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Abstract
Enabled with both magnetic resonance and geometric phase, dielectric nanobrick based metasurfaces have shown their unusual abilities to produce high-definition and high-efficiency holographic images. Herein, we further show that such a metasurface can not only project a holographic image in far field but also record a grayscale image right at the metasurface plane simultaneously, merely with a single-celled nanostructure design approach. Specifically, each nanobrick in a unit-cell of the metasurface acts as a half-wave plate and it can continuously rotate the polarization direction of incident linearly polarized light. Governed by Malus law, light intensity modulation is available with the help of a bulk-optic analyzer and a continuous grayscale image appears right at the metasurface plane. At the same time, the concept of orientation degeneracy of nanostructures can be utilized to generate a 4-step geometric phase, with which a holographic image is reconstructed in far field. We experimentally demonstrate this multifunctional meta-device by employing the widely used silicon-on-insulator (SOI) material and all results agree well with our theoretical prediction. With the novel features of easiness in design, high efficiency, broadband spectrum response, strong robustness, high security and high information density, the proposed SOI-based metasurfaces will have extensive applications in optical information security and multiplexing.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces, with the ultrathin two-dimensional (2D) planar structure designed artificially, have shown their excellent capabilities in manipulating light at the subwavelength scale [1–22]. With the superiority in the ultra-small size and ultra-light weight, metasurfaces have experienced a rapid development over the past decade. Early works were demonstrated by using metallic nanostructures [23,24]. However, due to the ohmic loss and low transmission efficiency of metallic materials, more attentions on all-dielectric metasurfaces have been attracted in recent years [25–37].
Because of low loss in visible spectra, economical fabrication and high compatibility with the semiconductor industry, crystalline silicon based on the silicon-on-insulator (SOI) structure provides a new potential option for metasurfaces. Therefore, more and more SOI-based metasurfaces have exhibited their excellent performances in meta-holography [35], wavefront shaping [36], high-resolution display [37], optical information multiplexing [38], and anti-counterfeiting technologies [39]. In the meanwhile, with the upgrading of the optical application requirements, multifunctional metasurfaces have emerged gradually [40,41], and researchers have focused on the combination of nanoprinting and holography with a single metasurface [32,42–46]. Among them, enabled with the orientation degeneracy of anisotropic nanostructures, the Malus-assisted metasurfaces has shown their unique advantages in ultra-simple structure and high information density. However, the diffraction efficiency of the Malus metasurface is generally lower than 8%, as limited by the design principle based on nano-polarizer rather than half-wave plate and the choice of the metallic materials [44]. Although the selection of dielectric materials can improve the diffraction efficiency of the multifunctional metasurface, it is still lower than 20% in recent reports [42,43].
Here, we design and experimentally demonstrate a SOI-based multifunctional metasurface to integrate two independent optical images, based on simultaneous polarization and phase controls. Both the polarization and phase manipulation depend on the configuration of nanobrick orientation rather than its dimensions. Hence, with the uniform dimensions of the nanobricks and the compatibility of the SOI structure, it can tremendously reduce the complexity of the metasurface design and fabrication. Moreover, since an ideal half-wave plate can reach a 100% polarization conversion efficiency in designing a geometric metasurface, the low-efficiency issue that multifunctional meta-devices always experience can be significantly alleviated. Under the linearly polarized (LP) light illumination, the proposed multifunctional metasurface shows the excellent polarization control characteristics; while under the circularly polarized (CP) light illumination, it is a typical holographic device based on the geometric phase modulation. The simultaneous controls of the polarization and phase can therefore generate a near-field grayscale image and a far-field holographic image independently, and thus one image can be hidden behind another totally different image. Therefore, our multifunctional metasurface can not only facilitate the large-scale production and applications, but also provide high efficiency and high security performance.
