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Dielectric 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, we report the realization of the polarization-independent and high-efficiency silicon metasurfaces spanning the visible wavelengths about 200 nm. The fabricated computer-generated meta-holograms exhibit a 90% diffraction efficiency, which are verified by gradient metasurfaces with measured efficiencies up to 93% at 670 nm, and exceeding 75% at the wavelengths from 600 to 800 nm for the two orthogonally polarized incidences. These dielectric metasurfaces effectively decouple the phase modulation from the polarization states and frequencies for visible light, which hold great potential for novel flat optical devices operating over a broad spectrum.
© 2016 Optical Society of America
1. Introduction
Metasurfaces can arbitrarily manipulate the phase, amplitude, and polarization of light with high spatial resolutions [1,2]. Their constituent units, or the sub-wavelength meta-atoms, are carefully designed to bring forth a specific phase delay for the scattering light. Therefore, the transmitted electromagnetic fields can be tailored by changing the materials or physical sizes of the meta-atoms. As a result, an abrupt phase discontinuity is obtained to allow directly manipulating the wave fronts of the scattering light. Many novel applications based on metallic metasurfaces have been demonstrated, including the anomalous refraction and reflection [1,3,4], beam shaping [5–7], transformation between propagating waves and surface waves [8], interaction of photonic spin and orbital momentum [9], polarization measurement [10] and holograms [11,12]. To address the low efficiencies of single-layer metal metasurfaces, a gap-plasmon structure is proposed to ensure the high efficiency in reflection mode [13–21] and extended to the successful phase control in transmission mode with a relatively high efficiency in the terahertz range [17].
A promising path to realize the high efficiency in transmission mode is to use dielectric metasurfaces consisting of monolayer dielectric resonators made of high refractive index materials [22–27]. The strong magnetic resonance in low-loss dielectric metasurfaces can provide directional scattering by exciting both electric and magnetic resonances simultaneously [28–32], which enables the effective phase manipulation with high transmittance [33–37]. In the meantime, the other type of taller Si metasurfaces [38–41] as well as flat binary diffraction gratings [42–45], which can be considered as a truncated waveguide and operate as a low-quality-factor Fabry–Pérot resonator, also show the phase shift ability with high efficiency. Up to now, most of demonstrated dielectric metasurfaces have operated at specific and/or infrared frequencies. Utilizing the Pancharatnam-Berry phase [4,22,46], the broadband meta-devices for visible light are demonstrated, but the polarization sensitiveness may complicate the design and the fabrication of integrated pure phase modulation systems (such as imaging system) because of the necessity of polarization preselection.
In this work, we successfully realize the complex two dimensional phase control at visible frequencies combining with broad bandwidth, polarization independence and subwavelength resolution by the elaborate analysis on the meta-atom level. We show that all the meta-atoms with a multi-fold symmetry have a polarization-independent response and the distortions induced by mismatched lattices are very weak, and thus the local response could be kept even in a non-periodic arrays. The broadband feature (550-800 nm) is achieved by introducing the TM10 waveguide mode in the silicon resonators so that the difference of the phase delays from two specially designed meta-atoms can remain constant. To exhibit these advantages, computer-generated meta-holograms are designed and fabricated, performing a good imaging quality in the whole visible light region with a 90% diffraction efficiency for red incident light as shown in Fig. 1. The image in the schematic is the experimental result under the illumination of 700 nm x – polarized light. In order to measure the diffraction efficiencies more accurately, gradient dielectric metasurfaces are also fabricated, with the diffraction efficiency as high as 93% in visible frequencies.
Fig. 1 Schematic of a meta-hologram. An array of amorphous silicon nano-resonators is arranged on a quartz substrate and the beam is normally incident along z-axis. The image is the experimental result under the illumination of 700 nm x – polarized light.
