Ray-tracing algorithm was used to simulate the pump absorption efficiency and pump absorption distribution of LD corner-pumped laser with different parameters of Nd:YAG composite slab crystal. Resonator experiment was performed to suppress the oscillation of higher-order modes and realize TEM00 operation. Experiment results showed that the output power was 11.94W with an optical-optical efficiency of over 26%, and the M2 factors of beam quality at width and thickness directions were 1.18 and 1.34, respectively. It has been proven that the corner-pumped configuration could obtain laser output with good beam quality as a result of high pump efficiency and good pump uniformity.
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As a new pumping method of LD pumped solid-state lasers, corner-pumped configuration was proposed by Mali Gong et al. [1,2]. The pump scheme is different from traditional ones such as end-pumped, edge-pumped and side-pumped configuration. Extremely high pump absorption efficiency and good pump uniformity can be obtained from the corner–pumped configuration  since the absorption length is greatly increased through the total internal reflection of pump lights in the laser medium. In this configuration, the pump face and laser output face are separated to save the cost of dichroic mirror. In addition, the corner-pumped configuration has great potential for power scaling. By now, a maximum CW output power of 1050 W from a Yb:YAG laser has been reported .
Although other materials such as Yb:YAG and Nd:YVO4 crystals have attracted much attention in recent years, Nd:YAG crystal is still a dominate gain material in solid-state lasers due to its excellent thermal and mechanical performance and outstanding power scalability , for which we choose it as the corner-pumped gain medium.
In many applications, solid-state lasers are required to operate in TEM00 mode to guarantee the smallest beam divergence, the highest power density, and hence the highest brightness . However, there is still no report on TEM00 output generated from corner-pumped lasers by now. In this article, we took advantage of the ray-tracing algorithm to simulate the pump absorption efficiency and pump absorption distribution of a LD corner-pumped laser with different parameters of a Nd:YAG composite slab crystal, and obtained the optimum parameters for the experiment and developed several rules in designing the corner-pumped coupled system. We also designed a type of resonator to suppress the oscillation of higher-order modes, in which the TEM00 operation could be well realized. In the light of these analytical results we performed the experiment on LD corner-pumped composite Nd:YAG slab crystal laser, and proved that the corner-pumped configuration is capable of achieving the laser output with good beam quality.
2. Design of optical coupling system
In the optical coupling system of the corner-pumped laser, it is necessary to focus and reshape the pump beam to fit the size of the pump face of the crystal in both directions of fast axis and slow axis. With the simulation of ray-trace algorithm, we chose a coupled system contains three cylinder lenses, as shown in Fig. 1 , one has a focal length of 12.7mm, focuses the pump beam in the fast axis direction and the other two have focal length of 25mm, reshape the pump beam in the slow axis direction.
3. Optimization of crystal parameter
In TEM00 operation of the corner-pumped laser, only the center region of the slab that matches the volume of the fundamental mode can convert the absorbed pump power to the laser output. Therefore we choose the composite slab doped only in center region  to raise the optical-optical efficiency.
As the pump lights are reshaped in both directions of the fast axis and slow axis and coupled into the slab, the analysis on the pump absorption distribution of the composite slab is very complex and it would be quite difficult to yield an analytical solution even with several approximations . Therefore, we use commercial ray-tracing software to simulate the pump absorption efficiency and the pump absorption distribution in the composite slab, and obtained some rules to design the composite slab:
- ■ Dopant concentration: Corner-pumped configuration has a long absorption length, making it suitable for lower dopant concentration to enhance the pump uniformity while keeping the high absorption efficiency at the same time. Additionally, low concentration can also decrease the influence of thermal effect as well.
- ■ Width of pump face: The width of the pump face should not be too great, otherwise the lights will escape from the pump face after very limited number of total internal reflections. On the other hand, the width of the pump face should not be too small, otherwise the divergence angle of pump lights will be too large to be acceptable. Too great or too small width will result in low absorption efficiency.
- ■ Angle of pump face: Because of the divergence of pump lights, the angle of pump face should be 45° to keep more pump lights remained in the slab through total internal reflection and thus enhance the absorption efficiency.
