## 1 Introduction  
As the thrust-to-weight ratio of aircraft engines gradually increases, the working thermal load and thermal stress that the turbine blades of the engine need to withstand are also increasing [1, 2, 3]. Due to the characteristics of high temperature resistance, strong fracture toughness, and good fatigue performance, nickel-based superalloy is usually used to manufacture the turbine blade. Nowadays, because the working temperature of turbine blades has long exceeded the material's bearing limit, the gas film cooling technology are usually necessary for turbine blades [4, 5, 6]. Film holes are the most important microstructures on turbine blades, and their drilling quality directly affects the service life of the blades. The sizes of film cooling holes are usually between 0.2 mm and 0.8 mm, and there are lots of such holes on a single blade. Meanwhile, the surface of the blade is the free-form curved surface, so the efficient and high-quality processing of film holes has always been a difficult problem in the manufacturing of aircraft engines. Mechanical drilling, electron beam machining (EBM) [7, 8, 9, 10], electrochemical machining (ECM) [11, 12], and Electrolyte jet machining (EJM) [13, 14] are all able to drill micro-holes. However, the tool breakage of mechanical drilling, micro-cracks and thicker recast layer of EBM, environmental pollution and lower efficiency of ECM, and low accuracy of EJM are the key problems that limit the application of the methods above in the processing of gas film holes. In recent years, laser processing technology has gradually become a research hot spot in the microstructure machining of aircraft engines. The long-pulse laser is usually not the ideal tool for micro-hole drilling [15; 16]. The interaction time between the long-pulse laser and the processed material is so long, the heat will diffuse around and inside the processed area. At the same time, the peak power of the long-pulse laser is much lower than that of the ultra-short-pulse laser, which means that the heat absorbed by the material cannot cause rapid evaporation; instead, most of the material is melted and blown off by the nozzle. Such long action times and melt-removing mechanisms result in the formation of a larger heat-affected zone and a thicker layer of recast. These defects are not allowed for high-speed rotating components such as blades. Ultra-short-pulse lasers, especially femtosecond lasers, can effectively overcome the above-mentioned defects of long-pulse lasers and are gradually becoming an ideal tool that can perform high-quality microprocessing for various materials. Due to the extremely short pulse width and high peak power, the thermal diffusion phenomenon is less obvious. The majority of the material is removed by gasification, which can effectively reduce defects such as recast layers, micro-cracks, and surface splashing, thereby achieving better processing quality [17; 18]. Lots of research work has focused on the interaction mechanism between femtosecond lasers and processed materials [18; 19; 20; 21], but the methods they used mainly include packing drilling or scanning drilling by two-dimensional galvanometers. However, because of the shielding effect of the pore wall and the lack of laser incident angle adjustment function, the above-mentioned methods can produce obvious tapering of micro-holes, which prohibits the application of such methods in blade component processing. The helical drilling method based on the Dove prism can overcome the taper defect mentioned above by deflecting the incident laser beam, and thus, it is becoming one of the ideal methods for manufacturing gas film holes. The research results of some scholars have confirmed the effectiveness of the helical drilling method in improving the taper defect [22; 23; 24] and obtaining a high-quality hole-wall, based on the multi-step expand method.