## Materials and Methods
### Characterization Techniques  
X-ray diffraction (XRD) analyses were performed on a Bruker D8 Discover diffractometer with Bragg-Brentano geometry operating with Cu-K\(\alpha\) radiation (\(\lambda\) = 1.54056 A, operating voltage 40 kV, current 40 mA, integration time 200 ms). The crystallized phase was compared to JCPDS data file number 79-1892 of yttrium aluminum garnet Y\({}_{3}\)Al\({}_{5}\)O\({}_{12}\). The mean nanocrystal size was calculated using in-built operating software. Dynamic light scattering (DLS) on the nanocrystals was used to determine the particle size distribution. The measurement and analysis were performed with ZetaPals particle size analyzer (Brookhaven instruments, Holtsville, NY, USA). High-resolution transmission electron microscopy was performed using a JEOL JEM 2100F UHR microscope equipped with an energy-dispersive X-ray electron spectrometer (EDX). The microscope operated at 200 kV (Schottky FEG cathode) with a point resolution of 1.9 A. A copper grid coated with a porous carbon support film was used as a sample holder. The sample powder was dispersed in ethanol and the resulting suspension was treated in an ultrasonic bath for 10 min and then applied to the grid.  
Refractive index profiles of preform were measured with Photon Kinetics's A2600 refractive index analyzer. Concentration profiles of the preforms were measured with Cameca SX100 electron microprobe. A thin carbon layer was sputtered on the samples prior to the analysis to prevent charging.  
Spectral attenuation and steady-state luminescence properties of the fibers were recorded by AQ-6315B (Ando, Tokyo, Japan) spectral analyzer. The longitudinal homogeneity of the fiber and background losses at 850 and 1310 nm were measured with an optical time-domain reflectometer (OTDR) EXFO 715B. The width of the excitation pulse was 5 ns and the integration time was 30 s. The analyzed fibers were spliced with a standard single-mode optical fiber which was connected to the spectrometer.  
The time-resolved luminescence properties of the fiber were measured by the cut-back method. The setup is depicted in Figure 1a. The analyzed fibers were spliced with a standard telecommunication wavelength division multiplexer (WDM) 980/1550 nm. The samples were excited by a power adjustable laser diode EM 4 (PowerNetix) operating at 976 nm. The luminescence at 1550 nm was detected by an InGaAs photodiode G8941 (Hamamatsu, Japan). The time-response of the photodiode was analyzed by a 1-GS/s oscilloscope 8461A (Agilent, London, UK). The oscilloscope was synchronized with a rising edge of the excitation pulse of the pulse generator Agilent 33512B.  
Lasing properties of the prepared fiber were measured in a ring laser arrangement [14] depicted in Figure 1b. Segments of the fiber were spliced (_\"1\"_ denotes the splices) into a fiber ring consisting of two WDM's operating at 980 and 1550 nm (FWDM-59-2-2-FA, Opneti, Hong Kong, China) and an output optical fiber coupler with splitting ratio of 5/95 (SQS Vlaknova optika, Nova Paka, Czech Republic). The WDMs and output couplers were standard optical fiber components used in telecommunications made by fused-biconical-taper process. The high output coupling ratio was chosen because in similar cavity arrangements and high-gain, low-loss active media, the optimum power conversion is achieved for resonators with high output couplin  
Figure 1: (**a**) Setup of the time-resolved luminescence measurement and (**b**) fiber ring laser setup.  
Er/Yb-doped ring fiber laser in similar setup, the output power was maximized for output coupling of 95% and the maximum was rather flat between 70% and 98% [30]. Intensities of the unabsorbed pumping signal at 980 nm and laser signal at 1550 nm were measured with a dual-channel optical multimeter AQ-2140 (Ando, Tokyo, Japan).