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Abstract
Metasurfaces offer a promising means for realizing compact high-performance optical devices. This study numerically and analytically investigated reflection control using a metal–dielectric–metal (MDM) metasurface. Its reflection wavelength and angle were determined using the thickness and refractive index of the dielectric layer owing to a phase change induced by the hybridized resonance mode formed therein. MDM metasurfaces with offset micropatches comprise a continuous metal layer with periodic dielectric and micropatch layers having different widths. These layers are offset to one side with respect to one another. These offset micropatches realized better control over the reflection direction and wavelength.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces have attracted increasing interest owing to their ability to manipulate light with their thin planar surfaces [1,2]. Metasurfaces typically consist of a single-layer metallic pattern (meta-atom) array on a substrate or a metal–dielectric–metal (MDM) three-layer structure [3]. Many applications have been identified, including meta-lenses [4], holograms [5], infrared sensors [6], absorbers [7], color pixels [8], and beam steering [9], along with the realization of optical control with higher efficiency than that provided by conventional refractive optical components. Recently, metasurfaces based on the generalized Snell’s laws of reflection or refraction have been used to control a wavefront with their gradient surface patterns [10,11]. Depending on the design of the topologically engineered surfaces, the functions of electromagnetic control, such as focusing [12], anomalous reflection [13,14] or transmission [15], and polarization conversion [16], can be selected. In particular, growing interest in light detection and ranging (LiDAR) applications for automotive applications [17] is increasing the importance of reflection angle control because LiDAR requires fast and efficient light direction control. MDM metasurfaces are recognized as providing a platform to steer incident light in an anomalous direction. Anomalous reflection is defined here as the reflection of light at angles that differ from the incidence angle, which cannot be achieved by conventional metallic-surface relief gratings [15,18]. Conventional approaches adopt a gradient surface pattern [13,19–21]. More advanced, reconfigurable metasurfaces with graphene [22,23], indium tin oxide [24,25], or phase-change materials [26] have demonstrated electrically tunable reflection angle control. Recently, high-efficiency and reconfigurable reflection angle control has been demonstrated in the terahertz range without the need for a gradient surface pattern, which is typically difficult to design and fabricate [27]. Therefore, investigation of the reflection properties of MDM metasurfaces is urgently required, not only to realize high-efficiency beam-steering devices, but also to exploit anomalous reflection for different applications and in various wavelength regions. Infrared (IR) wavelengths are particularly important given the demand for IR sensors for optical systems. However, although similar structures to MDM metasurfaces in terms of a guided-mode resonance [28,29] or a resonant waveguide grating [30] and the absorption properties of MDM metasurfaces [7,31,32] have been studied extensively, the reflection properties of MDM metasurfaces have to date not been adequately investigated.
In the present study, the fundamental origin of anomalous reflection from MDM metasurfaces was investigated and an analytical model was developed. Moreover, reflection control was demonstrated based on the asymmetry of the dielectric layer.
2. MDM metasurfaces
Figure 1 shows a cross-sectional view of the investigation model, an MDM metasurface with an aluminum (Al) outer layer and a silicon (Si) inner layer. In the calculation, a two-dimensional (2D) model in the direction of the x- and z-axes was adopted for simplicity. Micropatches were arrayed with a one-dimensional period. We defined this structure as a centered micropatch.
The incidence angle was defined as θi. Reflection is described as three parts: the specular reflection of R0, the anomalous reflection (AR) of R1, and that of AR of R−1, where the reflection angles are defined as θ0 (= θi), θ1, and θ−1, respectively. In the case of backward reflection, θ−1 is defined as a negative value. The transverse electric (TE) and transverse magnetic (TM) modes are defined as being parallel to the y- and x-directions, respectively. Al is used for the front periodic micropatches and as the back-reflector material. Si is used as the inner dielectric layer. The period and size of the Al micropatches and the thickness of the Si layer are defined as p, d, and h, respectively. The thicknesses of the top micropatches and the back reflector were both fixed to 100 nm. The total reflection R0, R1, and R−1 for the TE mode at normal incidence were calculated using rigorous coupled-wave analysis (RCWA) [33]. RCWA is a suitable method for the investigation of AR because the reflectance and reflection angle for each diffraction order can be calculated. The parameters p, d, and h were fixed to 7.0 µm, 4.0 µm, and 300 nm, respectively. The optical constants for Si and Al were taken from the literature [34,35]. The TM mode induces many absorption modes for one-dimensional MDM metasurfaces [7]. Therefore, only the TE mode was considered in this study.