2. Design and simulations
We first consider a simple infinite metasurface consisting of the same Si meta-atoms to illustrate how to realize the polarization-independence. We focus on the influence of the geometry of meta-atoms, and temporarily neglect the influence of Bravais lattice. In this case, rotating the entire infinite metasurface by an angle of θ is presumed to be equivalent to individually rotating each meta-atom by the same angle. Assuming that a right circular polarization plane wave is normally incident along z axis, rotating each meta-atom by 2π/n does not change the metasurface when the meta-atom has an n - fold symmetry. However, due to the Pancharatnam-Berry phase [46], rotating the metasurface by θ will induce a 2θ phase change in the cross polarization component with respect to that of the incident light. Therefore, the transmission electric field satisfies
To satisfy Eq. (1) for the multi-fold (n>2) symmetry meta-atoms, EL(z) must be zero which indicates the polarization-independent properties of the multi-fold meta-atoms.Furthermore, if the Bravais lattice of the metasurface has an m - fold symmetry with m being a multiple of n, the isotropic response should remain since a rotation operation can reproduce the original metasurface without any aberration. However, a slight deviation would occur as long as m is not a multiple of n. In this case, the rotation of the entire infinite metasurface by θ is not exactly equivalent to the rotation of each meta-atom by the same angle. To verify our analysis, numerical simulations are performed using the commercial software COMSOL. Using ports along z-axis, we characterize the phase delay and the amplitude of transmission electromagnetic fields. Both a normally incident plane wave and periodic conditions are assumed. The wavelength of the incident light is fixed at 633 nm from a He-Ne laser. The refractive index of the resonators and the quartz substrate are set to be 3.63 + 0.06i and 1.5, respectively. Figures 2(a)-2(d) show both the phase delay and the amplitude of the transmission electric field in two orthogonal polarizations as a function of the resonator dimension. The simulated data are in good agreement with our prediction. In Fig. 2(a) (square resonators (n = 4) in a square lattice (m = 4)) and Fig. 2(c) (regular triangle resonators (n = 3) in a hexagonal lattice (m = 6)), the two curves for x - and y - polarizations perfectly overlap. At the same time, the expected slight differences are observed in Fig. 2(b) (square resonators (n = 4) in a rectangular lattice (m = 2)) and Fig. 2(d) (regular triangle resonators (n = 3) in a square lattice (m = 4)) because of the mismatch of the symmetries of resonators and lattices. It can be seen that this kind of distortions induced by mismatched lattices is very weak. Because the meta-atom in a non-periodic array is somewhat similar to that in a mismatched lattice (both of them have the anisotropic local environment), it can be expected that the polarization independence can be almost retained even in the non-periodic arrays.
Fig. 2 Numerical simulations of the phase delay and the amplitude of the transmission light through an infinite metasurface as a function of the size of meta-atoms. The red solid line, the blue dash line, the yellow solid line and the gray dash line represent the phase delay of x - polarization, the phase delay of y – polarization, the amplitude of x - polarization, and the amplitude of y - polarization, respectively. The amplitude is normalized to the intensity of incident light. (a, b) Meta-atoms have a square cross section with a square lattice and a rectangular (d1 = 1.1d, d2 = 0.9d) lattice, respectively. The length a ranges from 50 nm to 160 nm, and the lattice constant, d = 300 nm. (c, d) Meta-atoms have a regular triangle cross section with a hexagonal lattice and a square lattice, respectively. The length a ranges from 50 nm to 240 nm, and the lattice constant, d = 200√3 nm.
We have demonstrated that the multi-fold symmetry can ensure the polarization independence of the meta-atoms. In the meantime, we can achieve the broadband 2π phase control at the visible wavelengths by carefully tailoring the specific dimensions and the thickness of the meta-atoms. As an example, we analyze the metasurface consisting of square resonators in a square lattice as shown in Fig. 2(a), which satisfies the polarization-independent conditions aforementioned. The lattice constant d is set to be 300 nm (about the half of the wavelength of the incident light) to avoid unwanted diffractions. It has been recently demonstrated that the perfect match of the electric and magnetic resonances results in a reflectionless effect thanks to the constructive interference for forward scattering light and the destructive interference for backscattering light [28–32]. The metasurfaces have a height about 100 nm for visible incident light [33] to accommodate the dipole excitation. The 2π phase change occurs around the resonant frequency and thus gives rise to the limited-bandwidth phase modulation. Here, instead of using the dipole overlap at a fixed wavelength [28–37], we stretch the height h of the resonators to 350 nm so that the light can propagate stably in the silicon posts to generate waveguide modes [39] that can be regarded as non-resonant since it is not dependent on a fixed wavelength.
