Varifocal Metalens Using Tunable and Ultralow‐loss Dielectrics

Abstract The field of flat optics that uses nanostructured, so‐called metasurfaces, has seen remarkable progress over the last decade. Chalcogenide phase‐change materials (PCMs) offer a promising platform for realizing reconfigurable metasurfaces, as their optical properties can be reversibly tuned. Yet, demonstrations of phase‐change metalenses to date have employed material compositions such as Ge2Sb2Te5, which show high absorption in the visible to near‐IR wavelengths particularly in their crystalline state, limiting the applicability. Here, by using a low‐loss PCM Sb2Se3, for the first time, active polarization‐insensitive phase‐change metalenses at near‐IR wavelengths with comparable efficiencies in both material states are shown. An active metalens with a tunable focusing intensity of 95% and a focusing efficiency of 23% is demonstrated. A varifocal metalens is then demonstrated with a tunable focal length from 41 to 123 µm with comparable focusing efficiency (5.7% and 3%). The ultralow‐loss nature of the material introduces exciting new possibilities for optical communications, multi‐depth imaging, beam steering, optical routing, and holography.

(a) The simulated transmission spectrum and phase response after the optimized Sb 2 Se 3 nanopillars are switched to crystalline state. (b) Electric and magnetic field profiles (at xz-plane) of the MD resonance at the resonance-overlapping wavelength (1550 nm) for amorphous-state Sb 2 Se 3 (left) and crystalline-state Sb 2 Se 3 (right). (c) Electric and magnetic field distributions (at yz-plane) of the ED resonance for amorphous and crystalline-state Sb 2 Se 3 . The Sb 2 Se 3 nanopillar is illuminated with a plane-wave light source propagating along z-axis and linearly polarized parallel to the x-axis.
Here explains the detail for the designing of a metalens with a radius R of 35 µm and focal length f of 120 µm. For design simplicity, the periodicity of the array of cylindrical Sb 2 Se 3 nanopillars is fixed at 1020 nm. In this case, the nanopillars with a height of 270 nm show the same trend of multipolar resonances with that of p=3*r (Figure 2d), but exhibit slightly reduced transmission as shown in Fig. S3a. The required phase profiles of a single-focal metalens with a focal length f follows a hyperbolic function, which is given by where f is the focal length, λ is the wavelength of the incident light, ( , ) is required phase at  any position ( , ) on the plane of the metalens and the origin o is the center of the metalens. [3] Using this equation and the phase-radius relation, we calculate the metalens with varying radii (r) that correspond to the required phase distributions ( , ) at the designated positions ( , ) as shown in Fig. S3b. Fig. S3c shows the generated phase modulation when light passes through the metalens consisting of nanopillars arranged with the designed radius when the Sb 2 Se 3 is in the amorphous state (green line) and crystalline state (blue line). The phase modulation matches well with the calculated hyperbolic phase profiles when the Sb 2 Se 3 is in the amorphous state, but mismatches when the materials is at crystalline state. Figure S4. Tunable single-focal metalenses using crystalline-state Sb 2 Se 3 . The simulated transmission and phase response for crystalline-state Sb 2 Se 3 nanopillars with radius (r) gradually increasing from 100 nm to 408 nm. h=225 nm, p=1020 nm. (b) The simulated light intensity distributions at xz-plane when light propagates through the metalens when the material is in the amorphous state (upper) and crystalline state (bottom). (c) The simulated light intensity distributions at the focal plane (z=117.13 µm). (d) The light intensity along x-axis at the focal plane (z=117.13 µm, y=0).

Near-unity transmission and 2π phase modulation by embedding the nanopillars in an optimized dielectric top layer
Transmission intensity (i.e. focusing efficiency) of a metalens is determined by the mode overlap between electric-and magnetic-dipoles of a Sb 2 Se 3 nanopillar. Although Sb 2 Se 3 nanopillars show tight field confinement, the difference in coupling strength between two dipoles can still exist due to non-trivial spatial mode mismatch. This can be further improved by either optimizing nanopillar geometries [4] or changing the surrounding environment to higher index dielectrics [5], such as transparent polymer (n ~ 1.4).
By using such techniques, we show the significant improvement of nanopillar transmission with achieving 2π modulation in Fig. S6. This is due to the enhanced electric field confinement within  the nanopillar by replacing surrounding medium with higher refractive index material. However, it is worth mentioning that further numerical optimization is still necessary to avoid or minimize the interelement electromagnetic coupling between the neighboring nanopillars of a metalens in order to improve its focusing efficiency. [6].

Schematic of the fabrication process and the measurement setup
Note that in our case, the Cr hard mark is kept at the end as a protection capping layer of the Sb 2 Se 3 .

Focusing performance of each region of the varifocal metalens as a separate intensity-tunable metalens
We calculated the focusing performance of each region separately in Fig. S9. We observed that  the focusing performance of the round-hole metalens (i.e. region 2) is similar to that of the fullcircle one in region 1 in terms of the intensity modulation. The round-hole metalens shows the intensity modulation (∆I/I 0 ) of 95.07%, while the one for the full-circle one is 96.1%. The FWHM of point-spread-function at focal point for the round-hole metalens is 2.46 µm, while the one for the full-circle one is 2.45 µm. This is because the large feature sizes of region 2 compensates for the degradation of focusing quality that can be caused by the void (i.e. open area). Therefore, each region of the metalens operates as an independent, intensity-tunable metalens with different focal lengths, realizing a varifocal metalens.

Broadband performance of the metalens
As shown in Fig. S10, we calculated the field distribution of a single focal metalens under the illumination at different wavelengths (1450 -1700 nm). One can observe that the focusing efficiency remains above 15% within the wavelength range between ~1500 and ~1700 nm, while the full-width-half-maxima (FWHM) of their point spread functions at focal point and focal lengths are unaffected (≤10% for FWHM, ≤5.81% for focal length). Therefore, the working bandwidth is estimated to be ~200 nm for both single and varifocal lenses since a varifocal lens is considered as a combination of two single focal lenses.