Multifunctional silicon metagratings based on multiple periodicity design

Optical metasurfaces have been studied significantly for structuring light [1] and miniaturizing optical elements [2]. They have numerous applications, such as light absorbers [3], metalens [4], and metamirrors [5]. Other recent examples include U-shaped metasurfaces for reflection display [6], silicon-on-glass metasurfaces for Rochon prisms [7], and nano-particle metasurfaces for anti-reflection coatings [8]. Furthermore, the scope of metasurface research is still developing, such as exploring reconfigurable metasurfaces [9] for versatility. The idea of flat optics design [10], derived from metasurface studies, provides a promising way to achieve more compact optical systems without using bulky conventional optical elements.

Generally metasurfaces can be divided into metallic metasurfaces and dielectric metasurfaces. However, at the visible and near infrared region, dielectric metasurfaces have two major advantages over their metallic counterparts [11]. Firstly, dielectric metasurfaces offer lower losses at this wavelength region. Secondly, they have better compatibility with complementary metal oxide semiconductor (CMOS) processes. Therefore, high-index dielectric metasurfaces that can support multiple resonances to effectively interact with light [11, 12] are investigated intensively [13–15].

Efforts have been taken to develop polarization-sensitive metasurfaces. One example [5] is the multifunctional metamirror that can split linear polarizations into two orthogonal directions and focus them to different locations. Another example [7] realizes circular polarization splitting with silicon metasurfaces. However, the integration of gratings, polarizers, and band-pass filters has not been demonstrated on the platform of dielectric metasurfaces yet. The usefulness of such optical elements might be pragmatic with regards to some polarization-controlled optical systems, such as polarimetric imaging systems. The polarimetric imaging system utilizes the difference between the scattered light of different polarization states to improve image contrast [16]. Hence, the multifunctional metasurfaces shall be instrumental in miniaturizing such systems.

In order to achieve the multiple functions, we propose a design of periodic silicon metasurface utilizing the near-field Moiré effect. Moiré metamaterials have been examined as chiral metamaterials [17] due to their own unique Moiré structure which makes polarization-sensitive applications possible. Although Moiré metamaterials [18] have been applied for sensing and lasing, their multi-layered structure is a disadvantage with regards to fabrication. Previously, single-layered configurations are studied as high contrast gratings (HCG) [19] for high reflectivity and high Q factor. Other similar dielectric metagratings are applied for efficient beam deflection [15, 20]. Our silicon metagrating device resembles these designs in terms of single-layered structures, periodic compositions, and high-index dielectric nanostructures but focuses on the integration of multiple functionalities with the Moiré effect. The near field Moiré effect [21] has been studied in the case of two metallic subwavelength gratings, where the key to achieve strong diffraction is the enhancement of the coupling of evanescent waves from subwavelength gratings. For our metagrating device, guided-mode resonance (GMR) [22–25] is employed to enhance the coupling of evanescent waves. GMR is the energy redistribution effect when leaky modes of grating structure are coupled with propagating wave. Strongly modulated GMR filters have been applied to integrate a polarizer with a band-pass filter [26, 27]. Furthermore, an example [16] of metal-dielectric polarization-sensitive band-pass filters has been demonstrated in the mid-infrared region. In a similar fashion, our metagrating device integrates a polarizer, and a band-pass filter with a transmission grating in the near infrared region.

The unit cell of the metagrating device is shown in figure 1(a). In the y direction, two subwavelength periods, p₁ and p₂, carry different frequency information. We use subwavelength periods here to suppress their individual diffraction so that only from the coupling of their evanescent waves can the diffraction occur in the far field. We set the ratio of p₁ and p₂ as 3:5 with a common fill factor 50%. An overall Moiré pattern is a result of mixing different frequency information of the double periodicity pattern in the y direction. In the x direction, the widths of two columns, w₁ and w₂, and the gap, d, can be tuned to control the coupling of leaky modes from GMR. The overall period in the x direction is set to be smaller than the incident wavelength to suppress diffraction in this direction. Hence, despite the two-dimensional nature of the metegrating device, the far-field diffraction occurs only in the y direction.

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The metagrating device is based on a silicon-on-glass wafer and works in the transmission region. The polarization-sensitive diffraction is illustrated in figures 1(b) and (c). The thickness of silicon layer is set at 290 nm, which is the same as our available silicon-on-glass wafer. We employ a finite difference time domain (FDTD) algorithm to calculate the diffraction efficiencies. The diffraction efficiency is defined as the diffracted energy in a specific order normalized against the incident energy. The incidence is assumed to be plane wave, polarized in either the x or y direction, and normal to the metagrating surface. When light is incident on the metagratings, the evanescent waves can be generated and decay in both the x and y directions according to leaky modes.