Generally speaking, there is often a trade-off between pump absorption efficiency and pump uniformity and we have to adjust parameters to realize the optimum condition.
In our configuration, the optimized parameters of the composite slab are listed in Table 1 .
The simulation results indicate that the pump absorption efficiency can reach 92.6% while keeping the pump uniformity comparatively well. The distribution of pump power absorption is shown in Fig. 2 .
4. Experimentation results
With the optimized design, we established a corner-pumped Nd:YAG laser oscillator.
At first, we chose a short cavity to allow the multimode operation within the slab. With mirror-slab separations of 45 mm and 50 mm respectively, 15.7 W of laser output power was obtained from 45.9 W of laser-diode output at the maximum pump power, corresponding to an optical efficiency of 34.2% and a slope efficiency of 40.8%. When the pump power is 45.9W, the M2 factors of beam quality at width and thickness direction were 3.38 and 2.52, respectively. The CW multimode output power vs. pump power is shown in Fig. 3 .
In order to realize the TEM00 mode operation by suppressing higher-order modes oscillation at high pump power, we used a stable resonator configuration, which was close to the stability edge of dωL/dfth < 0, where ωL is the laser beam radius on the crystal . This is because when dωL/dfth < 0, the spot sizes of these higher-order modes are correspondingly reduced so that they are similar in size as that of the fundamental mode. As a result, the gain for higher-order modes will decrease, by virtue of their stronger spatial overlap with the fundamental mode, and hence their oscillation is suppressed. Furthermore, we placed an aperture with a little larger size to suppress even higher-order transverse modes.
Figure 4 . shows the experimental setup of the corner-pumped Nd:YAG oscillator laser. The resonator was the unsymmetrical flat-flat cavity, whose arms were 55 mm and 81 mm respectively, and consisted of a highly reflective end mirror, an output coupler of 30% transimissivity and a slit of width 0.6 mm in the width direction at a distance of approximately 53mm from the output coupler.
The CW TEM00 output power vs. pump power of laser is shown in Fig. 5 . It produced the laser output power of 11.94 W at the pump power of 45.9 W with an optical-optical efficiency of above 26% and the slope efficiency of 31.2%. Table 2 lists the beam quality of laser output at four pump power levels. From the above results, we can conclude that the corner-pumped Nd:YAG composite slab laser keeps in fundamental mode output in all of the process when the pump power raised from the threshold to maximum scale. In addition, its output still has good beam quality at maximum pump power.
It is worth mentioning that the pump face of the composite slab was not AR coated at pump wavelength of 808 nm, thus the absorption efficiency decreased from 93% to 85%. Taking account of the fact that mentioned above, the TEM00 optical-optical efficiency of the corner-pumped Nd:YAG laser should be above 30%, higher than that of side-pumped Nd:YAG laser of 15~25% [10–12] and as much as that of end-pumped Nd:YAG laser [13,14].
Base on the waist radius and the output beam quality measured at certain pump power levels, we can calculate thermal lens focus length within the crystal, and the beam radius anywhere in the cavity . Figure 6 shows the beam size on the crystal (red line) and the output coupler (blue line) as a function of the power of thermal lens. The operating spots both at the width and thickness direction at the maximum pump power and 36.1W pump power in the stable region are marked respectively. It is obvious that spots in the thickness direction at the maximum pump power satisfy the condition of dωL/dfth < 0 so that the resonator can operate at TEM00 mode. The validity of the resonator design method can be confirmed as well in the fact that the beam quality of the thickness direction of the laser output at the maximum pump power is better than that at the pump power of 36.1W without aperture such as that of the width direction.
In summary, we simulated the pump absorption efficiency and pump absorption distribution of a LD corner-pumped laser and designed the composite slab with the optimum parameters. In experiment, we successfully implemented a resonator operating closely to the stability edge with dωL/dfth < 0 to suppress the oscillation of higher-order modes. We achieved about 12W output in a fundamental mode beam at an optical-optical efficiency of above 26% and the slope efficiency of 31.2% at the maximum pump power. Experiment results show that it is possible to scale corner-pumped lasers to high output power with good beam quality.
References and links
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