1. Introduction

Meta-surfaces are two-dimensional planar optical elements composed of artificially designed and fabricated sub-wavelength meta-atoms. They exhibit unique optical properties not existing in natural materials, such as negative refraction [1,2], near zero refraction [3–5], hyperbolicity [6–8], and optical chirality [9]. Traditionally, meta-atoms are made of particular metal materials, e.g. gold and silver. However, in the optical high-frequency region, the presence of ohmic damping which brings about absorption reduces operating efficiency of optical meta-surfaces. In order to manipulate the amplitude and phase of electromagnetic waves, meta-surfaces generally require complex geometric structures, such as V-shaped [10], H-shaped [11], and U-shaped [12], rendering the fabrication of low-cost and large-area devices impractical. Recently, all dielectric meta-surfaces have been widely used for holographic imaging [13], meta-lenses [14], and harmonic generation [15,16], etc. Due to its low loss, high efficiency, and the ability to manipulate the amplitude and phase of electromagnetic waves by scaling the size of simple geometric structures (such as discs [17], cylinders [18], and prisms [19]). However, whenever the metal meta-surface or the dielectric meta-surface, operating in the visible and near-infrared regions, they all require the size of meta-atoms to be hundreds of nanometers. To date, the widely used processing methods of electron beam lithography and focused ion beam lithography have some defects, such as high manufacturing difficulty, small area, and high cost [19–21], which hinder the commercialization of optical meta-surface functional devices.

Recently, researchers have proposed the use of dielectric meta-surfaces to realize perfect reflectors, mainly exploiting the electric and magnetic dipole resonances in dielectric meta-atoms to cause perfect reflections in specific spectral regions [22]. Compared with traditional infrared mirrors such as Bragg reflectors or gold mirrors, dielectric meta-surface reflectors have a thinner thickness and better signal-to-noise ratio performance, which can generate electric field nodes at the interface due to peculiar magnetic mirror behaviors [23]. The perfect reflection characteristic of the meta-surface reflector has the prospect of being used in full-color reflection displays [24], vertical cavity surface emitting laser cavity mirrors and protecting surfaces against high-power irradiation [25,26]. The realization of the perfect reflection is mainly due to the fact that the material constituting the meta-surface reflector has a single negative property (negative permittivity or negative permeability) in the designed spectral region. The negative permittivity and negative permeability of the meta-surface reflector are derived from electric dipole resonance and magnetic dipole resonance. Meanwhile, the frequency shift of the dipole resonance peak can be achieved by modulating the size of meta-atoms, thereby moving the perfect reflection spectrum to regions of interest. Similar to metallic split-rings, magnetic dipoles are induced by the presence of circular displacement currents in high-index dielectric meta-atoms [27]. As a result, the dielectric materials constituting the meta-surface reflector should have high refractive index and lossless characteristics (titanium dioxide in the visible region and silicon or gallium arsenide in the infrared region). The reason for utilizing silicon resonators is that silicon has a fairly high refractive index, almost zero absorption loss in the near infrared region, as well as its well-developed top-down nanofabrication process. Experimentally, meta-surface reflectors composed of tetragonally distributed disc-shaped and cross-shaped silicon meta-atoms are demonstrated using electron beam lithography, which achieved perfect reflection in the near-infrared region [28,29]. Due to the limited processing area and low efficiency of electron beam lithography technology, it cannot provide large-sized samples with acceptable cost, limiting the economic potential for practical applications. As an alternate, researchers developed nanosphere lithography technology to prepare large-area meta-surface reflectors [30]. However, this technology can only prepare a hexagonal periodically distributed disc or cylindrical structure and it is prone to multi-layer stacking and defects in the self-assembly process [31,32]. In order to overcome the shortcomings of the above-mentioned nanostructure preparation technology, researchers also used stepper lithography and deep ultraviolet projection lithography technology to prepare large-area nanostructure arrays [33–35], which is of very high cost. As a result, the current preparation technologies such as electron beam lithography, nanosphere lithography or deep ultraviolet projection lithography cannot meet the requirements of high precision, large area and low-cost at the same time.

