A generalized adjoint optimization method for metasurfaces enabled by phase-convergence

Metasurfaces enable lightweight, highly integrated optical systems, offering a compact alternative to conventional bulky components. However, forward design methods based on local periodic approximation inevitably suffer from efficiency degradation resulting from inter-element couplings. While adjoint-based inverse design methods can overcome these limitations, current adjoint optimization algorithms remain task-specific across different metasurface designs. Their adjoint excitations must be reconstructed for each prescribed target field, making the workflow cumbersome and often incurring high computational costs and propagation errors for far-field or off-axis objectives. To address this challenge, we propose a generalized adjoint-optimization method enabled by a phase-convergence mechanism. Central to this method is a gradient-to-structure mapping model that translates complex-valued adjoint gradients into physically realizable structural updates, establishing a stable iterative relation between structural perturbations and the resulting phase response. This mechanism ensures monotonic phase convergence at the device plane, enabling meta-element-level control of arbitrary phase profiles. Within this formulation, the adjoint simulation employs a single electric dipole excitation, independent of the desired metasurface function. Functional diversity is achieved solely by adjusting the update mapping rather than redefining the adjoint source or modifying the simulation model. This establishes a unified and computationally efficient inverse-design framework capable of handling multiple types of wavefront-shaping functionalities. As proof of concept, numerical validations are performed on diverse metadevices. Specifically, a 2D nanopillar metalens and a linear phase gradient metagrating achieved efficiencies of 83.9% and 72.4% (at 30° deflection), respectively. For arbitrary wavefront shaping, a bifocal lens showed a focusing efficiency of 67.2% and a holographic metasurface generated a hollow triangle pattern with 60.3% energy efficiency. Our results confirm that the proposed method features simplified source construction, high computational efficiency, and strong adaptability, providing a unified and viable framework for the engineering of metasurfaces in imaging, wavefront engineering, and ultraviolet detection.