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Abstract
Since the electromagnetic resonance that happens in dielectric nanobricks can be meticulously designed to control both amplitude and polarization of light, an ultracompact, high-resolution and continuous grayscale image display method based on resonant dielectric metasurfaces is proposed. Magnetic resonance occurs in dielectric nanobricks can yield unusual high reflectivity depending on the polarization state of incident light, which paves a new way for ultracompact image display when the resonant metasurfaces consisting of nano-polarizer arrays operate. Governed by Malus’s law, nano-polarizer arrays featured with different orientations have been demonstrated to continuously manipulate the intensity of linearly polarized light cell-by-cell. Hence, it can practically enable recording a high fidelity grayscale image right at the sample surface with resolution as high as 84,667 dpi (dots per inch). This proposed resonant metasurface image (meta-image) display enjoys the advantages including continuous grayscale modulation, broadband working window, high-stability and high-density, which can easily find promising applications in ultracompact displays, high-end anti-counterfeiting, high-density optical information storage and information encryption, etc.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces, a kind of artificially designed two-dimensional planar structures, are composed of sub-wavelength structure antennas. By elaborately designing the geometry parameters of the metasurfaces, functionalities of phase modulation [1–15], amplitude adjustment [16,17], polarization control [18,19] and wavelength selection [20] can be realized. Therefore, metasurfaces exert these advantages and provide a new method when implementing the image display with high resolution and compactness. Recently, metasurfaces have been used in designing meta-nanoprinting and color filters [21–39]. However, most of them implement image display by their structure colors, which generates variety of colors but can hardly modulate the intensity of output beam. By combining Malus’s law with half wave plates, a method of encoding grayscale image in the polarization profile with a metal-insulator-metal (MIM) metasurface has been proposed [38]. The image information was decoded into a distribution of light intensity after passing through an analyzer, then a grayscale image with high-resolution is displayed. However, an additional analyzer is required to decode grayscale image information in this approach and the fabrication of multi-layer structure of the MIM metasurface is relatively complex, which may limit its practical applications.
In this paper, we propose a general meta-image display platform enabled with magnetic resonance [40–42], which is simply realized by assigning a single layer of silicon nanobrick arrays sitting on a dielectric substrate. A well-designed silicon nanobrick serves as a nano-polarizer, which can divide an incident beam into two parts: the reflected sub-beam with polarization along the long axis of nanobrick and the transmitted sub-beam with polarization along the short axis of nanobrick. By combining the polarization spectroscopic characteristic of the metasurfaces with Malus's law, we can realize an accurate and continuous light intensity modulation right at the surface of the meta-nanostructures. As a result, high-resolution and continuous grayscale image storage and display are achieved.
2. Unit-cell design and simulation of a resonant metasurface
The proposed resonant metasurface is composed of silicon nanobrick arrays sitting on a dielectric substrate. To simplify the fabrication process, the widely used silicon-on-insulator (SOI) material in semiconductor industry was employed to form the resonant metasurface and the schematic diagram of one unit-cell structure is illustrated in Fig. 1(a). For SOI material we used, the structure consists of three layers: a ground crystalline silicon substrate, a medium silica layer (the thickness d is 2 µm) and a top layer of crystalline silicon used for nanobricks fabrication (the height H is 220 nm). The dispersion curves of silicon and silica are given in appendix A. All nanobricks in our design have identical dimensions with length L, width W, height H and cell sizes C but different orientation angles α (0° ∼ 90°). The size difference between the long and short axes of the nanobrick forms unequable electromagnetic responses in two orthogonal directions. As a result, we can adjust the electromagnetic responses along the long and short axes of the nanobrick and control the anisotropy. We used the commercially software CST STUDIO SUITE to perform the numerical simulations. By carefully optimizing the geometric parameters of the nanostructure (shown in Fig. 1(a)), the reflectivity of an incident beam with polarization direction along the short axis is suppressed to the lowest value whilst that along the long axis is almost reflected. The designed nanobrick is with L of 180 nm, W of 60 nm, H of 220 nm and C of 300 nm. With these nanobrick parameters, reflectivity versus wavelength and electromagnetic field distribution are simulated (details about the numerical simulations are provided in Methods), as shown in Figs. 1(b)–1(e). Here, the orientation angle of the nanobrick is fixed at 0°. The reflectivities of the incident beam with polarization direction along the long and short axes are labeled as Rl and Rs, respectively. From Fig. 1(b) we can see that most of the incident beam with polarization direction along the long axis of the nanobrick is reflected (85%), whilst only a small part of the incident beam with polarization direction along the short axis is reflected (9%) at the design wavelength (610 nm).
