Fundamental design framework of hybrid refractive-metalens system for axial aberrations correction and its validation in LWIR band.

Due to the limited phase coverage and dispersion range that meta-atoms can provide, the aperture of a single achromatic metalens typically remains below the centimeter threshold. This limitation has spurred the development of a hybrid refractive-metalens system (HRMS), which can offer the potential to overcome the performance limitations of single metalens while maintaining a more compact form factor compared to conventional refractive lenses, thereby presenting significant application prospects. However, previous studies have predominantly regarded the metalens as a corrector for refractive optics, with limited exploration into the specific role it plays within the HRMS and how the degrees of freedom inherent to metalenses can be effectively leveraged. Here, A ray tracing-based methodology that places emphasis on incorporating the dispersion characteristics of meta-atoms is introduced, and specifically, three types of phase formulas offering progressively greater freedom degrees of the dispersion modulation for metalenses are examined. We have presented two hybrid refractive-metalens axial aberrations correction systems, each utilizing distinct phase formulas, which share the same system parameters: an entrance pupil diameter of 25.4 mm, an effective focal length of 45 mm, within the 9.2-11.8 μm long-wave infrared band. Simulation results indicate that the superior HRMS system exhibits an average efficiency exceeding 85% across the designed wavelength range. Additionally, experimental results confirmed that the imaging performance of both HRMS configurations surpasses that of a single metalens, validating the effectiveness of the HRMS concept. Moreover, we explore the application scope of our method and clarify that the metalens in HRMS should undertake negative dispersion and positive optical power, striking a balance between dispersion modulation freedom and optical power. The framework is expected to find significant applications in compact and lightweight optical systems.