Asymptotic dispersion engineering for ultra-broadband meta-optics

Abstract

Dispersion decomposes compound light into its monochromatic components, which is detrimental to broadband imaging but advantageous for spectroscopic applications. Metasurfaces provide a unique path to modulate the dispersion by adjusting structural parameters on a two-dimensional plane. However, conventional linear phase compensation does not adequately match the meta-unit's dispersion characteristics with required complex dispersion, hindering at-will dispersion engineering over a very wide bandwidth particularly. Here, we propose an asymptotic phase compensation strategy for ultra-broadband dispersion-controlled metalenses. Metasurfaces with extraordinarily high aspect ratio nanostructures have been fabricated for arbitrary dispersion control in ultra-broad bandwidth, and we experimentally demonstrate the single-layer achromatic metalenses in the visible to infrared spectrum (400 nm~1000 nm, NA = 0.164). Our proposed scheme provides a comprehensive theoretical framework for single-layer meta-optics, allowing for arbitrary dispersion manipulation without bandwidth restrictions. This development is expected to have significant applications in ultra-broadband imaging and chromatography detection, among others.

Fig. 1. The schematic of dielectric metalenses for at-will dispersion engineering in an ultra-broad bandwidth.

a The schematic wavefronts of two different compensation methods: linear phase compensation and asymptotic phase compensation, for arbitrary dispersion manipulation. The left and the right embedded figure are the phase profiles of different wavelengths of the two methods, respectively. The wavelength decreases from gray to blue. b The comparison between the intrinsic phase dispersion of the meta-unit and constructed phase dispersion of linear phase compensation method in two narrow bands. c The comparison between the intrinsic phase dispersion of the meta-unit and constructed phase dispersion of asymptotic phase compensation method in the ultra-broadband range. d Scanning electron microscope image of the four types polarization-insensitive meta-units and the waveguide modes at two different wavelengths. e The relationship between the effective refractive index of four meta-units and the wavenumber.

Fig. 2. The design process and experimental results of ultra-broadband achromatic dielectric metalenses.

a The “phase-phase dispersion” library of meta-units calculated at 550 nm wavelength, where ${\mathrm{\lambda }}_{\max }$ = 1000 nm. The red line is the effective medium line representing the theoretical limit with minimal dispersion (no structural dispersion). b The asymptotic matching results in the radius dimension for a metalens with a radius of 25 μm and NA of 0.164 at different wavelengths, where the solid lines represent the constructed wavefront phase profiles and the scatters denote the phases of the matched meta-units. The embedding image is the phase dispersion figure of the structure at the position of 15.25 μm radius. c The RMS wavefront error of the metalenses with different NAs. The blue scatters and the orange scatters are the linear matched group and the asymptotic matched group, respectively. The NAs and lens sizes of the circular scatters, the star scatters and the rhombic scatters are NA = 0.243, R = 25 μm, NA = 0.164, R = 25 μm, and NA = 0.164, R = 50 μm respectively. d, e Scanning electron microscope (SEM) images of the fabricated achromatic metalens. f The experimental intensity distribution along the propagation direction (z axis) of the three metalenses. From top to bottom are the experimental results of the reference group, the linear matched group and the asymptotic matched group, respectively. g Focal length distribution at different wavelengths of metalens with NA = 0.164. The green line is the focal length of the asymptotic matched metalens, and the pink line is the normal negative dispersion reference curve. h The comparison of the performance of the single-layer achromatic metalens achieved in our work with previous studies in terms of bandwidth and limit proximity factor dimensions. The circular scatters and the star scatters are the experimental and simulation results, respectively. The working bands of the gray scatters are visible and near infrared, the orange scatters are from visible to near infrared.

Fig. 3. The focus characterization and imaging performance of the asymptotic matching achromatic metalens with NA = 0.164.

a, c Focal spot profiles and normalized intensity profiles for various wavelengths. b, d Images of element 5 and 6 in group 5 on the 1951 United States Air Force resolution target formed by the achromatic metalens. Scale bar, 20 μm. e, f Schematic diagram of a 24-h imaging detection. The right embedded image is the visible and NIR imaging results, respectively. The left embedded image is the schematic diagram of incident light band.

Fig. 4. Experimental results of arbitrary dispersion control metalens.

a–c The matching results of the enhanced negative dispersion, positive dispersion, and arbitrary dispersion manipulation metalenses designed by the asymptotic phase compensation method, respectively, where the solid lines are the constructed wavefront phase profiles at each wavelength, and the scatters are the phase of the matching structural phases. d–f Experimental light intensity profiles for the enhanced negative dispersion metalens, positive dispersion metalens and arbitrary dispersion metalens respectively at various incident wavelengths. The unit is nm. g–i The blue line is the focal length statistics at all wavelengths, and the crimson line is the normal negative dispersion reference curve. j Simulated light intensity distribution of wavelength routing at the focal plane for six wavelengths across 400~1000 nm bandwidth.