Fig. 1. Illustration and simulated results of the resonant dielectric metasurface based on SOI material. (a) Schematic diagram of the unit-cell nanostructure based on SOI material for polarization separation. The orientation angle α is defined as an angle between the x-axis and the long axis of the nanobrick. (b) Simulated reflectivity versus wavelength (540 ∼ 740 nm) when normally incident light is linearly polarized along the long and short axes, respectively. (c) Normalized electric fields at the cross-section of the nanostructure with incident light polarized along the long and short axes, respectively. (d-e) The vortex-like electric and enhanced magnetic field distributions at the cross-section of a nanobrick unit-cell when the incident light is polarized along the long axis direction. The orientation angle of the nanobrick in (b-e) is 0°, and the operating wavelength is 610 nm.
Due to the multi-beam interference occurs in the medium insulating layer (silica), Rs fluctuates between a maximum value of 37% and a minimum value of 7% when the wavelength varies from 540 nm to 740 nm, as shown in Fig. 1(b). The unwanted Rs will weaken the characteristic of polarizing separation. Fortunately, in the silica layer with a thickness of 2 µm, destructive interference happens in reflection while constructive interference happens in transmission at the design wavelength (610 nm). This makes most of the incident beam with polarization direction along the short axis be transmitted and then absorbed by the non-transparent silicon substrate. As a result, Rs exactly falls into one valley of the curve at the design wavelength, as shown in Fig. 1(b). Figure 1(c) shows the simulated electric field distributions at the cross-section of the nanostructure, which indicates that two orthogonal polarized beams are almost reflected and transmitted, respectively. Therefore, the designed nanostructure is capable to realize polarizing separation in reflection.
To investigate the unusual high value of Rl, we simulated electromagnetic fields with an incident beam polarized along the long axis direction, and the vortex-like electric and enhanced magnetic field distributions at the cross-section of a nanobrick are shown in Figs. 1(d) and 1(e). It indicates that a magnetic resonance happens in the long axis direction, accounting for the high value of Rl. The electromagnetic response difference between the two axes of the nanobrick and the multi-beam interference in the silica layer lead to a result that the resonant nanobrick can work as a reflective nano-polarizer.
3. Design of meta-image display
Since each nanostructure acts as a nano-polarizer, Malus’s law is applied to achieve precise and continuous intensity modulation by rotating the orientation angle α. With a linearly polarized (LP) incident beam, the Jones vector of output beam can be expressed as
Here, x-axis is chosen as the polarization direction of an incident LP beam and we define I0 as the intensity of the reflected beam when α = 0. As a result, the intensity of the reflected beam I can be expressed as
However, since Rs can’t be ignored, the influence has to be considered. Here, we can modify Eq. (2) as where I1 is the intensity of the reflected beam when α = 90° and I2 is intensity of the total reflected beam as a function of α. It is obvious that the nanobrick still can accurately modulate the intensity of the reflected beam. To verify this function, we simulated the reflectivity with variable α (details are described in Methods) and calculated the theoretical values of I2 according to Eq. (3), the corresponding results are shown in Fig. 2(a). It can be seen that the simulated and theoretical values are in good agreement, which proves that precise and continuous light intensity modulation can be realized by rotating the orientation angles of nanobricks. Figures 2(b)–2(d) illustrate the working principle of meta-image display based on light intensity modulation. When an x-axis polarized incident beam illuminates the designed metasurface normally, a grayscale image with 500 × 500 pixels is displayed right at the surface of silicon nanobrick arrays (the target image is shown in Fig. 2(c)). Figure 2(d) shows the specific details of the selected area from a square region with 5 × 5 pixels, and the left side shows the nanobrick orientations while the right side shows the modulated light’s amplitudes and polarization profiles. It shows that the intensity of the reflected beam can be modulated cell-by-cell with a theoretical resolution as the same dimensions of each unit-cell (300 nm × 300 nm), which proves the high performance of our proposed image display method based on resonant dielectric metasurfaces.Fig. 2. (a) Beam intensity of the simulated and theoretical results with different orientation angles, the normally incident beam is x-axis polarized and the nanostructure works at a design wavelength of 610 nm. All results are divided by I0 and then normalized to a range of 0 ∼ 1, where I0 is the beam intensity of the reflected beam when α = 0°. (b) Schematic diagram of the meta-image display. (c) Target grayscale image with 500 × 500 pixels and 256 grayscale levels. (d) Nanobrick orientations, modulated amplitudes of light and polarization profiles of the selected area from a square region with 5 × 5 pixels.