Figure 3 shows the near field distribution in the silicon posts with x - polarized incident light. The light is well confined in the posts and the coupling between adjacent meta-atoms is weak, and thus the local response can be almost retained even in the non-periodic arrays. Both the vortex electric field (white ellipses) and the transverse magnetic field (white arrows) clearly show the TM10 mode in the silicon posts. The conservation of the wave vector results in a shorter effective wavelength (which can be characterized by the period of these ellipses and arrows) with the increasing of the diameter of the posts, and gives rise to the phase retardation of the transmitted light. We should note that this kind of waveguide mode can be generated in a broad operating band since kz can be changed continuously. It not only ensures the relatively high transmittance of leaky-mode resonators in a broadband range and achieves a quasi-linear phase retardation to ease the harsh fabrication conditions encountered by the visible-frequency meta-devices; more importantly, the sum of the phase shift by the waveguide mode doesn’t have any theoretical limit, which is the underlying cause of the broadband effect.
Fig. 3 Near field distribution in the silicon posts. The diameters of the post are 120 nm (a, b) and 165 nm (c, d). The wavelength of the x - polarized incident light is 650 nm. The color of the images and the black arrows in (a, c) represent the magnitude of the magnetic field along y – axis and the electric field in x – z plane, respectively; and in (b, d) represent the magnitude of the electric field along x – axis and the magnetic field in y – z plane, respectively.
We find in Fig. 4(a) that by changing the dimensions of resonators, not only a 2π but also a 3π phase delay can be realized at short wavelengths. Although the phases change with the wavelength of the incident light for a dimension fixed resonator array due to different wave vectors for 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 2π at the longer wavelength and from π to 3π at the shorter wavelength. The simulations in Fig. 4(a) verify its feasibility. When the size a ranges from 110 nm to 250 nm, the phase delay changes from π to 3π at 600 nm but from 0 to 2π at 800 nm. At the same time, the amplitude of the transmission light shown in Fig. 4(b) is still relatively high and fluctuates only slightly from 600 to 800 nm. Figures 4(c) and 4(d) present the phase delays and amplitudes of the transmission lights for six constituent resonators to compose a super cell as shown below. The dimensions of the resonators labeled by 1 to 6 are 110, 120, 135, 150, 170 and 210 nm, respectively. The lattice constant d is 300nm. It is perspicuous that the phase delays of the six chosen meta-atoms uninterruptedly cover a range of 2π from 600 to 750 nm with high transmissions, which makes the fabricated metasurface achieve a considerable diffraction efficiency in this wavelength range.
Fig. 4 The broad bandwidth of the metasurface. (a, b) Numerical simulations of phase delay and amplitude of transmission light with an infinite metasurface as a function of wavelength from 550 nm to 800 nm and the length of meta-atoms from 50 nm to 250 nm. The dashed black lines represent the equiphase lines of π and 3π, respectively. (c, d) the phase delay and the amplitude of transmission light through the six chosen meta-atoms at wavelength of 600 nm (blue circle), 650 nm (orange square), 700 nm (gray diamond) and 750 nm (yellow triangle).
3. Experimental results
The computer-generated holograms were designed to show the complex two dimensional phase modulation with the polarization independence and the broad bandwidth. For a better image quality, we utilize eight basic meta-atoms with different diameters from 110 nm to 220 nm in a 300 nm square lattice to provide a more precise phase control. We fabricated the devices on a quartz substrate. The process began with the deposition of a 350nm-thick intrinsic amorphous silicon film using an Inductively Coupled Plasma Enhanced Chemical Vapor Deposition System (ICPECVD, Sentech SI 500D). A 50-nm thick aluminum film was then deposited via electron beam evaporation, used as a charge-dissipation layer and hard mask. The 300nm thick positive electron beam resist (ZEP-520A) was coated and patterned using electron beam lithography (EBL, Vistec EBPG 5000 + ). The patterns were transferred into the aluminum and Si layer by subsequent etching using an Inductively Coupled Plasma (ICP, Sentech PTSA SI 500) etcher. Finally, the aluminum layer was removed at room temperature using aluminum etchant.
