Polarization-Independent and High-Efficiency Dielectric Metasurfaces Spanning 600-800 nm Wavelengths

Artificial metasurfaces are capable of completely manipulating the phase, amplitude, and polarization of light with high spatial resolutions. The emerging design based on high-index and low-loss dielectrics has led to the realization of novel metasurfaces with high transmissions, but these devices usually operate at the limited bandwidth, and are sensitive to the incident polarization. Here, for the first time we report experimentally the polarization-independent and high-efficiency dielectric metasurfaces spanning the visible wavelengths about 200 nm, which are of importance for novel flat optical devices operating over a broad spectrum. The diffraction efficiencies of the gradient metasurfaces consisting of the multi-fold symmetric nano-crystalline silicon nanopillars are up to 93% at 670 nm, and exceed 75% at the wavelengths from 600 to 800 nm for the two orthogonally polarized incidences. These dielectric metasurfaces hold great potential to replace prisms, lenses and other conventional optical elements.

have a regular triangle cross section with a hexagonal lattice and a square lattice, respectively. The length a is changing from 50nm to 240nm, and d=200√3nm is the lattice constant.
Broadband at the visible wavelengths. The polarization-independent metasurfaces can be surprisingly realized only by tailoring the symmetry of constituent resonators and the Bravais lattice instead of the dimensions of resonators as demonstrated above. More importantly, this also leads freedom to achieve the amazing broadband at the visible wavelengths with a full 2 phase control, which is exceptionally beneficial for spatial phase modulation optical elements such as prisms and lenses. As an example, we analyze the metasurface consisting of square resonators in a square lattice as shown in Fig. 2a, which satisfies the polarization-independent conditions aforementioned. The resonators are made of the nano-crystalline silicon due to its pertinent refractive index and relatively low loss in visible frequencies as presented in Supplementary Fig. 1  We find in Fig. 3a that by changing the dimensions of resonators, not only a 2 but also a 3 phase control can be realized at short wavelengths. It may be trivial for a monochromatic device because only the difference of the phases other than phases themselves plays a key role. However, the 3 phase control indeed gives rise to the broadband feature. Although the phases change with the wavelength of the incident light for a dimension fixed resonator array due to different resonance excitations in different frequencies, we can keep the phase difference constant for resonators with different sizes (i.e. the chosen meta-atoms as the basic units to compose the metasurface) in a broad spectrum by setting the phase delay from 0 to 2 at the longer wavelength and from to 3 at the shorter wavelength.
The simulations in Fig. 3a verify its feasibility. When the size a ranges from 100nm to 250nm, the phase delay changes from to 3 at 550nm but from 0 to 2 at 800nm. At the same time, the amplitude of the transmission light shown in Fig Fabrication and characterization of the dielectric metasurfaces. According to our designs as shown in Fig. 1, we fabricated a gradient dielectric metasurface from a 370nm-thick nano-crystalline silicon film on a quartz substrate using the procedure described in the Methods section. Each super-cell is composed of six resonators arrayed from small to large in dimension. The scanning electronic microscope (SEM) images in Fig. 4a revealed that the configuration of the fabricated metasurface agreed very well with our design. The periodicity also induces weak high-order diffractions. The refraction angle can be calculated by the formula arcsin /6 , which is from 17.8° to 26.4° in the wavelength range from 550nm to 800nm. We measured all the intensities of the anomalous refraction beam (+1st order diffraction), the 0th order normal transmission beam, the -1st order diffraction beam and the incident beam from 550 to 800nm. Both the x-and y-polarized incident beams were adopted to verify the polarizationindependence. To visualize the results, a series of photos in Fig. 4b were taken to show the intensity distributions of transmission lights. From the images, the refraction angles do increase with the wavelength as expected. Figure 4c shows the measured diffraction efficiencies from 550 to 800nm, which are amazingly higher than 75% from 600 to 800nm. The peak efficiencies, 93% and 92%, are at 670nm and 710 nm for the x-and y-polarized incident beams, respectively. The experimental results agree well with the simulations. Such salient broadband is much larger than the reported values 20,[25][26][27]29,38 . In Ref. 20, the wavelength range is about 50nm with the efficiencies higher than 50% and a peak diffraction efficiency of about 75%. In addition, the transmittances are as high as 20% to 45% in the wavelength range of 550-800nm as shown in Fig. 4d, which conform to the simulations. They are much higher than the theoretical limit of 25% for ultrathin metasurfaces (the height of the meta-atoms is much smaller than the wavelength of the incident light) 37 . which significantly paves a promising way to promote the transmission further.
The combination of the polarization independence, the broadband, the high diffraction efficiency and the high transmittance in the visible frequencies can greatly facilitate the design, fabrication and application of higher performance optical elements such as prisms and lenses.

