Due to the characteristics of the fiber itself, the average power and single pulse energy of a single fiber output femtosecond pulse are limited by such as self-focusing effect, transverse mode instability (TMI), excessive nonlinear effect, etc., coherent combination in time and space Technology is an effective means to break through the average power and pulse energy of fiber lasers. As the output power continues to increase, the space occupied by the spatial coherent combining device, the number of components included and the complexity of the system will increase dramatically. In order to overcome this problem, Limpert’s research group in Jena, Germany used a multi-core fiber (MCF) to combine beams. On the basis of obtaining certain experimental results, the research group further analyzed the influence of the thermo-optic effect on the amplification and synthesis efficiency during the multi-core fiber synthesis process in 2020.

Due to the slender structure of the fiber, the heat in the general gain fiber will gradually decrease along the radial direction to the outer layer. Figure 1 (left) is a simulated temperature curve of a 5×5 MCF cross-section, from which it can be seen that the temperature reaches a maximum at the center of the fiber, a temperature gradient is formed along the radial direction, and the resulting thermally induced refractive index distribution will cause the mode field Area reduction and pattern deformation. As shown in Figure 1 (right), the mode field area shrinks and moves toward the center of the fiber.

Fig.1 Temperature profile (left) and corresponding transverse strength profile (right) in a 5×5 gain MCF under thermal load[1]

The research group also found that when the temperature of the fiber exceeds 500°C, the optical properties of the ytterbium-doped fiber, such as the absorption and emission cross-sections, will change drastically. Therefore, in the simulation experiment of MCF, 500°C is also used as the upper limit of the temperature that MCF can work safely. Another consideration that must be taken is the transverse mode instability (TMI) that occurs at high power. Previous experiments with single-core and multi-core fibers have shown that the TMI threshold for fibers around 1 m long can be estimated at 300 W/core. It can be seen from Figure 2 that the maximum temperature is almost linear with the extracted power of each fiber core; when the extracted power of each fiber core is fixed, the temperature will also increase with the number of fiber cores (2×2 to 10×10) And rise. In most cases, when the power extracted by each fiber core reaches 300W, the stable operation state of the fiber optic system is limited by the TMI threshold.

Fig. 2 Temperature range of Yb-doped MCF under different power. The green, red, and yellow regions represent the states of stable operation, thermal limit, and TMI initiation, respectively[1]

However, in a few cases, especially for MCFs with small core diameter and high number of cores, the thermal limit threshold can be reached before the TMI limit. Compared with 80μm core, MCF with 30μm core will reach a higher maximum temperature at the same extraction power. Therefore, when using 7×7, 8×8, 9×9, and 10×10 MCFs with 30 μm core diameters, the average output power per core is only 220 W, 200 W, 170 W, and 150 W, instead of 300 W.

Figure 3 Relationship between synthesis efficiency and extraction power[1]

It can be seen from Fig. 3 that in both core diameters, the combining efficiency decreases with increasing extracted power, which is caused by non-uniform mode field shrinkage/distortion. Furthermore, the drop in synthesis efficiency is more severe for larger cores because their propagation modes are more sensitive to thermally induced changes. In addition, having more cores also leads to lower combining efficiency with each core extracting the same power, since more cores generate more total heat in the fiber, which will lead to Pattern distortion is greater. It can be seen that for a 6×6 MCF of 30 μm, the combined efficiency can reach about 93% when the extracted power of each core is 300 W, which corresponds to a total output power of 10 kW. Combining Figure 3 with Figure 2, it can be seen that the average power of MCF with smaller core size and multiple cores is mainly limited by temperature.

Theoretical calculations predict that a single 1-meter-long MCF can output a total power of 10kW, and the combined single-pulse energy is expected to be 400mJ. To further improve the combined average power and pulse energy needs to alleviate the influence of thermal effects in the system. This work is an important step towards compact ultrashort pulse Joule-scale multicore fibers.