In this research, amplitude Fresnel zone plates (FZPs) were fabricated on fused silica glass with femtosecond laser. The focusing characteristics including focal length, diffraction efficiency, geometric concentrator ratio, spot energy uniformity, depth of focus and resolution were studied by simulations and experiments. To optimize the focusing characteristics of FZP, we proposed an optimized machining process, an extended FZP and an fractal FZP. The optimized machining process increased the diffraction efficiency of the amplitude FZP from 6.96% to 8.14%, the extended FZP broke through the limit of minimum line width in processing and improved the resolution, and the fractal FZP increased the focus depth from 4 mm to 10 mm. In addition, we wrote a FZP on the end face of multi mode fiber, the divergent annular beam converged and formed an focus ring at the focal plane. This research will provide broad applications in fiber tweezers, beam coupling and optical communication.