Unified Aberration Theory for Metalenses: Bridging Classical Optics and Metasurface Technology

Conventional lenses with mature theoretical foundations and emerging metalenses with distinctive miniaturization advantages are two essentialcomponents in optical systems. However, metalenses face three key challenges: lack of systematic aberration analysis, limited theoretical integration with classical optics, and achieving high image quality despite their ultrathin profiles. We address these challenges with our Unified Aberration Theory for Metalenses (UATM), providing quantitative design guidelines. This theory enables systematic analysis of aberrations originating from the designed phase profile and assessment of discrete implementation effects. By extending the generalized Snell's law to non-radial rays, we develop Seidel-compatible expressions identifying seven fundamental aberration types corresponding to actual optical aberrations. Our approach accurately predicts aberration values and enables coefficient superposition across both technologies, establishing a systematic workflow for hybrid system design that integrates seamlessly with standard optimization tools. The results demonstrate close agreement between theoretical predictions and performance. To demonstrate UATM's effectiveness, we validate it through simulation of three systems: a wide-field dual-metalens, a UV reflective hybrid, and achromatic telescope eyepieces. Additionally, we design a spherical-substrate metalens with wide field-of-view, large aperture, and enhanced chromatic correction across visible wavelengths. In conclusion, UATM bridges conventional and metalens technologies, advancing optical development toward higher integration and enhanced performance.