**2. Materials and Methods**

LN:Mg polycrystalline powders were synthesized by a wet chemistry method. Nb(OH)5 (99.99%) was firstly weighted, and excess HCl (38%) was added into a container. Then, they were heated at 90 ◦C and stirred for 30 min. During this process, the mass of active Nb2O5·nH2O was precipitated. After being cooled, the observed white precipitate was NbOCl3, which should be completely dissolved by adding deionized water. Malic acid (C4H6O4, MA) as the ratio of (MA):(Nb) = 3:1 was added into the former solution and stirred. Then, the pH value of the suspension was adjusted to 8 by the addition of NH3·H2O to get solution A. The chemical reactions happened in producing solution A were as follows:

$$\text{Nb(OH)}\_{5} + 3\text{HCl} \rightarrow \text{NbOCl}\_{3} + 4\text{H}\_{2}\text{O} \tag{1}$$

$$\text{R 2NbCl}\_3 + (\text{n} + \text{3})\text{H}\_2\text{O} \rightarrow \text{Nb}\_2\text{O}\_5\cdot\text{nH}\_2\text{O} + \text{6HCl} \tag{2}$$

$$\text{Nb}\_2\text{O}\_5\text{-nH}\_2\text{O} + \text{MA} \rightarrow \text{Nb} - \text{MA} + \text{nH}\_2\text{O} \tag{3}$$

According to the congruent composition of (Li)/(Nb) = 48.38/51.62 and the selected doping concentration of MgO (0, 3 mol%, 5 mol%), Li2CO3 (99.99%) and MgO (99.99%) were weighted and dissolved by dilute HCl. Until no more bubbles produced, the pH value was adjusted to 8 by the addition of NH3·H2O to get solution B. Afterward, solutions A and B were mixed to be of high homogeneity by ultrasonic machine. The mixed solution was filtered and spray dried into powders. At last, the powders were sintered at 820 ◦C for 6 h to obtain LN:Mg polycrystalline powders.

Using the prepared LN:Mg polycrystalline powder, we firstly grew Ø1" LN:Mg crystals and served them as seed crystals continue to grow Ø2" LN crystals doped with different MgO concentration of 0, 3%, and 5 mol% by the Bridgman method with multi-crucible [31], which were labeled as LN, LN: Mg3, and LN: Mg5, respectively. The prepared LN: Mg polycrystalline powder was placed in three Pt crucibles with the same dimension of Ø50 mm × 100 mm. After putting them into three Al2O3 pipes with the dimension of Ø110 mm × 200 mm, they were simultaneously placed in a furnace. Some mullite fiber mixed with Al2O3 powders was used as the thermal insulation material to keep a stable thermal field. In order to be sufficiently melted, the LN: Mg polycrystalline powder was heated by medium-frequency induction and held at 100 ◦C above the melting point for 2 h. LN, LN: Mg3,

and LN: Mg5 crystals were grown in a sealed environment and along the c-axis. In the procedure of crystal growth, the falling rate was governed in the range of 0.5 mm/h to 1.0 mm/h. The vertical temperature gradient above the solid-melt interface was about 0.3 ◦C/mm, which was measured by using a thermocouple. In order to avoid the cracks occurring in large crystals, they were cooled down to room temperature at a low rate of 30 ◦C/h after the growth process. Finally, LN: Mg crystals with Ø2" in diameter and 40 mm in length were grown along the c axis. It was necessary to anneal the as-grown crystals at 1230 ◦C for 30 h to escape thermoelastic stress and improve optical homogeneity. The single-domain structure would be formed by polarization with an electric current density of 7 mA/cm<sup>2</sup> for 20 min at 1190 ◦C. The 3 mm and 1 mm thick c-oriented plates were cut along the c-axis of the crystals and then polished to optical grade. The distance between the top and bottom part was about 4 cm.

The UV absorption edge wavelength and OH− spectra of 1-mm-thick plates were measured at room temperature on using a Beckman DU-8B spectrophotometer and Magna-560 Fourier transform IR spectrophotometer, respectively. High-resolution X-ray rocking curves of 3 mm plates were recorded by a Bruker HRXRD-5000 to examine the crystalline quality of LN: Mg3 and LN: Mg5 crystals. The refractive index of 1-mm-thick plates was also measured by METRICON 2010/M prism coupler at 632.8 nm to evaluate the optical homogeneity.
