Single crystal fibers are crystals with a fibrous shape. They combine the advantages of bulk crystals (high thermal conductivity, high laser damage threshold, wide light transmission) and glass fibers^{[1,2,3,4,5,6,7]} (large specific surface area, high laser conversion efficiency). Theoretical analysis proves that the theoretical single-mode output limit of YAG SCF is 50 times more than that of silica glass fiber, thus YAG based SCFs are a promising candidates for the development of next generation high power lasers^[8,9,10].

During the past years, Yb:YAG SCFs have been extensively investigated for use in high power laser systems due to simple energy level structure of Yb³⁺ ion, high quantum and slope efficiencies and other excellent physical and chemical properties^[11]. Yb:YAG crystals are considered one of the most promising fiber materials for lasers in 1 μm region^[12,13,14]. The two main growth methods of SCFs are Micro-pulling Down(μ-PD) technique and Laser Heated Pedestal Growth (LHPG) technique. At present, the μ-PD method may be used to grow SCFs with diameter greater than 0.5 mm^[15]. However, in order to fully take advantage of the large specific surface area of SCFs, Yb:YAG SCFs of larger length-to-diameter ratio and higher shape homogeneity are necessary. Under the circumstance, LHPG method exhibits its advantage of growing SCFs of small diameter, because crucibles are not needed during the growth process and the dimensions of the SCFs are not limited by the shape of crucibles. In this paper, we present the results of our studies on as- grown high-aspect ratio Yb:YAG SCFs with a diameter of 0.2 mm and a length of 710 mm that were grown using a self-developed laser-heated base SCF furnace.

The schematic diagram of the LHPG technique is shown in Fig. 1. For the first pulling we used a Ф2 mm×100 mm rods that were cut out of bulk Yb:YAG crystals (Yb concentration were 1at% or 2at%). The diameter of the SCF can be controlled by adjustment of the ratio of the seed crystal pulling speed to the source rod feeding speed. Usually this ratio is set to 1/2-1/3^[16]. The diameter of the first grown fibers were 0.7 mm. Subsequently, the first- grown SCFs were used as a source rod and seed crystal for the second growth. The second-grown SCFs with diameter of 0.2 mm were grown by adjusting the appropriate pull to feed ratio. The growth rate can reach up to 200-300 mm/h.

After two times of growth, we obtained 1at% Yb:YAG and 2at% Yb:YAG SCFs with a diameter of 0.2 mm and a length of 710 mm (the length-diameter ratio is greater than 3500:1). Photographs of obtained SCFs are shown in Fig. 2 and Fig. 3.

The axial distribution of Yb³⁺ ions was characterized by Energy Dispersive Spectrometer (EDS). The X-ray rocking curves of the SCFs were measured by 18 kW target-rotating X-ray diffractometer (D/Max 2550 V) to characterize their crystal quality. Laue diffraction patterns were obtained using a real-time back-reflection Laue camera system (Multiwire MWL 120 with Northstar software).

The stability of optical system is the prerequisite for the growth of SCF of high quality. If the power of the CO₂ laser in the optical heating system fluctuates during the growth of the fiber, it leads to the fluctuation of fiber diameter. When the change is too large, it results in solidification of the melting zone or the seed crystal detaches from the melting zone and stops growing. Therefore, the LHPG SCF furnace needs a CO₂ laser with relatively stable power output. In addition, the adjustment of the optical path also has great influence on the crystal quality. If the laser beam fails to achieve symmetrical focus heating, as shown in Fig. 1, it results in asymmetric melting zone, as shown in Fig. 4. The asymmetric melt zone causes instability of the fiber diameter or even leads to the stop of the growth. In the process of designing the LHPG SCF furnace, the dimension deviation of each part of the optical system from the theory is not more than 0.01%. We also added a visible laser system parallel to the side of the CO₂ laser with the distance of 2 cm. The system allows to adjust the position of each component while observing the heating ring change dynamically. Using trial and error approach, taking the quality of the grown fiber feedback parameter, the best focusing position is found, which laid a foundation for the growth of high-quality fibers.