2. Working principle for simultaneous polarization and geometric phase controls
We assume that each SOI nanobrick can act as a reflective half-wave plate, and the complex reflection coefficients along the nanobrick’s long and short axes are 1 and -1, respectively [35]. The Jones matrix of the nanobrick can be written as
When a LP lightwave polarized along x axis illuminates the half-wave plate, the Jones vector of the reflected light can be expressed as
Therefore, through elaborately controlling the orientation distribution of nano-half-wave plates, we can encode two different types of meta-images within a single metasurface under the illumination of different polarized light. One is the continuous grayscale image based on the polarization rotation, and the other is the holographic image based on the geometric phase manipulation. When carefully analyzing the output intensity of LP light, it can be found that there are four different choices of the orientation angle (e.g. $- \frac{\pi }{2} - \alpha ,{\; } - \alpha ,{\; }\alpha ,$ and $- \frac{\pi }{2} - \alpha)$ corresponding to an equal intensity, which can be named as the orientation degeneracy of anisotropic nanostructures. The orientation degeneracy indicates that for each pixel in a metasurface, there is a one-to-four mapping relationship between the intensity design of the grayscale image and the phase option of the holographic image. Consequently, the independence between these two images can be guaranteed. According to the intensity distribution of the grayscale image, we can use the simulated annealing algorithm [47] to get an optimal phase distribution to generate the totally different holographic image.
3. Design of the multifunctional metasurface
SOI material, widely used in the semiconductor industry, is employed to form our multifunctional metasurfaces. The SOI-based metasurface has three layers: the crystalline silicon nanobrick layer, the silica layer, and the crystalline silicon substrate layer, which is illustrated in Fig. 1(a). Silicon nanobricks, with identical dimensions but different orientations angle α, are distributed on the silica layer periodically. Determined by the thickness of the top layer of the SOI wafer we chose, the height H of the nanobrick is fixed at 220 nm. In order to avoid high diffraction orders and reduce the near-field coupling effect between adjacent nanobricks, the unit size C is carefully chosen to be slightly less than half of the working wavelength, which is 300 nm. For an ideal half-wave plate, the co-polarization reflected light should be extinct under the CP light illumination. Hence, we first simulate the reflectivities of the cross-polarized and co-polarized parts of outgoing light by using the commercial software (CST Studio Suite). Reflectivities of the cross-polarized and co-polarized parts are associated with the response of the long and short axes of the nanobrick [35]. The dimension variation influences not only the reflectivities along these two axes but also the phase delay between them. Through careful design, we find a balance between the high efficiency and the required phase delay of π. As a result, the dimension of the nanobrick are optimized with the length L of 200 nm, width W of 100 nm, height H of 220 nm and unit size C of 300 nm. The simulation result in Fig. 1(b) shows that the reflectivity of the cross-polarization part can be higher than 60% in the design wavelength range (620 nm ∼ 630 nm), while the unwanted co-polarized part is compressed to be lower than 2%. Therefore, the designed nanobrick can act as an effective half-wave plate.
Fig. 1. (a) Schematic diagram of a unit-cell of the SOI-based metasurface. The thickness of the silica layer d is 2 μm. (b) Simulated reflectivities of the cross-polarized (cro-pol) and co-polarized (co-pol) parts with the CP light incidence. α is equal to 0° in the simulation. (c) Simulated reflectivities of the LP light with the polarization direction along the long and short axes of the nanobrick. (d) Simulated phase delay between the long and short axes of the nanobrick.
However, in a wider range from 500 nm to 700 nm, the reflectivities shown in Fig. 1(b) fluctuate greatly with the optical wavelength. It is resulted from the variation of the complex reflective coefficients along the long and short axes. Figures 1(c) and 1(d) are the simulated results of the reflectivity of LP light polarized along two different axes and the phase delay between them, respectively. Here, the orientation angle is fixed at 0°. For the LP light polarized along the short axis, the maximum reflectivity (∼ 85%) can be obtained near 610 nm, while for the LP light polarized along the long axis, the reflectivity reaches its peak (∼ 95%) near 683 nm. When exploring the electromagnetic field located in the nanobrick, we find the magnetic resonances happen at these wavelengths, which are illustrated by Fig. 2. From the simulated electromagnetic field results, it can be seen clearly that magnetic fields are enhanced in the nanobrick along both the long axis (x-axis) and the short axis (y-axis) at the wavelength of 610 nm and 683 nm, respectively. It reveals that the existence of the magnetic dipole resonance along different axes leads to the high reflectivity at different wavelengths. Under the influence of the dual magnetic resonances, the reflectivities along the long and short axes are equal to each other (about 70%) near 627 nm. At the same time, because of the anisotropy of nanostructures, the phase delay result in Fig. 1(d) shows that a phase difference of π between these two axes can be also obtained at the same wavelength. Therefore, our design ensures the high cross polarization conversion efficiency of about 70% and the suppression of the unwanted co-polarization part at 627 nm, as shown in Fig. 1(b).
