The spherical-aberration-free 3D beam forming inside materials via the modified Ewald cap

In the framework of laser precision machining, spherical aberrations of the laser beam increase gradually along the machining depth, which is widely observed due to the refractive index difference between the material of the working pieces and the surrounding medium. In this paper, we report on a simple and effective approach for spherical-aberration-free 3D beam forming inside the materials. This new technique is based on the modified Ewald cap which is related to the numerical aperture of the objective lens, the machining depth, and the refractive index of the material. This method is verified on a laser machining platform, where the phase loaded on the spatial light modulator is acquired by the modified 3D Gerchberg-Saxton algorithm. In the experiment, we have realized line and helical structures with SA compensation, which demonstrate that customized arbitrary intensity distribution inside the material can be realized.