In this work, in order to efficiently fabricate the meta-surface reflector on a large scale, a digital holography lithography technique that can continuously change the spatial frequency and orientation of interference fringes is adopted to fabricate the silicon resonators array. By controlling two orthogonal interference exposure dosages and spatial frequency, resonators of different shapes can be prepared, such as discs, diamond-shaped discs and elliptical discs, indicating the high flexibility of the newly proposed technique. Compared with electron beam lithography, this technology has higher work efficiency and simpler operation process. For example, the 100 mm² sample prepared in this article only takes 4 mins, it contains millions of resonators, and its processing speed is about 500 times higher than that of electron beam lithography. We have also analyzed in detail the physical mechanism for achieving perfect reflection using high refractive index silicon discs in the near-infrared region, which is attributed to the spectral separation of electric and magnetic dipole resonances.

2. Experimental section

Considering the convenience of experimentally preparing two-dimensional (2D) resonator arrays, the polarization-independent characteristics of meta-surface reflectors, and the tunability of perfect reflection spectral region by changing the aspect ratio, we propose two 2D subwavelength resonator structures with conventional shapes. The two proposed meta-surface reflectors for near-infrared region are composed of pixelated 2D silicon (Si) disc resonator arrays and Si diamond-shaped disc resonator arrays, as shown in Figs. 1(a) and 1(c), where the middle spacer is a 2 µm thick buried silicon oxide (SiO₂) layer and the substrate is Si, respectively. The geometric parameters of the discs array are: period (P1 = 720 nm), diameter (D = 390 nm), and height (H = 200 nm). We use FDTD Solutions to perform numerical simulations on meta-surface reflectors, in the simulation model, the meta-surface reflector was treated as a transverse infinite plane by considering a single meta-atom with periodic boundary conditions in x and y directions. Perfect Match Layer boundary conditions were used in z direction so that reflected and transmitted light from meta-surface is not reflected via the boundaries. The incident light propagates along the z direction, and the polarization is along the x direction. The meta-surface reflector composed of the disc resonators array was designed to achieve perfect reflection in the near-infrared (1050 to 1110 nm) as shown in Fig. 1(b). The geometric parameters of the diamond-shaped discs array are as follow: period (P2 = 760 nm), length (L1 = L2 = 460 nm), and height (H = 200 nm). The meta-surface reflector composed of the silicon diamond-shaped disc resonators array achieves perfect reflection in the near-infrared from 1040 nm to 1100 nm as shown in Fig. 1(d).

 

Fig. 1. (a) The schematic architecture of the designed meta-surface reflector composed of discs. (b) The simulated reflection spectrum of the meta-surface reflector composed of discs. (c) The schematic architecture of the designed meta-surface reflector composed of diamond-shaped discs. (d) The simulated reflection spectrum of the meta-surface reflector composed of diamond-shaped discs.

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The designed meta-surface reflectors were realized by fabricating disc resonators in the crystalline Si device layer of a silicon-on-insulator (SOI) wafer. The SOI wafers consisted of a Si handle wafer, a 2 µm thick buried SiO₂ layer, and a 200 nm thick crystalline Si device layer. Since the SOI wafer has a reflectivity of about 50% at the laser wavelength of 355 nm, the incident light and reflected light will produce a standing wave effect in the photoresist and damage the photoresist mask structure. In order to reduce the influence of the standing wave effect, we will use low pressure chemical vapor deposition (LPCVD) to deposit a layer of silicon nitride (Si₃N₄) on the SOI wafer for anti-reflection purpose. We utilize the transfer matrix method to calculate that the thickness of the silicon nitride layer is 40 nm [36], which can achieve the lowest reflectivity of 25% (Fig. 5). Figure 2(a) schematically illustrates the fabrication process of the proposed meta-surface, including low-pressure chemical vapor deposition of silicon nitride, spin-coated photoresist, orthogonal interference lithography, development, reactive ion etching, and removal of the photoresist mask. Before being spin-coated with the photoresist, the Si₃N₄-SOI sample was placed in an oven with a tackifier (HMDS) for pretreatment at 90 ${\circ{C}}$ for 30 min. The photoresist (RZJ-390PG) layer of ∼350 nm was firstly spin-coated onto a Si₃N₄-SOI substrate using spin-coater at 3500 r/min for 30s and baked on a 100 ${\circ{C}}$ hot plate for 1 min.

 

Fig. 2. (a) The preparation process of the metasurface reflector. (b) The optical principles of digital holographic lithography. (Inset (b1) shows ${\pm} 1$ orders of diffracted beams in the experimental light path. Inset (b2) shows the working principle of theoretical calculation). (c, d, e) The light intensity distribution diagram of two orthogonal interference exposures used to prepare discs array, diamond-shaped discs array, and elliptical discs array. (f) SEM images of pixelated two-dimensional silicon discs array and 10 mm${\; } \times $ 10 mm sample image.