4. Experiments
The designed metasurface has dimensions of 150 × 150 µm2 (500 × 500 pixels), and the sample was fabricated by the standard electron-beam lithography (EBL) (detailed process is described in Methods). The photo and partial scanning electron microscopy (SEM) image of the sample are shown in Figs. 3(a) and 3(b). The orientation angles of the nanobrick arrays varies from 0° to 90°. Since the grayscale image is recorded right at the surface of the meta-nanostructures, an optical microscope (Motic BA310Met) is used to observe the image. No analyzer is required to acquire the meta-image since the intensity of reflected light can been modulated by the SOI metasurface pixel-by-pixel. A red filter with a center wavelength of 610 nm is inserted into the optical system of the microscope to match the designed wavelength. Meanwhile, an objective with magnification of 50 × is used to magnify the grayscale image and the results are shown in Figs. 3(c), 3(e)–3(h). Without a linear polarizer, the normally incident light acts as natural light with random polarization direction. Therefore, there is no pattern display, as shown in Fig. 3(e). If a polarizer is put into the optical system of the microscope, a clear image with abundant grayscale information appears when the incident beam is polarized along the x-axis, as shown in Fig. 3(c). Figure 3(d) is a partial zoom-in view of the image (observed by a 100 × objective), which shows that details of the image “cat” such as beards and textures can be seen clearly. Since the pixel dimensions are 300 nm × 300 nm, the resolution reaches 84,667 dpi (dots per inch), which is 63 times of conventional image display techniques based on liquid crystals (the pixel size of a general liquid crystal display is 19 µm × 19 µm) [43] and 29 times of conventional piezoelectric ink-jet printing (the resolution is 2,880 dpi). Therefore, a high-density and continuous grayscale image can be recorded and displayed resorting to the dielectric metasurface enabled with magnetic resonance. Figures 3(f)–3(h) show the images with different polarization states (θ = 45°, 90°, and 135°, respectively), and it should be noted that the light intensity distribution changes with different polarization states and only the image with θ = 0° (as shown in Fig. 3(c)) is close to the original target image. The transformation law of images’ brightness variation with different θ can be readily interpreted by Malus’s law, which indicates that the displayed meta-image strongly relies on the polarization state of an incident beam.
Fig. 3. (a) Photo and (b) partial SEM image of the fabricated dielectric metasurface. (c) The experimentally captured image with the sample illuminated by an x-axis polarized incident beam (θ = 0°). (d) A zoom-in view of the meta-image shown in (c). (e-h) Optical micrographs with other different polarization states of incident light at an operating wavelength of 610 nm. The scale bars and polarization directions are marked in the figures. (c, e-h) are captured with an objective of 50 × and (d) is captured with an objective of 100 × .
To explore the compatibility of the dielectric metasurface with different illumination conditions, we employed two different light sources to illuminate our sample and the experimental results are shown in Figs. 4(a)–4(c). We find that the displayed meta-images with sample illuminated by broadband sources (a halogen lamp and a flashlight) are also clear, although the contrast is slightly reduced. This phenomenon can be readily interpreted by observing the broadband responses of Rl versus wavelength shown in Fig. 1(b). The unwanted light Rs fluctuates when the wavelength varies in visible range, but the average value of parameter Rl/Rs which determines the contrast of the reflective image is still high, so the overall performance of image display is still acceptable in broadband spectra. Hence, it confirms that the proposed metasurface based on SOI material works well with the illumination of a broadband light source. Such a broadband response of the proposed meta-device can greatly reduce the observation requirements for practical applications.
Fig. 4. Optical micrographs of the metasurface sample illuminated by a halogen lamp of an optical microscope with (a) and without (b) a red light filter and (c) a general flashlight.