In the process of growth, it is found that the ratio of pulling speed, feeding speed and laser power had a great influence on the melting zone, thus affecting the fiber quality. Let the laser power in the growth process be P, the heat dissipated from the molten zone to the source rod direction be Q₁, and the heat dissipated from the molten zone to the seed crystal direction be Q₂. The heat dissipation of the molten zone itself is contained in the η factor. According to the reference^[17], the total energy conservation equation is as follows:

∆H_f is the melting heat of the source rod; D and V_S are the diameter and feeding speed of the source rod respectively; d and V_f are the diameter and pulling speed of the seed crystal. When the growth process is stable, $\Delta {{H}_{\text{f}}}\frac{\text{ }\!\!\pi\!\!\text{ }{{D}^{2}}}{4}{{V}_{\text{S}}}$=$\Delta {{H}_{\text{f}}}\frac{\text{ }\!\!\pi\!\!\text{ }{{d}^{2}}}{4}{{V}_{\text{f}}}$. Assuming that P changes slightly under V_S, it can be approximated that Q₁, Q₂ and η do not change, while V_s, V_f and D are constant. Therefore, d changes with the change of P, thus affecting the melting zone, and the melting zone responds quickly to the laser power. But the response of the melting zone to the push- pull ratio is slightly delayed. The corresponding process is shown in Fig. 5. The seed crystal pulling speed of 300 mm/h and the source rod feed speed of 40 mm/h are chosen for fiber growth in the second growth.

On continuous SCFs with sufficient length, no macroscopic defects were observed. We record the fiber diameter by taking a measurement every 20 mm. Results are shown in Fig. 6(a). The diameter change is calculated by a formula $A=\Delta d/\bar{d}$, $\Delta d=\ |d-\bar{d}|$. Where d is the diameter of each measurement point on SCF, and $\bar{d}$ is the average diameter value. The diameter fluctuations are shown in Fig. 6(b). It can be seen that the diameter fluctuation is less than 5%. Better diameter uniformity is beneficial for the fabrication of cladding and related devices^[16]. The growth quality of the fiber was characterized by measuring the rocking curve of Yb:YAG SCF (111) crystal plane Fig. 7. It can be seen that the rocking curve presents a symmetrical shape without splitting. The full width at half maximum (FWHM) of the fitted peaks for each sample are gathered in Table 1. The FWHM values for SCF are lower than that of the source rods, indicating that the as-grown crystal fibers have higher quality than source rods. It also can be clearly seen from Fig. 8 that the characteristic Laue XRD patterns of Yb:YAG SCFs with two concentrations are uniform, clear and bright.

The Energy Dispersive Spectrometer (EDS) was used to check the axial distribution of Yb³⁺ ions along the SCF by line scanning. The variation of Yb³⁺ concentration along the axial direction is shown in Fig. 9. The results show that Yb³⁺ ions are relatively evenly distributed along axial direction. The effective ionic radius of Yb³⁺ ion is similar to that of Y³⁺ ion, so Yb³⁺ ions can easily enter Y³⁺ sites in YAG crystals^[18]. On the other hand, the molten zone formed in the process of LHPG growth is small, and the rapid melting and solidification are influential for the inhibition of segregation. The uniform distribution of Yb³⁺ ions along material is one of the key factors for single-mode lasers materials.

Various YAG SCFs grown by LHPG method were already reported (as shown in Table 2). It can be seen from the table that the fiber quality is comprehensively characterized in this study. It also has some advantages in fiber quality and fiber length and diameter.

High quality Yb:YAG SCFs with a diameter of 0.2 mm and a length of 710 mm were successfully grown by LHPG. The fiber diameter fluctuation is less than 5% and Yb³⁺ ions are homogeneously distributed along the fiber axis. The X-ray rocking curve indicates the as-grown crystal fibers are of high quality. The growth of high quality SCFs lays the foundation for the further experiments with the fiber cladding and construction of the fiber laser.