Adjoint Optimization of Laser Optics for Target Spatiotemporal Intensity Profiles

Efficient control of laser pulse intensity profiles is critical for applications such as laser wakefield acceleration and plasma channel formation. Flying focus (FF) is one technique that combines a hyperchromatic (e.g., diffractive) lens with a chirped laser to control the spatial and temporal properties of the pulse. As a forward design method, FF starts with a known optic and tunes it to achieve the desired profile. In contrast, our approach uses inverse design: we specify a target intensity profile and use an algorithm to generate the corresponding optical structure, offering greater flexibility beyond existing optics. In this work, we apply adjoint optimization to design a mirror that shapes the spatiotemporal intensity profile over an extended focal region. By simulating forward and backward wave propagation, the method efficiently computes gradients of a cost functional, enabling high-dimensional optimization of the optic's surface. We demonstrate this method by recovering a parabolic mirror with a different focal length and reconstructing an axiparabola's on-axis profile from a parabolic baseline. Future work will aim to extend this to designing ignitor pulses for ionization injection in trapezoidal density plasmas.