Diffraction and dispersion effects on the wavelength dependence of the focal length of metalenses

We investigate the wavelength-dependent focal length of singlet metalenses, highlighting the physical mechanisms that influence it. We present calculation methods to quantify the contribution of each effect and apply them to three distinct metalenses. The results reveal significant variations in focal length with wavelength and lens diameter, driven primarily by diffraction. For positive focal length metalenses, the focal length generally decreases with increasing wavelength, particularly for lenses with Fresnel numbers below 10. Material dispersion, which counteracts this trend, is insufficient to fully balance diffraction and achieve achromatic performance across all cases. Consequently, achieving achromaticity requires careful consideration of the metalens size, focal length, and Fresnel number. Notably, achromatic design becomes increasingly challenging for metalenses with Fresnel numbers exceeding 10.