High-efficiency SOI-based metalenses at telecommunication wavelengths

: We demonstrated silicon-on-insulator (SOI)-based high-efficiency metalenses at telecommunication wavelengths that are integrable with a standard 220 nm-thicksiliconphotonicchip.Anegativeelectron-beamresist (ma-N) was placed on top of the Si nanodisk, providing vertical symmetry to realize high efficiency. A metasurface with a Si/ma-N disk array was numerically investigated to design a metalens that showed that a Si/ma-N metalens could focus the incident beam six times stronger than a Si metalens without ma-N. Metalenses with a thick ma-N layer have been experimentally demonstrated to focus the beam strongly at the focal point and have a long depth of field at telecommunication wavelengths. A short focal length of 10 μ m with a wavelength-scale spot diameter of approximately 2.5 μ m was realized at 1530 nm. This miniaturized high-efficiency metalens with a short focal length can provide a platform for ultrasensitive sensors on silicon photonic IC.

There are several methods to realize the concept of a metasurface. The first method uses Mie resonance in the nanostructures. Generally, the incident light is scattered at wavelength-scale optical structures, which modulate the amplitude of the scattered light with a phase delay in the propagation direction. The first generation of metasurfaces was demonstrated using localized surface plasmon resonance [1]. The second method to create a metasurface is the so-called Huygens metasurface, which spectrally overlaps the electric dipole (ED) and magnetic dipole (MD) resonances without intensity reduction [32]. The third method for realizing 2 phase modulation is the Pancharatnam-Berry (PB) phase or geometric phase [9]. Because the phase of light accumulates owing to the orientation of the anisotropic nanostructure, the amplitude is maintained as a constant. However, a PB-phase metasurface can control the phase of scattered light for a certain circular polarization. An alternative method for phase control with high efficiency was realized using an effective index of meta-atoms [33].
Photonic integrated circuits (PICs) on silicon are wellknown in the photonics society owing to their unique advantages in overcoming electric circuits, such as highspeed modulation, direct fiber-to-chip signal delivery, and low power consumption [34]. Therefore, a silicon-oninsulator (SOI)-based metasurface is an important platform in terms of compatibility with photonic chips [35]. Recently, several attempts have been made to integrate metasurfaces on PIC chips at telecom wavelengths, including wavefront shaping, for efficient coupling [36]. However, owing to symmetry breaking along the out-of-slab direction, the ED and MD resonances do not spectrally coincide, resulting in a reduction in metasurface efficiency [32]. In addition, owing to the thin Si slab of a standard SOI wafer, the operation wavelength should be shorter than the telecommunication wavelength [35,37]. Otherwise, the Si slab should be thick [38].
In this study, we propose a new type of metalens based on a standard SOI wafer, which is a periodically arranged double-layer meta-atom composed of an electron-beam (e-beam) resist and Si disks. This meta-atom is designed to have a low-refractive-index material both on the top and bottom of the Si disk, hereby preserving the structural symmetry for high efficiency. We believe that the symmetrypreserved SOI-based metasurfaces can be a good platform for on-chip high-efficiency metasurfaces for various Si photonic devices.