3. Results and discussion
3.1 Centered micropatch
Figure 2(a) shows the calculated reflectance and total absorbance (A) spectra at normal incidence. Note that R−1 is equal to R1 at normal incidence. AR occurs at wavelengths of less than 7.0 µm, which corresponds to p. The reflectance dip at a wavelength of approximately 3 µm is attributed to the absorbance. This absorption is induced by gap resonance between the micropatches. The minimum value of R0, and the maximum values of R1 and R−1 were obtained at a wavelength of 4.15 µm, which is defined as the AR wavelength (λAR). The reflection angles θ0, θ1, and θ−1 were calculated at λAR. The reflectance and the reflection angles were calculated using RCWA, with the results shown in Fig. 2(b). R0, R1, and R−1 correspond to zero, +1, and −1 order diffraction, respectively. No higher- or lower-order diffractions were observed at normal incidence.
Fig. 2. (a) Reflection and absorption spectra for total reflection, R0, R1, and total absorption at normal incidence. (b) Reflection angles of R0, R1, and R−1 at wavelength of 4.15 µm.
The θi dependence of R0, A, and R−1 was then calculated as a function of wavelength using RCWA. Figures 3(a), 3(c), 3(e), and 3(g) show the calculated results for R0, A, R1, and R−1, respectively. Figures 3(b), 3(d), 3(f), and 3(g) show the calculated spectra of R0, A, R1, and R−1 for θi = 0°, 20°, 40°, and 60°, respectively.
Fig. 3. θi dependence of (a) R0, (c) A, (e) R1 and (g) R−1. Calculated spectra of (b) R0, (d) A, (f) R1, and (h) R−1 for θi = 0°, 20°, 40°, and 60°. The color bar indicates the reflectance.
Figure 3 shows that the main λAR of the MDM metasurfaces described herein is almost independent of θi and maintains a constant value of approximately 4.2 µm as long as anomalous reflection occurs. The other dips of R0 and peaks of R1 and R−1 at the wavelengths of 3.3 and 3.7 µm are attributed to the absorption. As depicted in Figs. 3(a) and 3(e), the guided mode dispersion relation appears at the vicinity of λAR On the other hand, in cases involving conventional metallic-surface relief and resonant waveguide gratings, the diffracted waves are highly dependent on θi. Equation (1) describes the former case. Here, m denotes an integer, and the diffracted wavelength λ is highly dependent on θi.
Equation (2) describes the latter case [29], wherein i and m are integers, and once again, the resonant wavelength λ is highly dependent on θi.
The dependence of R−1 on structural parameters h, p, and d at normal incidence was also calculated using the RCWA method in order to determine the analytical model of the anomalous reflection and retroreflection of MDM metasurfaces, with the results shown in Figs. 4(a)–(c).
Figure 4 demonstrates that the main structural parameter defining λAR is h, and that λAR is almost proportional to h despite the slight dependence on p and d. This is a unique property of the anomalous reflection of MDM metasurfaces, which differ from conventional metallic-surface relief gratings.
The electromagnetic amplitude distribution was calculated using the finite-difference time-domain (FDTD) method to investigate the origin of this strong dependence on h. The calculation model used for the FDTD method was the same as that in the RCWA calculation, where the 2D calculation model as shown in Fig. 1 was used. Incident light with the TE mode at normal incidence was used. Figures 5(a) and 5(b) show the calculated amplitudes of the electric and magnetic field distributions at λAR = 4.15 µm for normal incidence, respectively.