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In order to fabricate the meta-surface on a large scale, the periodic photoresist discs array was fabricated by means of the fast and simple continuously variable spatial frequency and fringe orientation photolithography (SVG Corporation, Nanocrystal) process. Digital holographic lithography technology adopts the strategy of combining multi-beam interference exposure and digital control of the precise movement of the two-dimensional translation stage, which can realize 8 inches of processing area, and the processing efficiency can reach 25 $\textrm{m}{\textrm{m}^2}$ per min. The principle of lithography is shown in the Fig. 2(b). Firstly, the laser beam of 355 nm is expanded and collimated by an expander system, secondly, this plane wave is transmitted through a 4F system with a diffraction grating, and the function of the diffraction grating is to form ${\pm} 1$ orders of diffracted beams at the focal plane. After that, only ${\pm} 1$ orders of diffracted beams are allowed to pass through the objective lens (Inset (b1) shows ${\pm} 1$ orders of diffracted beams) and are focused on the photoresist to form an imaged interference pattern. Interference fringes of different periods and orientations can be obtained by changing locations and orientations of the diffraction grating (Inset (b2) shows the working principle of theoretical calculation). When the diffraction grating location changes, ${\pm} 1$ orders diffracted beams with different distances will be formed at the focal plane, which will change the double-beam interference angle on the photoresist plane, and finally form imaged interference patterns with different periods. In order to obtain 2D resonator arrays, we adopt an orthogonal interference lithography strategy, which only needs to automatically control the two orthogonal orientations of the diffraction grating. Since digital holographic lithography technology can automatically change the fringe orientation and space frequency of the output light field and the output power of the laser, we can obtain meta-surfaces with different resonator geometries by modulating the exposure parameters of the two orthogonal interference lithography steps such as exposure dosages and the space frequency. As shown in the theoretical model of Fig. 2(c), the discs array can be prepared by making the two orthogonal interference lithography exposure dosages equal and the fringe space frequency equal. By making the two orthogonal interference lithography exposure dosages unequal and the fringe space frequency equal, the diamond-shaped discs can be obtained, as shown in Fig. 2(d). The two orthogonal interference lithography exposure dosages have equal energy and unequal fringe space frequency, and elliptical discs can be obtained, as shown in Fig. 2(e). In the future, the third strategy can be used to engineer the shape anisotropy of the nano-antennas, which may be exploited for polarization dependent applications, such as meta-surface polarization splitters [37]. Because we utilize the method of combining pixelated interference lithography and digitally controlled two-dimensional translation stage to prepare meta-surface devices, it has the advantages of large area and high efficiency. Figure 2(f) shows the prepared sample image and the SEM image showing the pixelated arrays. As an example of the process efficiency, we point out that it only costs 4 min to fabricate millions of photoresist discs over an area of 100 $\textrm{m}{\textrm{m}^2}$, which is about 500 times faster than the e-beam lithography process.

In our process, the photoresist discs array was developed in NaOH solutions (6‰) for 6 s and dried by electric blow drier. The photoresist discs act as a mask during the subsequent etching process. The device layer of the wafer was then etched using reactive ion etching (RIE) to create the arrays of Si3N4-Si resonator arrays. The gas used to etch Si3N4 are SF6, CHF3 and He, and the corresponding gas flows are 8 sccm, 10 sccm and 150 sccm. In addition, the gas used to etch $\textrm{Si}$ are SF6 and He, and the corresponding gas flows are 15 sccm, and 150 sccm. Etching rates of Si3N4 and Si are 200 nm/min and 400 nm/min, respectively. Finally, the device was placed in a small beaker with acetone and sonicated for 5 minutes, then it was rinsed with deionized water for 2 min to remove redundant photoresist and was dried with electric blow drier.