Design of the SOI-based metalens
Generally, the thickness of the Si layer of an SOI wafer for a PIC chip is set to 220 nm to operate a single guided mode at the waveguide structures [39]. A method to realize a high-efficiency metasurface with an ultrathin high-index contrast slab is to spectrally overlap the ED and MD resonances not only with the spectral position but also with the strength and the width [40]. It is worth noting that the quality factor (Q-factor) of both the ED and MD resonances should be the same for unity transmission. To satisfy this condition, the structure should be symmetric along the transmission direction, including dielectric conditions. Therefore, in the case of broken vertical symmetry of the meta-atom, the spectral shapes of the ED and MD resonances are slightly different, and the transmission is significantly reduced. In this study, we propose a highefficiency compact metalens composed of a Si nanodisk with a remaining e-beam resist on top of a buried SiO 2 box to preserve vertical symmetry. Figure 1(a) shows the illustration of the high-efficiency compact metalens with Si/ma-N disk arrays, in which ma-N is a negative-tone e-beam resist (Micro Resist Technology GmbH). To investigate the effect of the ma-N layer on transmittance, we performed numerical calculations of the transmission and phase as functions of the radius (r) of the Si/ma-N disk using the three-dimensional finite-difference time-domain (3-D FDTD) method. In the simulations, the thicknesses of the Si and ma-N disks were fixed at 220 and 200 nm, respectively, and the period (a) of the Si/ma-N array was fixed at 980 nm, because the spectral widths of both ED and MD resonances become similar when the thickness of the ma-N layer becomes thick as shown in Figures S1 and S2 in the Supplementary Material. The refractive indices of ma-N and SiO 2 were set as 1.607 and 1.4657, respectively. Figure 1(b) and (c) show the transmittance and phase of the transmitted light as functions of the wavelength and normalized radius r/a of the arrays of Si/ma-N and Si meta-atoms, respectively. In the case of the Si/ma-N meta-atom, broadband 2 phase modulation can be achieved from 1400 to 1600 nm by varying r/a. In particular, the transmittance was over 70% near 1500 nm, marked with white dashed lines in Figure 1(b) and (c) (see Figure S1). However, for the Si meta-atom without the ma-N layer, the bandwidth of 2 phase modulation is narrow (1430-1500 nm), and the transmittance is near zero in the bandwidth. Additional data on the transmittance and phase as functions of the disk radius can be found in Figure S3 in the Supplementary Material. From these results, we expect that Si/ma-N metasurfaces can perform as SOI-based high-efficiency compact metasurfaces, which are compatible with a standard CMOS fabrication process.
The SOI-based high-efficiency compact metalens was designed with a simple relationship between the required phase and structural parameters extracted from Figure 1(b). For a given focal length f , the desired phase profile (x, y) at the metasurface follows equation [2]: where is the wavelength in free space. In the simulation, we fixed at 1500 nm. The left inset in Figure 2(a) shows the calculated phase map for the metalens with f = 10 μm and its corresponding structure. Figure 2 However, metalens consisting of a Si disk array cannot efficiently focus light on the focal plane, as shown in Figure 2(b). From Figure S2(a) and (b), the peak intensity of the Si/ma-N metalens on the focal plane is six times higher than that of the Si metalens. Conversely, the focal length and FWHM of the beam spot is slightly reduced to 9.42 and 0.93 μm, respectively. As a quantitative measure of the performance of metalens, the focusing efficiency is defined as the ratio of the incident power to the focused power within a square area of the focal plane. The focusing efficiency of the Si/ma-N metalens was four times higher than that of the Si metalens, as shown in the right inset of Figure 2(b). In particular, half of the incident light was focused within an area of λ 2 by the Si/ma-N metalens. This significant difference between the Si/ma-N and Si metasurfaces indicates that a low-index layer on top of the Si disk is essential for achieving high efficiency.