Moreover, in the y direction, the evanescent waves have different frequency information so that they can couple with each other during propagation. Therefore, a Moiré pattern can be observed due to the coupling of these leaky modes in the transmission region. When GMR condition is satisfied, the mixing of frequency information can be enhanced to generate strong diffraction. After optimization is performed at 1570 nm, metagrating parameters are obtained as follows: p₁ = 825 nm, p₂ = 1375 nm, w₁ = 364 nm, w₂ = 290 nm, d = 130 nm. In addition, the overall period of the metagrating device is 4125 nm in the y direction from the simulation, which agrees with the Moiré period calculation. Diffraction patterns are also examined, revealing that the diffraction efficiency of the second order is significantly higher than the first one. This can be explained by the condition [21] that diffraction modes must satisfy

$$\begin{eqnarray}&&{\vec{k}}_{m,n}=p{\vec{k}}_{{\rm{overall}}}=m{\vec{k}}_{1}+n{\vec{k}}_{2}\end{eqnarray} \tag{ 1 }$$

where ${\vec{k}}_{m,n}$ is the diffracted wave vector projected on the device plane, p is the diffraction order, and ${\vec{k}}_{{\rm{overall}}}$ is the grating vector of overall Moiré pattern. ${\vec{k}}_{1}$ and ${\vec{k}}_{2}$ are respectively the grating vectors of Columns 1 and 2 in the y direction. Having examined the grating vectors of the subwavelength gratings in the y direction according to equation (1), we can calculate the respective coefficients of two grating vectors. Thus, we find that the second diffraction orders are comprised of the first order evanescent waves from the two columns (i.e. m = +1, n = −1 for p = +2; and m = −1, n = +1 for p = −2), while the first diffraction orders consist of higher order evanescent waves (i.e. m = +2, n = −3 for p = +1; and m = +1, n = −2 for p = −1). As the first order evanescent waves decay slower than the higher orders ones during propagation, the second order diffraction efficiency is thus generally higher than the first order in our device here.

Having obtained the dimensions of metagratings, we perform FDTD simulations to investigate the spectral responses of diffraction efficiencies upon different incident polarizations from 1520 nm to 1620 nm. We plot the second order diffraction efficiency against the incidence wavelength in figure 2, because the second diffraction order generally has a higher efficiency than that of the first diffraction order. In this figure, the diffraction efficiency with y polarization incidence behaves like a band-pass filter with a full width at half maximum (FWHM) of 46 nm, reaching its maximum 13.2% at 1570 nm. Compared with the y direction, the diffraction efficiency of x polarization incidence is negligible. This is because GMR is sensitive to the incident polarization. Therefore, the metagrating device based on GMR is also sensitive to the incident polarization state.

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In order to illustrate the coupling of evanescent waves between the silicon nanoblocks, the electric field distributions of different cross-sections are examined with FDTD simulations. When the incidence is 1570 nm and polarized in the y direction, the electric field distributions are shown in figure 3. Strong electric field concentrations are observed between the columns in the unit cell. It indicates that the coupling occurs between the evanescent waves of two different frequency subwavelength patterns.

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The fabrication of the multifunctional metagrating device was conducted with the silicon-on-glass substrate. First, electron beam resist ZEP520 was spin-coated on the wafer, followed by Espacer 300z which was also spin-coated as a charge dissipation layer. Then, the metagrating pattern was created with standard electron beam lithography (Jeol JBX-6300FS EBL). After the exposed resist was developed, the remaining resist was used as a mask for silicon etching to form the silicon nanoblocks of 290 nm thickness with deep reactive ion etching (Oxford Plasma Pro Cobra 100 Deep RIE). Finally, the resist mask was removed in the remover PG and the metagrating device was obtained. The characterization job was conducted with a scanning electron microscope (SEM) (FEI Verios 460). We found that the smallest features of the metagratings are successfully fabricated, and the pattern is in overall accordance with the design as shown in figure 4(a).

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The testing system is schematically shown in figure 4(b). A tuneable laser source (ANDO AQ4321D) connected with a beam collimator via a single-mode (SM) fibre is used to provide plane wave incidence at 1570 nm. After the polarizer which controls the polarization, the light is reflected on the mirror (Thorlabs PF10-03-M01) and incident on the metagrating device. The diffracted light is captured with an infrared (IR) lens (Thorlabs AC080-010-C) and an infrared (IR) camera (Xeva-2563). Considering the fact that the distance between the laser spots of adjacent diffraction orders are much greater that the field of view of the camera, the IR camera is mounted on a linear stage. Thus, each individual diffraction pattern can be captured by moving the camera to align to the spot. The captured images, shown in figure 4(c), serve as a straightforward demonstration of the predicted diffraction phenomenon.