Fig. 2. (a) and (b) 2D normalized electric and magnetic fields around the nanobrick with the incident light polarized along the short axis (y-axis). The simulation wavelength is 610 nm. (c) and (d) 2D normalized electric and magnetic fields around the nanobrick with the incident light polarized along the long axis (x-axis). The simulation wavelength is 683 nm.
After the design of the nano-unit-cell, we proceed to arranging the orientation distribution of the metasurface according to two different target images (a “lion” picture for near-field and a “rose” picture for far-field). The initial orientation distribution of nanobricks located in an interval of [0, 90°] can be determined firstly from the target “lion” image based on the relationship of output light intensities and nanobrick orientations. As we mentioned before, the orientation angle of each nanobrick has four candidates ($- \frac{\pi }{2} - \alpha ,{\; } - \alpha ,\;\alpha,$ and $\frac{\pi }{2} + \alpha$) to produce an identical light intensity, which provides the design degrees of freedom employed to generate a phase-only holographic image under CP light incidence. By taking the “rose” picture as target image and utilizing the simulated annealing algorithm, the final orientation distribution can be determined. Therefore, the designed single-celled metasurface can be employed to generate a grayscale image in near field and a holographic image in far field simultaneously.
4. Experiment and discussion
To verify our design, a SOI-based multifunctional metasurface was fabricated by the standard electron-beam lithography. The dimensions of the fabricated sample are 150 μm × 150 μm with the unit cell sizes of 300 nm × 300 nm. Due to the thorough design of the orientation distribution, the multifunctional metasurface can record a holographic image and a totally different grayscale image at the same time. Specifically, the holographic image of “a rose” is generated in far field and the experimental optical setup is illustrated in Fig. 3(a). The laser beam first passed through a polarizer to generate the linearly polarized light. Then, a quarter-wave plate (QWP) was used to transform the LP light into CP one. After reflected by the metasurface, the CP light reconstructed a holographic image in far field and the holographic image was projected on a white screen, which was about 0.2 m far away from the sample. The holographic image formed on the screen was captured by a commercial camera (Nikon D5100). By rotating the QWP, the experimental results under the left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) light illumination can be obtained. As shown in Figs. 3(b) and 3(c), the holographic “rose” with the LCP light illumination appears at the upper left corner of the screen, while the holographic “rose” with the RCP light illumination emerges at the bottom right corner. These two roses are located in the conjugated position, which can be easily understood with the geometric phase principle [48]. With the same sample, the grayscale image of “a lion” can be observed based on the polarization rotation of the LP light. The polarization directions of the incident LP light and the bulk-optic analyzer are perpendicular to each other. Since the grayscale image is generated right at the metasurface plane, the size of the image is equal to the sample size and keeps unchanged under the illumination of light with different wavelengths. Therefore, a broadband halogen lamp was chosen to be the experimental illumination source. The continuous-grayscale image was captured by an optical microscope (Motic BA310MET-T) with a magnification of 100 ×, as shown in Fig. 3(d). Beside the lion, the plant details can be observed clearly, verifying the high resolution of the grayscale image.
Fig. 3. (a) Experimental setup of the holographic image. A polarizer and a quarter-wave plate (QWP) are used to generate the circularly polarized incident light. (b)-(c) Experimentally captured holographic images in far field with the left-handed and right-handed circularly polarized light, respectively. The operation wavelength is 620 nm. (d) Experimentally captured near-field grayscale image located right at the metasurface plane. The sample was illuminated by LP light.
Next, we further explore the broadband response of the proposed SOI-based multifunctional metasurface. In order to investigate the spectral response in far field, the wavelengths of incident laser beam are altered from 540 nm to 640 nm in steps of 20 nm. We remove the QWP from the optical path this time to investigate the images under the illumination of the LP light, which are illustrated in Figs. 4(a)–4(f). Since the LP light can be considered as the superposition of LCP and RCP light, each holographic image has the twin roses. According to the diffraction theory, the holographic image size is proportional to the laser source wavelength. We can find that the twin roses are getting larger as the wavelength increases. However, the geometric phase is independent with the light wavelength [35]. Therefore, although the nanobrick cannot always be equivalent to a half-wave plate at all wavelengths, it will not affect the generation of holographic image, but only influence the diffraction efficiency of the hologram. As shown in Figs. 4(a)–4(f), the hologram can be always observed clearly in a wide spectral range. As for the near-field, the grayscale image is generated based on polarization control. If the nanobrick is not an ideal half-wave plate, only parts of incident light beams experience polarization rotation, while the light without polarization rotation is completely eliminated by the bulk-optic analyzer, whose polarization direction is perpendicular to the incident light polarization [49]. It indicates that the brightness of the grayscale image changes under the light illumination with different wavelengths, but the grayscale distribution of the image can remain unaffected, as shown in Figs. 4(g)–4(i). The results of the far field and the near field images confirm that the proposed multifunctional metasurface provides the excellent performance in the broad operating spectra.