Fig. 5. Amplitudes of (a) electric, and (b) magnetic field distributions at an λAR of 4.15 µm for normal incidence.
Figures 5(a) and 5(b) clearly depict the occurrence of quarter-wavelength resonance in the Si dielectric region between micropatches. This resonance mode is manifested via hybridization of the gap resonance between the micropatches, the Fabry–Pérot mode, and the waveguide mode, which is strongly confined in the Si dielectric region owing to the high-index dielectric medium of Si. Therefore, the excitation is almost independent of the incidence angle. It should be noted that this resonance mode significantly differs from the gap plasmonic resonance confined between micropatches and the back reflector, thereby resulting in strong absorption [36]. Additionally, it has been confirmed that no such resonance occurs at other wavelengths. Therefore, the observed anomalous reflection can be attributed to the quarter-wavelength resonance, and λAR can be determined using the relation
where n is the refractive index of the Si-based dielectric layer. Equation (3) agrees with the results of the h dependence of λAR shown in Fig. 4(a). In the present case, λAR was determined to be 4.12 µm with n = 3.43 [34] and h = 300 nm, coinciding with the calculated λAR shown in Fig. 2(a). The material used in the dielectric layer is an important factor affecting the operation wavelength. Some materials, namely, Si, Ge, GaAs, and InP are suitable for obtaining an anomalous reflection in the IR region because of their refractive index. In particular, Si is the optimum material owing to its low cost. SiO2 [37] has a smaller refractive index than Si, allowing the anomalous reflection or retroreflection wavelength to be shortened to the visible or near-IR regions, and further tuned by adjusting the thickness of the dielectric layer.These results demonstrate that the anomalous reflection in MDM metasurfaces described herein is induced by the quarter-wavelength resonance in the Si dielectric layer between the micropatches. This causes a periodic phase difference, and λAR is thus independent of θi, as shown in Fig. 3. Equation (3) shows that λAR can be reduced to a wavelength shorter than the surface period using MDM metasurfaces. These properties are the main differences from Eq. (1) for conventional metallic-surface relief gratings. It was also determined that MDM metasurfaces with an isolated dielectric layer, where there is only the dielectric under the micropatches, exhibits no anomalous reflection when there is no cavity for the quarter-wavelength resonance. This confirmed that the anomalous reflection of the MDM metasurfaces with a continuous Si dielectric layer was induced by the quarter-wavelength resonance in the Si region sandwiched between the micropatches.
From these calculated results, analytical models were investigated. The optical distance of each diffracted wave at the micropatches and the dielectric region should be increased by λAR/2 because of the quarter-wavelength resonance in the dielectric region, as shown in Fig. 5. This phase difference should occur for a gap size of p/2 between the micropatches and the dielectric region. Therefore, the optical distance of λAR/2 was considered, and the variable p in Eq. (2) was changed to p/2 in Eq. (1). In cases involving MDM metasurfaces, when λAR, determined using Eq. (3) and θi, is given, the value of θ±m yielding an ±m order must satisfy Eq. (4).
As shown in Figs. 6(a) and 6(b), Eq. (4) coincides well with the RCWA simulation results. This result indicates that the origins of AR of MDM metasurfaces are attributed to the θi independent of λAR, which is almost proportional to h.
3.2 Offset micropatch
The dielectric layer plays a key role in the reflection of MDM metasurfaces. To realize the selection of R1 and R−1, we introduced an offset micropatch. Figure 7 shows a cross-sectional view of the MDM metasurfaces with an offset micropatch. In this structure, the dielectric layer is not continuous. As shown in Fig. 7, the Al micropatches were made narrower than the discontinuous Si dielectric islands and offset to one side of each island to create a void. The length of this void was defined as d.
Parameters p, d, and h were fixed to 7.0 µm, 4.0 µm, and 330 nm, respectively. The value of h was changed slightly (from 300 nm) to obtain the maximum reflectance in this offset micropatch structure. Figures 8(a) and 8(b) show the calculated R1 and R−1 for d values of 600, 650, 700, 750, and 800 nm, respectively. Figure 8(c) shows the calculated electric field profile of the reflected wave for d of 800 nm at a wavelength of 3.58 µm, where the maximum R−1 was achieved. It should be noted that interference with the incident wave occurred.