Fabrication and experimental results
The metalens samples were prepared using a standard SOI wafer composed of a Si slab on top of a 2 μmthick SiO 2 box layer. The thickness of the Si slab was The fabricated metalens were characterized using a tunable laser and infrared charge-coupled device (IR CCD) sensor. Figure 3(c) shows the schematic of the experimental setup. First, the fabricated sample with the proper design parameter was found using illuminator and IR CCD, and placed on the optical axis by adjusting the xyz stage of the sample's mount. The laser light (HP 8168F tunable laser source) delivered by a single-mode fiber was focused on the metasurface using a 20× objective lens (NA = 0.4). The diameter of the incident beam was approximately 20 μm.
By moving the stage, the focused beam after metalens was imaged using a 40× aspheric lens (NA = 0.6) and captured by a CCD sensor. Figure 4 shows the characteristics of the beam focused by metalens at f = 10 μm. Based on the captured image of the beam, as shown in Figure 4(a), it is clear that metalens focused the beam at the designed focal length. From the intensity distribution of the light on the metasurface (z = 0 μm), scattered beams at the edge of metalens and a ring-shaped beam at the center were observed (see more details in Movie S1). As the propagation distance (z) increased, the ring pattern shrank and finally merged at the focal plane (z = 10 μm) as a spot. At = 1570 nm, metalens still worked well in focusing the beam at the designed focal length; however, the intensity outside the beam spot became slightly bright. From the normalized peak intensity at the focal plane shown in Figure 4(b), the metalens with a thick ma-N layer focuses the light more efficiently by approximately 20% than that with a thin ma-N layer, which could be improved over 20% when the thickness of the ma-N becomes 200 nm (see the Figures S6 and S7 in the Supplementary Material). We also examined the evolution of the propagation beam through metalens for quantitative analysis. Figure 4(c) shows the intensity  profiles of the focused beam at = 1530 nm as the propagation distance changes. The intensity was maximized at the focal position and the FWHM of the beam spot was approximately 2.5 μm. As the wavelength increased, the ripples in the intensity profiles became large, as shown in Figure 4(d). This indicates that the metalens becomes less efficient over the target wavelength of 1500 nm as shown in Figure S5 and Table S1 in the Supplementary Material. However, metalens still worked well in terms of focusing performance.

Discussions
To quantitatively understand the performance of metalens, the peak intensities and FWHMs of the propagated beam were extracted from the intensity distributions of the transmitted beam. Based on the normalized peak intensity distributions with the z-position, as shown in Figure 5(a), the focal length of both the thick and thin ma-N metalenses is 10 μm at = 1530 nm, which matches well with the designed value. However, the focal length at = 1570 nm was slightly shifted to 9 and 12 μm for the thick and thin Si/ma-N metalenses, respectively, owing to the wavelength mismatch with the target wavelength. In addition, the focusing efficiency of the thick Si/ma-N metalens was approximately 20% higher than that of the thin metalens at both = 1530 and = 1570 nm. Based on the FWHM as a function of the z-position shown in Figure 5 approximately 45 and 15% longer than that of the thick Si/ma-N metalens, respectively. Considering the small difference (<10%) between the beam spot sizes of the thick and thin metalenses, this large difference in DOF is caused by the phase mismatch owing to the thickness difference of the ma-N layer. Hence, we conclude that the thickness of the ma-N layer is important for creating efficient metalenses with a long DOF and small beam spot. SOI-based metalenses at telecommunication wavelengths can be good candidates for ultrasensitive sensor platforms. In this study, we numerically investigated the possibility of a highly sensitive surface plasmon resonance (SPR) sensor composed of an SOI-based metalens with a single bowtie air hole in an Au thin film. The center of the bowtie-shaped air hole in the Au thin film was placed at the focal spot of the Si/ma-N metalens, as shown in Figure S3 in the Supplementary Material. Because the incident light is collected by the bowtie-hole nanoantenna by the surface plasmon effect and transmitted through it, the intensity at the Au nanogap could be significantly enhanced [41]. Based on the numerical simulation, the maximum field intensity at the bowtie hole with metalens of f = 3 μm can be enhanced twelvefold compared with the bowtie hole without metalens, when the bowtie hole lies on the focal plane.

Conclusions
We demonstrated high-efficiency SOI-based metalenses with a short focal length at telecommunication wavelengths that are integrable with conventional silicon photonic chips. To increase the transmittance, a negative e-beam resist (ma-N) was placed on top of a Si meta-atom to preserve the vertical symmetry. A compact metalens was designed and numerically investigated using the 3-D FDTD method. The metasurface composed of Si/ma-N disks can achieve broadband phase modulation by changing the radius of the disk, and the Si/ma-N metalens can focus light six times stronger than the Si metalens. We experimentally demonstrated that the Si/ma-N metalens can focus the incident beam at the focal plane with a spot size approximately equal to the wavelength. In particular, a thicker Si/ma-N metalens focuses the light more efficiently at the focal point and has a longer DOF than the thin Si/ma-N metalens. We believe that SOI-based metalenses can provide a good platform for ultrasensitive sensors on silicon photonic IC.