Figure 5(a) shows the target image of the designed hologram and Fig. 5(b) is the phase mask containing 800 × 800 pixels generated by the standard Gerchberg-Saxton phase-retrieval algorithm [47]. The scanning electronic microscope (SEM) image in Fig. 5(c) reveals that the configuration of the fabricated metasurface agreed very well with our design. In the high-efficiency band (600 nm – 800 nm), the high-quality reconstructed images for two orthogonal polarizations were taken by a single lens reflex camera (Canon 5D Mark II) as shown in Figs. 5(d)-5(g). The diffraction efficiencies (the ratio between the power of the target image field and the sum power of all transmitted light), which were measured by a power meter (Thorlabs PM100D) after a focusing lens to collect the transmitted lights, are as high as 88% and 90% for the two wavelengths (700 nm and 633 nm), respectively. What’s more, the absolute imaging efficiencies (the ratio between the power of the target image field and that of the incident light) are also measured as 32% and 31% for the two incident wavelengths. It is worth noting that although the green (532 nm) and blue (473 nm) holograms have a lower efficiency due to the intrinsic loss of silicon and the phase distortion, they still perform a good image quality as shown in Figs. 5(h)-5(k). Recently, meta-holograms using metasurfaces have been extensively investigated [48,49] as presented in Table 1. Our meta-holograms are fabricated for polarization-independent and broadband phase modulation with high efficiency for visible light in the transmission mode.
Fig. 5 Computer-generated meta-holograms. (a) The target image to generate using the metasurface. (b) The calculated phase mask for the target image. (c) The scanning electronic microscope (SEM) images of the fabricated sample (local view). The photographs of the generated holograms with (d, e) x – polarized and y – polarized incident red lights (700 nm), (f, g) x – polarized and y – polarized incident red lights (633 nm), (h, i) x – polarized and y – polarized incident green lights (532 nm), and (j, k) x – polarized and y – polarized incident green lights (473nm), respectively. The measured diffraction efficiency, related to the signal to noise ratio, is defined as the ratio between the power of the target image field and the sum power of all transmitted light. The absolute imaging efficiency is defined as the ratio between the power of the target image field and that of the incident light.
Table 1. Important parameters of recent reported meta-holograms.
To measure the precise broadband diffraction efficiency of meta-devices, we fabricated a standard gradient dielectric metasurface. Each super-cell is composed of six 350 nm-high resonators arrayed from small to large in dimension. Figure 6(a) is the local scanning electronic microscope image of the designed hologram pattern. The refraction angle can be calculated by the formula , which is from 17.0° to 24.0° in the wavelength range from 550 nm to 800 nm.
Fig. 6 Simulations and Experimental results of gradient metasurface. (a) Top-view and titled-view SEM images of the sample. The dimensions of the six chosen meta-atoms are 110 nm, 120 nm, 135 nm, 150 nm, 170 nm and 210 nm, respectively. (b) Photographs of the transmission light distribution at the wavelength of 550 nm to 710 nm. (c) The simulated near field distributions of gradient metasurface under the x – polarized and (d) y – polarized illuminations. The units of the legends are arbitrary. (e) The simulated far field distributions of gradient metasurface under the x – polarized and (f) y – polarized illuminations. The wavelength of the incident light is 650 nm in (c)-(f). (g) Measured and simulated diffraction efficiency (defined as the ratio of the power of anomalous refraction beam ( + 1 order) and the sum power of the + 1, 0, and −1 orders transmission light) spectra from 550 nm to 800 nm with x - and y -polarized incident light, respectively. (h) Measured and simulated transmittance (defined as the ratio of the power of anomalous refraction beam and the power of incident beam) spectra from 550 nm to 800 nm with x - and y -polarized incident light, respectively.
The periodicity and amplitude fluctuations of different meta-atoms can induce the weak undesired diffraction orders. To evaluate the bending efficiency, both the near field and far field distributions are depicted for two orthogonal polarizations as shown in Figs. 6(c)-6(f). In Figs. 6(c) and 6(d), the transmitted wavefronts are clearly deflected by the same angle, exhibiting the polarization-independent phase control of the gradient metasurface. The far field distributions shown in Figs. 6(e) and 6(f) reveal the high diffraction efficiency at the operating wavelengths.