3. Results and discussion

Firstly, we will introduce in detail the physical conditions that a meta-surface reflector needs to meet. In case of normal incidence, the reflectance for the semi-infinite medium can be expressed as

Utilizing the processing methods introduced in the experimental section, we experimentally prepared three nano antennas, namely discs, truncated cones and diamond-shaped discs, as shown in Figs. 3(a)–3(c). The etching mask of the first two structures is the nano-disc patterned photoresist, and the etching mask of the third structure is diamond-shaped nano-disc patterned photoresist. The reflectance from the meta-surface reflectors were measured using a custom-built infrared spectrometer and the incident light was at small tilt angle to the meta-surface reflector normal. The reflectance from the meta-surface reflectors was normalized to the reflectance from a silver mirror. In order to better compare the experimental spectrum and the simulated spectrum, the material properties in the simulation model are derived from the ellipsometer measurement data, as shown in Figs. 6(a) and 6(b), and the structural geometric parameters are closer to the experimental values. In principle, we should remove the anti-reflection layer (Si₃N₄) on the device, but through simulation results, it is found that the presence of the anti-reflection layer will not have a noticeable impact on the overall reflection performance of the meta-surface reflector. We anticipated that the thickness of the Si₃N₄ layer is only 40 nm and may not affect strong dipole resonances in resonators. Therefore, we did not remove Si₃N₄ layer in the experiment, because the presence of Si₃N₄ can prevent the oxidation of Si and prevent the performance degradation of the meta-surface reflector from long-term exposure to the air.

 

Fig. 3. SEM image of discs array (a), truncated cones array (b), and diamond-shaped discs array (c). Measured and simulated reflectance spectra of discs array (d), truncated cones array (e), diamond-shaped discs array (f). Electric and magnetic dipole spectra of a disc (g) truncated cone (h), diamond-shaped disc (i).

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The reflectance spectra of meta-surface reflectors composed of resonators with different shapes are measured and are compared with the numerically calculated reflectance spectra in Figs. 3(d) –3(f). For the disc resonators array, the geometric parameters are D = 370 nm, H1 = 200 nm, H2 = 40 nm, P = 720 nm, where H1 is the thickness of the Si layer, H2 is the thickness of the Si₃N₄ layer, and the roughness is added to the side wall of the disc (the inset in Fig. 3(d)). The reflection spectrum results show that the numerically calculated results are in good agreement with the experimental results in the perfect reflection region of 1020 nm to 1095 nm, and that the presence of Si3N4 layer can only cause a slight extension, as shown in Fig. 3(d). The maximum measured reflectance is 99.95% at 1055 nm and the average reflectance is 97.93% over the wavelength span of 75 nm. For the truncated cone resonators array, the geometric parameters are D1 = 340 nm, D2 = 390 nm, H1 = 200 nm, H2 = 40 nm, P = 720 nm (the inset in Fig. 3(e)), where D1 is the diameter of the upper plane and D2 is the diameter of the lower plane. The reflection spectrum results show that the numerically calculated results are in good agreement with the experimental results in the perfect reflection region of 1025 nm to 1105 nm, as shown in Fig. 3(e). The maximum measured reflectance is 99.5% at 1040 nm and the average reflectance is 97.61% over the wavelength span of 80 nm. For the diamond-shaped disc resonators array, the geometric parameters are L1 = 430 nm, L2 = 430 nm, H1 = 200 nm, H2 = 40 nm, P = 760 nm (the inset in Fig. 3(f)). The reflection spectrum results show that the numerically calculated results are in good agreement with the experimental results in the perfect reflection region of 1020 nm to 1105 nm, as shown in Fig. 3(f). The maximum measured reflectance is 99.21% at 1045 nm and the average reflectance is 97.41% over the wavelength span of 85 nm. Outside the perfect reflection region, there are some deviations between the experimental results and the simulation results. We speculate that this is caused by the deviation of the structural parameters from the design values, the scattering from surface roughness of the SiO₂ film resulting from the etching process, and the interference of the multilayer films between the pixelated arrays. In order to verify that the perfect reflection region mentioned above is mainly derived from the spectral separation of electric and magnetic dipole resonances, the spectrum of multipole decomposition can be calculated using Green dyadic method that is a frequency domain technique, solving Maxwell’s equations for monochromatic fields [40]. For each resonator structure, corresponding electric and magnetic dipole spectrums are shown in Figs. 3(g)–3(i), respectively. From the decomposition spectrum, we can confirm the existence of electric and magnetic dipole resonances in the perfect reflection region.

