Dual-layer achromatic metalens design with an effective Abbe number

Planar achromatic metalenses with a thickness of the order of wavelength have attracted much attention for their potential applications in ultra-compact optical devices. However, realizing single-layer achromatic metalenses across a wide bandwidth requires that the corresponding meta-atoms have complex cross-sections for correct phase profile and dispersion compensation. Herein, we introduce an effective Abbe number and use lens maker equations to design a dual-layer achromatic metalens in which we compensate the dispersion by using a plano-convex liked metalens combined with a plano-concave liked metalens. The stacked metalens are designed based on simple high refractive index dielectric cylindrical meta-atoms with different radii, which simplify the design and fabrication processes. We demonstrate that a dual-layer achromatic metalens has a small focal length difference across the visible wavelength range and an average focusing efficiency above 50%, which proves that the design method is promising for many potential applications in multi-functional flat optical devices.