent electromagnetic field in the surroundings of the surface, allowing the detection of analytes linked to the surface by monitoring the changes in the resonance frequency that they promote [26]. Likewise, among other sensor types (e.g., gas, humidity), they can also be used as temperature sensors, since temperature leads to deviations in the resonance frequency of the microcavity [26]. Nevertheless, producing high sphericity particles with dimensions in the micrometer range, mandatory for highly efficient lasing, remains a challenge [25]. The main fabrication approaches typically involve the melting of glass materials or the sol-gel process [26]. Other methods to produce crystalline spheres of different sizes (from nano to some millimeters) have been reported and include laser ablation [25; 28; 29; 30], spray pyrolysis [31; 32], microfluidic synthesis strategies [33], hydrolysis-precipitation methods [34], hydrothermal [35], and even other laser sintering approaches [36]. Although Al\({}_{2}\)O\({}_{3}\) is a very well-known material, there is still plenty of room to improve its fabrication methods toward simplicity, low-cost, and eco-friendly approaches [21; 27; 37]. Therefore, there is a growing interest in finding new strategies to attain Cr-doped Al\({}_{2}\)O\({}_{3}\) crystals with excellent optical properties, including high transparency [21; 38; 39].