Meanwhile, S-parameter retrieval and generalized sheet transition conditions (GSTCs) can be performed to obtain meta-surface properties [41,42], which were numerically calculated using FDTD SOLUTIONS. Figures 7(a) and 7(b) illustrate the equivalent electromagnetic properties of the meta-surface, namely a region where $\frac{{\mu _{eff}^{\prime}}}{{\varepsilon _{eff}^{\prime}}} < 0$ and ${Z^{\prime}} = 0$ from 1020 nm to 1095 nm. Perfect reflection is essentially a collective effect of meta-atoms array directional radiation. To illustrate the perfect reflection more vividly, next, we will give a qualitative explanation from the perspective of radiation. Figure 4(a) graphically illustrates that when the phase difference between the electric dipole and the magnetic dipole radiation is $\pi $, the meta-surface reflector can achieve perfect reflection. They interfere destructively with each other in the forward direction, and interfere constructively in the backward direction. When the meta-surface is composed of silicon disks with this property, due to the destructive interference between adjacent disks in the lateral direction, only the scattering into the + z direction exists and causes perfect reflection in the + z direction. In order to illustrate that the phase difference between the electric dipole radiation and the magnetic dipole radiation in the perfect reflection region is $\pi $, we calculate the phase difference between the electric dipole moment and the magnetic dipole moment, as shown in Fig. 4(b), the result shows that the phase difference in the perfect reflection region is close to $\pi $.

 

Fig. 4. (a) The schematic diagram of backward constructive interference between ED and MD radiation and perfect reflection in the xz-plane. (b) The phase difference between the electric dipole moment and the magnetic dipole moment. Demonstration of the radius (c) and period (d) of the disc effect on the reflection performances of the meta-surface reflector at normal incidence.

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To further understand the origin of the perfect reflection region, the influence of the disc radius on the reflection spectrum has been investigated. As shown in Fig. 4(c), when the radius of the disc decreases, the perfect reflection band splits into two perfect reflection peaks. As the radius value decreases further, the reflection peak caused by electric dipole resonance disappears, and the reflection peak caused by magnetic dipole resonance blue shifts. This is because the magnetic dipole resonance appears approximately at the spectral position of $\lambda $=n*D (n refers to the refractive index of silicon). In order to reveal whether there is electromagnetic field coupling between disc resonators to affect the performance of meta-surface reflectors, we examined the influence on the reflection spectrum of the meta-surface reflector with a change of the period (P), as depicted in Fig. 4(d). It clearly shows that the change of the period will not seriously affect the performance of the perfect reflection zone, but will only cause a slight red shift of the perfect reflection zone. This result demonstrates that the resonance of the electric dipole and the magnetic dipole produce the local field enhancement without coupling.

4. Conclusion

In summary, utilizing the electric and magnetic dipole resonances generated in high refractive index dielectric silicon resonators, we design and fabricate meta-surface reflector that achieve perfect reflection in the near infrared short wavelength region. The peak reflectance and average reflectance of the meta-surface reflectors composed of three structures of disc, truncated cone and diamond-shaped disc prepared experimentally in their perfect reflection regions are 99.95% and 97.93%, 99.5% and 97.61%, 99.21% and 97.41%, respectively. Furthermore, digital holography lithography with continuously variable spatial frequency and fringe orientation is adopted to fabricate large-area perfect reflection meta-surface. The fabrication strategy with the high processing efficiency and low cost will open up a new avenue for large-area optical meta-surfaces, particularly advantageous in mass production of optical communication devices, semiconductor lasers, and image differentiation, etc [43].

Appendix

• 1. Anti-reaction layer thickness design and anti-reaction effect.
• 2. Refractive index of silicon and silicon nitride measured by ellipsometer.
• 3. Equivalent electromagnetic parameters of meta-surface reflector.

 

Fig. 5. (a) The relationship between silicon nitride film thickness and reflectivity. (b) Comparison of the reflectivity of the film system before and after depositing the anti-reactive layer.

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Fig. 6. (a) The real and imaginary parts of the refractive index of silicon. The measurement data show that silicon has low loss and high refractive index characteristics in the designed perfect reflection spectrum region. (b) The real and imaginary parts of the refractive index of silicon nitride.

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Fig. 7. (a) Real part of equivalent permittivity and equivalent permeability of meta-surface reflector. (b) The imaginary part of the equivalent refractive index and the real part of the equivalent impedance of the meta-surface reflector.

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Funding

National Natural Science Foundation of China (51873060, 61822504, 61974100); Natural Science Foundation of Jiangsu Province (BK20181166); National Science Foundation of the Jiangsu Higher Education Institutions of China (18KJB510040); Collaborative Innovation Center of Suzhou Nano Science and Technology; Priority Academic Program Development of Jiangsu Higher Education Institutions.

Disclosures

The authors declare no conflicts of interest.

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