Linearly polarized Gaussian beams in the range of 550 nm to 800 nm were generated by a supercontinuum laser (Fianium SC400-4). 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 800 nm. Both the x - and y - polarized incident beams were adopted to verify the polarization-independence. To visualize the results, a series of photos in Fig. 6(b) were taken to show the intensity distributions of transmission lights. From these images, the refraction angles do increase with the wavelength as expected. Figure 6(g) shows the measured diffraction efficiencies from 550 to 800 nm, which are higher than 75% from 600 to 800 nm. The peak efficiencies, 93% and 92%, are at 670 nm 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 [22,33]. In [22], the wavelength range is about 50 nm with the efficiencies higher than 50% and a peak diffraction efficiency of about 75%. In addition, the transmittances are 20% to 45% in the wavelength range of 550-800 nm as shown in Fig. 6(h), which conform to the simulations. Although the intrinsic loss of silicon at visible frequencies impedes the transmissions, they are still higher than the theoretical limit of 25% for the ultrathin metasurfaces (the height of the meta-atoms is much smaller than the wavelength of the incident light) [50]. The transmittances of 44% and 46% are observed at 760nm and 770nm for the x – and y - polarized incident beam, which are quite comparable to the recently reported light bending meta-devices such as 42% at 705 nm in [33], 36% at 1550 nm in [37], and 20% at 1800 nm in [51]. It should be noted that the 46% transmittance is absolutely not the upper limit. By exploring new materials with lower loss in the visible frequencies, higher transmittance can be expected. Two recently published articles [27,39] reported a 77% transmission for the anomalous refraction at 915 nm and a 75% transmission for the holograms around 1250 nm, where silicon exhibits a zero imaginary part of refractive index, which significantly paves a promising way to promote the transmission further.
The slight aberrations between two orthogonal polarizations were observed in Figs. 6(g) and 6(h). In fact, practical metasurfaces can hardly achieve a perfect polarization-independence even if the theoretical conditions are satisfied and the fabrication aberrations are reduced to infinitesimal. The intrinsic reason is that practical metasurfaces are surely composed of different types of meta-atoms to provide the arbitrary spatial phase modulation. Unlike the ideal periodic settings in simulations, the meta-atoms surrounding one specific meta-atom are different, and the resultant aberrations cannot be completely removed by improving the fabrication processing. Nevertheless, we have demonstrated in Fig. 2 that the phase distortions induced by the mismatched lattice, which is similar to the case of non-identical adjacent meta-atoms, are very weak and thus the aberrations between two orthogonal polarizations have been reduced to a very small degree. As mentioned above, one of the feasible ways to further improve the polarization-independence is to replace the standard basic units by specifically tailoring spatially dependent meta-atoms according to their surrounding environments. Furthermore, for a standard gradient metasurface composing of identical supercells as shown in Fig. 6(a), simultaneously optimizing the six resonators in one supercell should be better. If the light distribution also has a multi-fold symmetry, the polarization-independence can be guaranteed by the geometry symmetry of the light.
4. Conclusion
In conclusion, we both theoretically and experimentally demonstrate the realization of polarization-independent broadband dielectric metasurfaces with high efficiencies for visible light. The polarization-independence originates from the proper symmetries of resonators and arrays, and the broad bandwidth is achieved by inducing the TM10 waveguide mode in the resonator. Our metasurfaces decouple the phase manipulation from the polarization states and frequencies in transmission mode and possess the great potential to not only replace most of the conventional phase modulation optical elements such as lenses, prisms and phase plates by flat ones but also to design the next generation integrated photonic systems for imaging, communications and information processing.
Funding
National Basic Research Program of China (2013CB921904); National Natural Science Foundation of China (11474010, 61590933); Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (Y5691I11GJ); Youth Innovation Promotion Association CAS (Y5442912ZX).
Acknowledgments
The authors would like to thank Lipu Liu and Dong Yang for their help.
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