End-pumped lasers offer the advantages of high efficiency, good beam quality, and compact structure. However, the exponential decay of pump absorption along the longitudinal direction in commonly used conventional uniformly-doped crystals, produces a large temperature gradient, which leads to a series of thermal problems such as severe thermal lensing effects and end-face deformation, inevitably leading to the deterioration of laser performance. In addition, the thermal stress restricts the pump power limit, beyond which thermal stress leads to crystal damage. Currently, many researchers use gradiently-doped crystals to improve the thermal effect and reduce the temperature gradient. Gradiently-doped crystals are simple in structure, and yet improve the pumping limit with excellent performance in high-power pumping; however, the different concentration distributions of gradiently-doped crystals cause the mode-matching to differ from that of traditional uniformly-doped crystals. Therefore, maximizing the advantages of the gradiently-doped crystal is still a difficult problem. At present, research on the mode-matching of gradiently-doped crystals is lacking. Consequently, studying the mode-matching problem in end-pumped gradiently-doped crystal lasers is of great significance.

In this study, the effects of pump beam waist radius, beam quality factor (M²) value, and waist position on the mode-matching efficiencies of gradiently-doped and uniformly-doped crystal lasers are theoretically calculated. Subsequently, the effect of pump beam waist position on mode-matching of gradiently-doped crystal lasers is experimentally investigated by changing the pump beam waist position when the radius is 0.4 mm and 0.5 mm, respectively. Finally, the crystals are placed at the center of the resonant cavity and at a position close to the input mirror, with pump beam waist radius of 0.5 mm and beam waist position close to the pump input face of the crystals, to study the performance of gradiently-doped and uniformly-doped crystals under high-power pumping conditions, thereby verifying the excellent performance of the gradiently-doped crystals under high-power pumping conditions with identical pumping optical parameters.

The effects of waist radius, waist position, and M² value of the pump beam on the mode-matching efficiency of gradiently-doped crystals are theoretically calculated (Fig. 5). The effects of the waist position of the pump beam on gradiently-doped and uniformly-doped crystals are compared and analyzed through experiments (Fig. 10). The influence of the position of the pump beam waist on the two kinds of crystals is analyzed using the temperature distributions of the crystals with the pump beam waist at different positions (Fig. 11). Gradiently-doped crystals exhibit more stable mode matching and are less susceptible to pumping optical parameters. The output characteristics of the crystals under high-power pumping conditions are investigated for crystals located at the center of the resonant cavity and close to the input mirror. The output power of the gradiently-doped crystal increases by 4.67% and 11.84% at the two positions, respectively. Thus, it is concluded that gradiently-doped crystals display excellent performance under high-power pumping (Figs. 12 and 13).

In this study, the mode-matching efficiencies of the end-pumped laser with uniformly-doped and gradiently-doped crystals are examined theoretically and optimized experimentally. First, the influence of the waist radius, M² value, and waist position in the oscillator of the Gaussian-distributed pump beam on the mode-matching efficiency is analyzed through numerical simulations. Considering the variations of the three parameters, it is demonstrated that the gradiently-doped crystal laser exhibits a more stable and greater mode matching efficiency than the uniformly-doped crystal for a pump waist radius of 0.5 mm and M² values of 10 and 50. Specifically, the influence of the waist position of the pump beam on mode-matching efficiency is studied through experiments. Through the comparison of the laser output power for pump beam waists located at different positions, it is shown that the mode matching efficiency suffers less from fluctuations in gradiently-doped crystals than uniformly-doped ones, which agrees well with the theoretical analysis. Under the condition of pump power reaching over 70 W, the gradiently-doped laser has a maximum output power of 44.8 W with the laser crystal set in the middle of the oscillator, which is 4.67% greater than that of the uniformly-doped one. For the laser crystal close to the input mirror, the gradiently-doped laser output power reaches 34.0 W, which is 11.84% greater than that of the uniformly doped laser. Therefore, it is concluded that the gradiently-doped crystal has excellent performance for high-power pumping laser systems.