We investigate the prediction of the infrared laser emission in the ${\mathrm{Yb}}^{3+}$ -doped cubic $\mathrm{K}{\mathrm{Y}}_3{\mathrm{F}}_{10}$ crystal that can be pumped by a laser diode. Bulky single crystals have been grown by the Czochralski technique at Tohoku University, and crystalline fibers have been grown by the laser heated pedestal growth technique at Claude Bernard/Lyon 1 University. Absorption and emission spectra were recorded to contribute to the determination of electronic and vibronic energy levels by using in addition the Raman spectrum and the barycenter law. ${\mathrm{Yb}}^{3+}$ concentration dependence of the ${}^{2}F_{5∕2}$ experimental decay time was analyzed using concentration gradient fibers in order to attempt to understand involved concentration quenching mechanisms. Under ${\mathrm{Yb}}^{3+}$ ion infrared pumping, self-trapping has been observed at low concentration, whereas upconversion nonradiative energy transfer to unexpected rare-earth impurities $({\mathrm{Er}}^{3+},{\mathrm{Tm}}^{3+})$ has been observed in the visible region and interpreted with a limited diffusion process within the ${\mathrm{Yb}}^{3+}$ doping ion subsystem toward impurities. Main parameters useful for a theoretical approach of laser potentiality have been given and compared with other fluoride crystals.