Rotationally symmetric phase filter design for extended depth-of-focus using automatic differentiation

Abstract Generation of needle-like beams with narrow lateral responses has been sought in many applications, which include laser machining, optical trapping and biomedical imaging. Pupil engineering, among various strategies, has been extensively studied to realize beams with long depth ranges using phase and amplitude modulations. However, the depth-of-focus (DoF) extension performance of conventional design methods is limited by the limited capacity in handling of design complexity and design variables. Here, we present an automatic differentiation (AD)–based framework for designing rotationally symmetric phase filters to generate elongated focal responses. By utilizing differentiable beam propagation model and AD-based optimization of multiple design variables, we achieved flexible control of the beams with a DoF more than 40×, with scan-robust characteristics. The proposed method was also validated in numerical simulations and experiments, demonstrating over 40× DoF extension compared with a clear pupil.