Fig. 4. (a)-(f) Experimentally captured holographic images under LP light illumination with different wavelengths. A super-continuum laser source (YSL SC-pro) was taken as the illumination source. (g)-(i) Optical micrographs at the surface of the metasurface sample. A halogen lamp with different color filters was used as the illumination source.
Regarding to the hologram, we measured the diffraction efficiency of the proposed metasurface while the wavelength ranged from 510 nm to 680 nm. The measured efficiency is defined as the ratio of the optical power of the reconstructed holographic image to the power of the incident laser beam. The diffracted light was collected by a lens to make sure that as much optical energy as possible could be received by the optical power meter. The experimental result is shown in Fig. 5. The maximum efficiency is 28.65% at the wavelength of 625 nm, which is lower than the theoretical prediction shown in Fig. 1(b). This deviation comes from many reasons. At first, the reflectivity of cross-polarized light shown in Fig. 1(b) is the polarization conversion efficiency calculated by setting all nanobricks as identical orientation angles; while for the meta-hologram, the measured efficiency is the overall diffraction efficiency of nanobrick arrays with specific orientation distribution. To make an exact comparison, one should further consider the hologram design efficiency, 4-step phase-quantification efficiency and the coupling efficiency between adjacent nanobricks. Secondly, the fabricated metasurface sample is quite small (150 μm × 150 μm), but the spot size of our incident laser is larger than the sample size. The overestimation of the optical power irradiated on the metasurface leads to the low experimental efficiency. Recently, some feasible approaches, such as the high-throughput stepper photolithography, the surface plasmon lithography and the femtosecond laser lithography, have been proposed to fabricate large-area nanostructures [46,50–51]. With these advanced fabrication techniques, metasurfaces can be designed with large area and receive more laser energy, and the diffraction efficiency can be improved accordingly. At last, the fabrication errors of the nanobricks (the dimensions and the orientation) influence the anisotropy of the nanobricks and the phase distribution (the SEM image of the fabricated sample is shown in Fig. 6). It will also affect the diffraction efficiency of the hologram device, leading to the difference between the experimental and simulated efficiencies. Nevertheless, we can find that the efficiency of the proposed multifunctional metasurface is three times larger than the efficiency of the Malus-assisted metasurface, which is designed based on nano-polarizers [44]. The result sufficiently verifies that the half-wave plate design we used is beneficial to the efficiency improvement of the multifunctional metasurfaces.
5. Conclusions
In summary, we propose and experimentally demonstrate a SOI-based all-dielectric multifunctional metasurface, which can manipulate the polarization state and geometric phase of incident light simultaneously. Through careful design of orientation angles, the proposed multifunctional metasurface can display not only a continuous grayscale image at its surface based on polarization control, but also project an independent holographic image in far field applying the geometric phase design. Being composed of SOI-based nanostructures in a single-size design approach, the metasurface shows its significant superiority in ultra-simple design, easiness in fabrication, and manufacturing compatibility. Due to the half-wave plate design and the low-loss SOI material, the multifunctional metasurface has a relatively high diffraction efficiency of 28.65% at visible light. In addition, the experimental results of the near-field and far-field images also confirm that it has excellent performance in the broad spectra and strong robustness against fabrication errors. Based on these brilliant characteristics, the proposed SOI-based metasurface can gain more attentions and have promising applications in the field of anti-counterfeiting, information security, information multiplexing, information storage, etc.
Appendix
SEM image of the multifunctional metasurface
Funding
National Natural Science Foundation of China (11774273, 11904267, 91950110); National Postdoctoral Program for Innovative Talents (BX20180221); China Postdoctoral Science Foundation (2019M652688); Natural Science Foundation of Jiangsu Province (BK20190211).
Disclosures
The authors declare no conflicts of interest.
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