Broadband achromatic and polarization-insensitive metalenses in the visible inspired by Rayleigh criterion

Objective Metasurfaces, a planar optical element composed of subwavelength structural units, can flexibly tailor the phase, amplitude, polarization, and frequency of the optical field, providing a robust platform for the integration and miniaturization of optical components. Metalenses stand out as a crucial application of metasurfaces, with achromatism playing a key role in ensuring high imaging quality. Nonetheless, the existence of metacell resonances with varying dispersions and restricted resonance bandwidths causes metalenses to display considerable chromatic aberrations when functioning beyond the specified wavelength range, thereby hampering their utility in multi-wavelength or broadband applications. To tackle this challenge, this paper proposes a novel design strategy for visible broadband achromatic and polarization-insensitive metalenses, guided by the Rayleigh criterion principle for resolving the focal spot. By leveraging the theory of conjugate phase spin multiplexing design, a composite metacell element of metalenses is constructed using two differently-sized anisotropic TiO₂ nanofins that operate efficiently at two distinct edge wavelengths, with their rotation angles limited to 0° or 90°. Through the complementary dispersion effects between the two nanofins, this design achieves wideband achromatism and polarization-insensitive focusing performance in the visible light spectrum (λ=470-650 nm), while maintaining high focusing efficiency. This advancement marks a significant step forward in the realm of broadband achromatic metalenses and paves the way for potential applications in compact, chip-level devices.

Methods Inspired by the Rayleigh criterion for spot resolution, this work presents a novel design strategy for visible broadband achromatic and polarization-insensitive metalenses. By utilizing the Pancharatnam-Berry (PB) phase and leveraging the theory of conjugate phase spin multiplexing, we construct metalenses using two sets of anisotropic TiO₂ nanofins that operate efficiently at two distinct edge wavelengths, with their rotation angles constrained to 0° or 90°. Through the complementary dispersion effects between the two nanofins, this design successfully achieves wideband achromatism and polarization-insensitive focusing performance in the visible light spectrum (λ=470-650 nm), while maintaining high focusing efficiency.

Results and Discussions The simulated normalized intensity distributions in the x-z planes for the designed broadband achromatic metalens under left circularly polarized (LCP) light incidence across the visible spectrum, ranging from 470 to 650 nm (Fig.2(a)). The results indicate that the center of the focal spot of the broadband achromatic metalens remains close to the predetermined focal length (indicated by the white dashed line) at approximately 40 μm throughout the visible spectrum, thereby confirming the feasibility of the proposed broadband achromatic design. The normalized intensity distributions along the x=0 cross-section of the designed broadband achromatic metalens, sub-metalens 1, and sub-metalens 2 under LCP light incidence at different wavelengths (Fig.3(a)-(c)). It is evident that the focal length of the designed broadband achromatic metalens remains close to the preset focal length of 40 μm. The designed metalens maintains a focusing efficiency of approximately 40% across the entire visible light spectrum, resulting in an average efficiency value of 38.2% (Fig.4). According to the quantitative analysis (Fig.5(b)), the maximum focal length shift of the designed metalens under different polarization states of incident light is only 4.5%, which is nearly negligible. Furthermore, an examination of the peak intensities, full widths at half maximum (FWHMs), and focusing efficiency of the focal spots generated by incident light with varying polarization states (Fig.5(c)-(d)) reveals that the metalens designed in this work exhibits strong robustness to the polarization state of the incident light.

Conclusions In summary, inspired by the Rayleigh criterion for focal spot resolution, this paper proposes a novel design strategy for broadband achromatic and polarization-insensitive metasurfaces tailored for the visible light spectrum. By utilizing a pure phase-based approach and employing the theory of conjugate phase spin multiplexing, we construct a composite metasurface element composed of anisotropic TiO₂ nanofins of two different sizes, with their rotation angles constrained to 0° or 90°, optimized for efficient operation at two distinct edge wavelengths. The simulation results demonstrate that, through the complementary dispersion effects between the two nanofins, this metasurface achieves broadband achromatism and polarization-insensitive focusing performance across the visible spectrum (λ=470 to 650 nm), while maintaining high focusing efficiency (with a maximum efficiency of 43.6% and an average efficiency of 38.2%) alongside diffraction-limited performance. Compared to existing broadband achromatic metalenses, the micro-nano structures involved in this study are simpler and more amenable to large-scale fabrication, offering a new approach for developing broadband achromatic and polarization-insensitive metasurfaces, with potential applications in ultra-compact chip-level devices.