Design and optimization of zone plates for flying focus applications

Flying focus laser pulse technology, characterized by programmable velocity profiles and the ability to break the traditional link between focal spot motion and group velocity constraints, holds significant potential for revolutionary advances in high-intensity laser related fields. While numerous schemes have been explored, the development of low-cost, high-precision techniques for generating a flying focus remains a key objective. Leveraging modern nanofabrication technology, we propose a novel flying focus scheme based on a zone plate whose zone widths are modulated by a sinusoidal random distribution. Numerical simulations demonstrate that this modulated amplitude mask can suppress the higher-order foci by more than two orders of magnitude. The speed of the focus is tunable across a wide velocity range, including superluminal regimes, and maintains stability over 100 Rayleigh lengths. This scalable scheme provides a robust method for generating flying-focus profiles, with significant implications for terahertz radiation, X-ray optics, and more.