Lithography plays a vital important role in modern information technologies. Patterning at the nanoscale in a handy way is highly desired for both scientific and industrial purposes. In this work, we propose a convenient nanolithography method based on Fresnel diffraction patterns. We start with the explanation of the "dense-inside-sparse-outside" Fresnel diffraction fringes resulted from apertures of finite extent, using the fast Fourier transform algorithm by appropriately choosing the number of uniformly spaced samples. Moderately focusing the diffraction patterns via high-numerical-aperture objectives (we term the method “Fresnel diffraction lithography”), the rotationally symmetric patterns with a minimum feature size of ~190 nm, and the scanning lines with a width of ~350 nm are realized, respectively, though the calculation using vectorial diffraction theory suggests a better resolution when perfectly focused. This method shows good tolerance to defocus and does not require complex lens combinations or micro/nano-diffraction optical elements, may therefore find applications in widespread areas, e.g., functional metasurfaces, as a novel and low-cost nano-patterning technology with sub-wavelength resolution and high flexibility.

The development of OPCPA numerical simulation platform involves physical models such as broadening and compression of optical pulse, parametric amplification and focusing output. In the simulation platform, the Fresnel far-field diffraction equation is usually used to simulate the characteristics of ultrashort pulse focusing.Firstly, we need to calculate the optical field distribution of different wavelength components in the ultrashort pulse, and then use the inverse Fourier transform to obtain the temporal and spatial distribution characteristics of the pulse. However, for different wavelength components, the size of focused field grids obtained by the far-field algorithm is not equal, and subsequent resampling is required, which will increases the amount of calculation. In addition, due to the limitation of the calculation range of the light field in the pulse broadening and compression, there is also a problem of poor resolution of the focused field. In this paper, the mathematical expression that can adjust the range of the output light field and use the fast fourier algorithm is derived. The main mechanism of this algorithm is as follows:based on the Fresnel far-field diffraction equation, the output field is sampled independently in the discrete calculation process to meet the requirements of adjustable range of the output field. After identity transformation, the output field results can be calculated by fast Fourier algorithm. Furthermore, the sampling conditions that need to be satisfied when using the algorithm are further analyzed and discussed. It solves the problem of how to improve the resolution of light field and keep the computational grid size of each wavelength component consistent when the traditional Fresnel far field diffraction is used to simulate the focusing process, which provides convenience for the subsequent direct time-frequency inverse transformation. The numerical simulation results reveal that the dark ring region of the ultrashort pulse focusing field shows strong spatiotemporal coupling characteristics.This algorithm has been successfully applied to the development of OPCPA numerical simulation platform, and is expected to play an important role in the optimization design of ultrashort laser pulse device.