Chromatic aberration caused by dispersion usually degrades the system imaging quality in optical imaging systems. Therefore, a large number of researchers have used various methods to correct chromatic aberration in devices and systems. However, chromatic aberration is of practical value in certain specific areas, such as wavelength-controlled optical zoom by chromatic aberration, so that mechanical moving parts are no longer required in zoom systems with fast, continuous, and repeatable zoom by only changing the incident wavelength. It effectively improves the detection efficiency of optical systems and promotes the development of optical zoom systems in the direction of integration and miniaturization. Optical metasurfaces have powerful multi-dimensional light field modulation capabilities. Metasurface planar lenses, namely metalenses, are realized based on the local abrupt phase introduced by sub-wavelength structures, which allow complex and bulky conventional lens sets to be converted into single-layer structures with multi-functional integrated modulation characteristics. In addition, the dispersion of a metalens is more pronounced than that of a conventional refractive lens, but the zoom mode and axial zoom range of conventional diffracted metalenses are influenced by the inherent diffraction dispersion, and its resolution is constrained by the diffraction limit. To address this challenge, one method of designing super-resolution wavelength-controlled zoom metalenses has been proposed by simultaneously modulating the phase, dispersion, and amplitude. After enhancing the axial zoom capability of the metalens, we utilize a hierarchical particle swarm optimization (HPSO) algorithm to further compress the point spread function of the metalens, which makes the full width at half maximum (FWHM) of the metalens close to or even less than the diffraction limit (0.5λ/NA).

First, the relation between the focal length and angular frequency, i.e., the dispersion constraint relationship, is set to n=2, and the theoretical group delay (GD) and group delay dispersion (GDD) are obtained by Taylor expansion. Then, the unit structure database is created. The wavelength range is set to 68-80 μm, and 37 wavelengths are sampled at equal intervals. The amplitude and phase of the unit structure within the bandwidth are sequentially calculated by the commercial software FDTD Simulation. The simulated GD and GDD of each structure are obtained by fitting the simulated data. In order to minimize the fitting error, the unit structures with R² values of fitting accuracy less than 0.98 are screened out to create the unit structure database, which consists of more than 30000 different structures. In order to cover a larger range of group delay, the simulated data points are shifted. In the next step, based on the unit structure database, a reasonable matching error is set to create ring-band-dataset by dispersion engineering. The structures in each ring-band-dataset have similar dispersion and different amplitude, thus randomly selecting structures from the datasets can achieve a zoom metalens. Although the above zoom metalenses have a greater axial zoom capability than conventional diffracted metalens, none of their FWHM values within the bandwidth is less than the diffraction limit. Finally, in order to further compress the point spread function of the metalens while keeping the zoom capability of the metalens unchanged, each structure located in the ring is selected from the created datasets, and the amplitude of the metalens is optimized by using the vectorial angular spectrum method (VASM) and the HPSO, resulting the FWHM of the metalens close to or even less than the diffraction limit.

The focal length variation of the zoom metalens operating in the range of 68–80 μm basically meets the demand of set value, and the zoom range is about 80.6 μm while that of the conventional diffracted metalens with the same diameter is about 53 μm. Hence, the zoom capability of the zoom metalens is about 1.52 times that of the conventional diffracted metalens (Fig. 8 (a)). The FWHM of the conventional diffracted metalens is close to the diffraction limit within the bandwidth, and none of its focal spots is less than 0.5λ/NA. However, the optimized zoom metalens operating in 73-78 μm (i.e., λ₁₆-λ₃₁) achieves super-resolution focusing (Fig. 8 (b)). Although the focal spots of other wavelengths are still limited by the diffraction limit, the spot size of the zoom metalens can be effectively compressed by amplitude modulation compared with the randomly composed metalens. The two-dimension intensity profiles of the zoom metalens (n=2) and the conventional diffracted metalens (n=1) along the propagation direction are depicted in the figure, which shows that the range of the focal shift of the zoom metalens is larger than that of the conventional diffracted metalens.

The existing optical zoom systems usually require mechanical scanning, and these systems are complex, bulky, and difficult to be integrated. To meet this challenge, we propose a wavelength-controlled optical zoom metalens with enhanced axial zoom capability by simultaneously modulating the phase and dispersion. Affected by the diffraction effect, the resolution of the randomly composed zoom metalens cannot break the diffraction limit. Therefore, on the basis of maintaining the preset zoom performance by adjusting the matching error of GD and GDD, we utilize the HPSO algorithm to further compress the point spread function of the zoom metalens. Simulation results show that the axial zoom capability of the designed zoom metalens is about 1.52 times that of the conventional diffracted metalens, and the transverse resolution within the working bandwidth (68-80 μm) is approaching the diffraction limit. Particularly, the resolution is less than the diffraction limit in the range of 73-78 μm. Due to the response characteristics of the unit structure within the operating bandwidth, a few unit structures can be selected in the center and edge rings, and the range of amplitude is relatively small, resulting in limited device diameter and focusing efficiency. The unit structure database will be further expanded to provide more choices for amplitude modulation, thereby realizing a high-performance broadband super-resolution wavelength-controlled optical zoom metalens and providing a core element for a highly compact, high-resolution, and non-moving zoom system.