Fig. 8. Calculated (a) R1 and (b) R−1 for d of 600, 650, 700, 750, and 800 nm. (c) Electric field profile of d of 800 nm, showing the direction of the reflected wave.
Figures 8(a)–8(c) show that although R1 was suppressed, R−1 was wavelength-selectively enhanced. The reflection selectivity was realized by the offset micropatch. The maximum R1 or the minimum R−1 can be defined by d. As schematically shown in the inset of Fig. 8(c), the reflectance was enhanced in the opposite direction to the void. This selectivity was attributed to the phase shift of λAR/2 induced in the dielectric layer, as shown in Fig. 5 and described by Eq. (4). The value of λAR increases in accordance with an increase in d because the resonance mode confined within the dielectric region of the void becomes more prominent with an expansion of the void dielectric region. The intensities of R1 and R−1 remain nearly constant. As described above, a change in the value of h causes these intensities to change.
Figures 9(a) and 9(b) show the calculated R1 and R−1 as a function of d and the wavelength.
Fig. 9. Calculated (a) R1 and (b) R−1 as a function of d and wavelength. Color bar indicates reflectance.
Figure 9 demonstrates that reflection selectivity between R1 and R−1 was realized. It was also confirmed that reflection selectivity becomes weak when d exceeds 1.0 µm because the asymmetry is reduced and, as a result, R1 and R−1 become equivalent, as shown in Fig. 1(b). Therefore, the reflection selectivity becomes more obvious as the value of d decreases.
Figures 10(a)–10(d) show the calculated results of the incident angle dependence of R1 and R−1 for d values of 500 and 750 nm.
Fig. 10. Incident angle dependence of (a) R1, and (b) R−1 for d value of 500 nm, and (c) R1, and (d) R−1 for d value of 750 nm. Color bar indicates reflectance.
Figure 10 indicates that the wavelength selectivity of R1 and R−1 is insensitive to the incident angle and almost fixed at the anomalous reflection wavelength, which is more evident than that of MDM metasurfaces without an offset micropatch, as shown in Fig. 3. The dispersion relation is less evident than in Fig. 3. These are attributed to the guided resonant waveguide modes being reduced by the discontinuous Si layer, which coincides well with the anomalous reflection mechanism of the conventional MDM metasurfaces discussed in the previous section.
It was demonstrated that MDM metasurfaces with an offset micropatch could efficiently select the reflection light direction and wavelength based on d because of the phase change in the dielectric void region. This selectivity engenders a new design strategy for the construction of compact optical devices for reflecting light.
4. Conclusions
The reflection properties of MDM metasurfaces were numerically investigated using RCWA and the FDTD method to determine analytical models based on diffraction theory. It was found that the origin of the anomalous reflection was the incident angle independence of the anomalous reflection wavelength and the quarter-wavelength resonance in the dielectric layer region sandwiched between the micropatches, which gives rise to a phase difference between the diffraction wave at the micropatch and that at the dielectric region. The analytical models obtained from the simulation results show that the anomalous reflection wavelength is proportional to h and the refractive index of the dielectric layer. This is the main difference from the conventional diffraction condition for metallic-surface relief gratings. Thus, the anomalous reflection angle can be determined by the incidence angle, h, p, and n. Moreover, the use of an offset micropatch was proposed to select the direction of the reflection. In the MDM metasurface with an offset micropatch, the dielectric layer was discontinuous and composed of structures wider than that of micropatches offset to one side of the dielectric structures, thus forming an asymmetric step. The reflection was enhanced in the opposite direction to the void owing to the phase difference induced by the void. The reflection direction selectivity was insensitive to the incident angle and almost fixed at the anomalous reflection wavelength. These results will contribute to the fabrication of efficient metasurface reflection control devices.
Disclosures
The authors declare no conflicts of interest.
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