Inverse Design of Multi-Wavelength Achromatic Metalens Integrated On-Chip with Planar Waveguide

Waveguide-integrated metasurfaces offer a promising platform for ultracompact on-chip optical systems, enabling applications such as fluorescence sensing, holography, and near-eye displays. In particular, integrated achromatic metalenses that couple guided modes to free-space radiation are highly desirable for single-molecule fluorescence sensing, where high numerical aperture (NA), efficient light focusing, and consistent focal volume overlap across excitation and emission wavelengths are critical. However, designing integrated high-NA metalenses with multi-wavelength operation remains fundamentally challenging due to the wavelength-dependent propagation of guided modes. Here, we present an inverse design framework that simultaneously optimizes the geometries and positions of silicon nitride nanofins atop a slab waveguide to achieve diffraction-limited focusing at three wavelengths with unity NA. The resulting metalens outperforms conventional segmented designs in focusing efficiency and sidelobe suppression, particularly at wavelengths corresponding to the excitation and emission bands of the model fluorophore Alexa Fluor 647. Numerical analysis shows that the design yields a high molecule detection efficiency suitable for epi-fluorescence single-molecule sensing. This work highlights the potential of inverse-designed metalenses as a versatile on-chip platform for advanced applications in fluorescence spectroscopy, augmented reality, or optical trapping.