Discussion
The slight aberrations between two orthogonal polarizations were observed in conditions. In addition, the high quality of the metasurface here can also be ascribed to the big enough step sizes chosen for the six meta-atoms such as 10nm, 15nm, 15nm, 20nm and 40nm which can be fairly readily processed by both electron beam lithography and plasma etch. Even in the visible-frequency, the designed meta-device is also processible. It is worth noting that by optimizing the designs (say, using cross shape resonators) to eliminate the excursion of the difference of phases between two different meta-atoms, we can further improve linear responses of the meta-atoms to further broaden the operating band to cover the full visible wavelengths.
In conclusion, we both theoretically and experimentally demonstrate the first After the first polarizer to select the initial linear polarization, a quarter-wave plate was applied to change the linear polarization into the elliptical polarization.
Then either x-polarized or y-polarized beam was selected by the second polarizer.
The photos of the light distributions on a white screen were taken by a camera (Canon 5D Mark Ⅱ). The intensities of the transmission beam were measured by a power meter (Thorlabs PM100D).
Simulations. We performed the simulations in frequency domain by commercial software COMSOL. Using ports along z-axis and perfect matched layer, we characterize the phase delay and the amplitude of transmission electromagnetic fields. Both a normally incident plane wave and periodic conditions were assumed to save the computation time. However, we should concede that our simulation results, used as a local response, actually were derived under the conditions of an infinite metasurface with an array composed of the same resonators, which indeed may have some differences from our experimental conditions. To justify our simulation methods, we conducted full-field simulations for the whole super cells, and the results have a reasonable agreement with our expectations ( Supplementary Fig. 3). is quite consistent with our experimental results (93% peak efficiency for x polarized incident beam at the wavelength of 670nm and 92% peak efficiency for y-polarized incident beam at the wavelength of 710nm).

Supplementary Notes Supplementary Note 1: Characterization of the deposited nano-crystalline silicon film
The nano-crystalline silicon film is deposited using an ICPECVD system and characterized using a spectroscopic ellipsometer (Sentech SE 850 DUV). The thickness and complex refractive index of the film are obtained by fitting the measured data. The measured complex refractive in the wavelength range from 500nm to 800nm is shown in Fig. S1. The relatively high real part (n) makes for a full 2 phase control and a very low imaginary part (k) offers low loss in visible frequencies.

Supplementary Note 2: Two ways to control the wave fronts
There are two major ways for either plasmonic arrays or dielectric resonators to provide a full 2 phase delay: the first way is to change the physical geometry of meta-atoms so that the leaky-modes in resonators are tailored and varying phase delay of the scattering light is enabled. The other way, which is based on a purely spatial geometry effect, known as Pancharatnam-Berry phase, is to simply rotate meta-atoms with a circularly polarized incident light, which indicates that the analytical solution for the scattering field never changes in the local coordinates fixed in the meta-atoms. We should note that though the different geometry of meta-atoms significantly influences manipulation efficiency, the second way is genuinely general rather than only feasible to some specific geometry of resonators. Here we choose the first way to control the wave fronts because the concept of Pancharatnam-Berry phase is fundamentally based on polarization status. In fact, it is Pancharatnam-Berry phase that gives rise to the polarizationdependent properties, and our work is to figure out what kinds of symmetries of meta-atoms are immune to that general effect.