5. Applications and Discussion
One direct application of the proposed dielectric metasurface enabled with magnetic resonance is ultracompact image display, which can provide a continuous intensity manipulation right at the nanostructure surface. In addition, the proposed metasurface is promising to be combined with wavelength multiplexing [27,39] to produce colorful images in the near field. Besides ultracompact image display, here we propose another promising application with the proposed meta-device: optical anti-counterfeiting. Because of the polarization-dependent characteristic of the dielectric metasurface, the near-field information can be clearly viewed only by using illumination light with a given polarization state. Therefore, our proposed dielectric metasurface can improve the security of anti-counterfeiting compared with conventional anti-counterfeiting techniques.
6. Conclusions
We present a resonant meta-image display by using SOI material based on light intensity modulation. By manipulating the magnetic resonance, a nanostructure acting as a nano-polarizer is designed to reflect most of light with polarization direction along the long axis of the nanostructure. As the target grayscale image is reproduced clearly (the resolution reaches 84,667 dpi) with the fabricated sample illuminated by different light sources, it is proved that an accurate and continuous grayscale modulation can be achieved by merely rotating the orientation angle of each silicon nanobrick. With the advantages of continuous grayscale modulation, broadband working window, high-stability and high-density, simplicity and compatibility with SOI material, our proposed meta-device for image display possesses a great potential in high-density optical information storage, high-end anti-counterfeiting, information encryption and so on.
7. Methods
7.1 Numerical simulations
The reflected spectra and electric/magnetic field profiles for the proposed SOI metasurface were investigated by approach of commercial simulation tools, CST STUDIO SUITE. We optimized the geometric parameters of the silicon nanobrick (cell size C, length L and width W), and the unit-cell structure is shown in Fig. 1(a). A normally incident plane wave was assumed to be polarized along the long or short axis, and a periodic boundary condition of the unit-cell structure was satisfied, so that the SOI based nanobrick arrays with identical orientation angles could be emulated. The reflectivity was obtained by the reflection port and electromagnetic field distributions were collected by field monitors when α = 0°. Our optimization goal was to make the magnetic resonance only happen along the long axis of the nanobrick and realize polarization separation. We swept L and W from 50 nm to 240 nm in steps of 10 nm while the cell size C was fixed at 300 nm. The wavelength of the incident beam varied from 540 nm to 740 nm; the thickness d of the silica layer and the height H of nanobricks were fixed at 2 µm and 220 nm respectively due to the fixed structure of the SOI material. Then we selected an optimized unit-cell structure (length L = 180 nm, width W = 60 nm and cell size C = 300 nm) and the corresponding simulated results are shown in Figs. 1(b)–1(e). Meanwhile, in order to testify that the nanostructure could modulate light intensity continuously and accurately, we swept α from 0° to 90° in steps of 5° at an operating wavelength of 610 nm when the incident beam was x-axis polarized and the simulated result is shown in Fig. 2(a).
7.2 Sample fabrication
The sample was fabricated on a SOI substrate (220 nm top silicon and 2 µm buried oxide) with a standard EBL process. Firstly, a standard electron beam process was used for patterning a polymethyl methacrylate (PMMA) mask on the SOI substrate. After that, a 30 nm Cr film was deposited on the sample via thermal evaporator. Subsequently, the sample was immersed in hot acetone of 75°C and cleaned by ultrasonic waves. Here, Cr was used as an etch mask, and the Cr-free part was removed by reactive ion etching (RIE). In this process, a mixture of 300 sccm (standard-state cubic centimeter per minute) CHF3, 250 sccm SF6, and 95 sccm O2 (at 200 W RF power) was used for etching. Then the Cr mask was removed by a Cr etchant. Finally, only silicon nanobrick arrays remain on the substrate.
Appendix A: Dispersion characteristics of crystalline silicon and silica
Figure 5 shows the refractive indexes versus wavelength (540 ∼ 740 nm) of crystalline silicon and silica used in the SOI material. Red and green curves in Fig. 5(a) represent the real and imaginary parts of the refractive index, respectively.
Funding
National Natural Science Foundation of China (11574240, 11774273, 61965006, 61640409, 61805184); Outstanding Youth Funds of Hubei Province (No. 2016CFA034); the Open Foundation of State Key Laboratory of Optical Communication Technologies and Networks, Wuhan Research Institute of Posts & Telecommunications (No. OCTN-201605); Postdoctoral Innovation Talent Support Program of China (BX20180221); China Postdoctoral Science Foundation (2019M652688); Natural Science Foundation of Guangxi Province (2017GXNSFAA198048).
Disclosures
The authors declare no conflicts of interest.
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