Apart from the qualitative results obtained by the CCD camera, experiments were also conducted to verify the polarization-sensitive diffraction of this metagrating device quantitatively. We removed the IR lens and replaced the CCD camera with a photodetector in figure 4(b). The infrared detector (Newport 918-IR) connected with a power meter (Newport 1930C) was utilized to collect the diffracted light directly in the transmission region. The laser source can provide the simulated infrared incidence ranging from 1520 nm to 1620 nm. In this range, the diffraction power of the metagrating device was measured at a 5 nm interval. After the measurements, the diffraction efficiencies were obtained by normalizing the measured diffraction power against the incident power. Results of respective orders from experimental measurements and FDTD simulations are compared in figure 5. First, the diffraction patterns of different incident polarizations are illustrated in figures 5(a) and (b). From these figures, it can be observed that the diffraction efficiency of each order from experiment is in good agreement with that from the simulation. Then, the spectral responses of the second diffraction order for x and y polarizations are plotted in figure 5(c). As illustrated in the figure, the experimental spectral curves follow extremely well with those from the FDTD simulation results. For the y polarization, it has a band-pass characteristic with a peak centred around 1570 nm. The diffraction efficiency at 1570 nm reaches 10.8%, and the FWHM of the spectral response is around 56 nm, whereas the FDTD simulation results show a diffraction efficiency of 13.2% and a FWHM of 46 nm. For the x polarization, only around 1% of incidence is diffracted in both simulations and experiments. Although there are some discrepancies between the experimental results and the simulation results, the polarization-sensitive diffraction with a band-pass functionality has been experimentally verified. The discrepancies between simulations and experiments can probably be attributed to fabrication errors, loss of beam collimation, and the inaccurate alignment of the polarizer. On the whole, the design of the multifunctional metagrating device has been experimentally verified.

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After the metagrating design is verified experimentally, it is desirable to explore the influences of other design parameters on the diffraction efficiency. In the previous optimization, the thickness of the silicon layer is limited by the available wafers, as shown in the figure 6(a). We perform FDTD simulations to obtain the diffraction efficiencies of the second order with silicon thickness ranging from 100 nm to 500 nm. The results are summarized in figure 6(b). It indicates that the diffraction efficiency can be higher than 20% with the same unit cell design but different silicon thickness. Therefore, the metagrating device has the potential of high diffraction efficiency after a comprehensive parameter optimization.

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In our metagrating design, the parameters in the x direction can be tuned to change the peak wavelength. Since we try to keep the same Moiré period as the previous design, the parameters in the y direction are kept the same. Then we vary the dimension parameters to: w₁ = 354 nm, w₂ = 280 nm, d = 160 nm. With these new dimensions, the peak wavelength is numerically calculated to be near 1585 nm. We fabricated the metagrating device using the same processes and characterized it with SEM, shown in figure 7(a). Using this device, we conducted the experiments of measuring diffraction efficiencies with the same setup to obtain the spectral curves of each diffraction order. Figure 7(b) shows the diffraction efficiencies of different orders obtained from FDTD simulations and experimental measurements. As reflected in this figure, the simulation results and the experimental results again agree well. The new metagrating device is experimentally proved to exhibit strong polarization-dependent band-limited diffraction at 1585 nm with the second order diffraction efficiency of 10.7%. Hence, the parameters in the x direction can be used to modify the peak wavelength of the metagrating device.

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FDTD simulations are further performed to investigate the detailed effects of the individual parameters in the x direction while keeping those in the y direction fixed. First, the spectral response of the second order diffraction efficiency is examined when the gap distance d varies from 50 nm to 200 nm. Next, similar simulation procedures are respectively applied to investigate the effects of the two widths of silicon nanoblocks, i.e. w₁ and w₂. The results are summarized in figure 8. From the figures, these geometric parameters have a similar effect on the diffraction efficiency. Strong diffraction (efficiency above 12%) can occur when 120 nm < d < 170 nm, 354 nm < w₁ < 424 nm, and 280 nm < w₂ < 360 nm. Within these parameter ranges, when the dimension is increased, the maximum diffraction efficiency can vary slightly and the corresponding peak wavelength will red shift.

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In summary, we have proposed and experimentally demonstrated a silicon metagrating device that integrates the functions of a grating, a polarizer, and a band-pass filter in the near infrared region. GMR is used here to enhance the near field Moiré effect of subwavelength periods to produce strong diffraction in the far field. The influences of different parameters on the diffraction efficiency have been studied.

We believe that the multifunctional metagratings may play a positive role in the miniaturization of polarization-controlled optical systems. Furthermore, this study introduces extra design parameters into metasurface design. Utilization of multiple periodicity may be extended to other metasurface designs. For example, multiple metasurface absorbers with various periodicity can be superposed to form an ultra-broadband absorber.

The authors acknowledge the financial support from Ministry of Education (MOE) Research Grant R265000585114 at National University of Singapore.