Terahertz Silicon Metagratings: High‐Efficiency Dispersive Beam Manipulation above Diffraction Cone

Optical wavefront engineering is essential for the development of next‐generation integrated photonic devices. It is used for reflecting terahertz waves in a predesigned nonspecular direction with near‐unitary efficiency, which is a longstanding challenge for high‐performance functional devices. Recently, metagratings have offered an efficient solution for beam steering at large angles without the need for a discretization phase or impedance profile. Here, all‐dielectric metagratings fabricated using a silicon cuboid complex lattice are proposed and demonstrated experimentally to achieve anomalous terahertz beam reflections above the diffraction cone with unitary diffraction efficiency. For the bipartite metagrating system, a single dispersive scatterer per unit is effective for achieving broadband beam steering because of Brillouin zone folding, and another perturbative synergetic scatterer is introduced to slightly tailor the array coupling and improve the performance. High‐efficiency beam steering, including both retroreflection under oblique incidence and one‐way diffraction under normal incidence, can be achieved by breaking structural symmetry and coherently suppressing unnecessary radiation channels. Moreover, silicon metagratings with spatially dispersive response features show perfect anomalous reflection operation in the broadband region, which is promising for leveraging terahertz spatially separated devices.


Introduction
Terahertz waves are readily absorbed by water in biological tissues and they interact with macromolecules and the weak bonds between them. Thus, terahertz waves have many potential applications in biomedicine, chemistry, and detection. [1][2][3] However, fewer studies exist on the light-matter interactions in the terahertz spectral region than those in other spectral regions owing to a lack of efficient devices for generating, manipulating, and detecting terahertz waves. [4] In the past decade, significant progress has been made in the effective control of terahertz waves using metasurfaces. [5][6][7][8][9] Investigations on 2D metamaterials, i.e., metasurfaces [10][11][12][13][14][15][16][17][18] have drawn considerable attention in recent years in light wavefront engineering, nonlinear optics, and topological photonics owing to their novel optical properties. [19][20][21] Among these, terahertzintegrated on-chip metadevices are essential for the generation, detection, and modulation of terahertz light on a miniaturized single chip, which has attracted research interest owing to its potential applications in high-speed communication, sensing, and imaging. [22] As a promising route, researchers recently demonstrated a silicon-based on-chip device employing topological valley transport to enable error-free communication with a data transfer rate of up to 11 Gbit s −1 at 0.335 THz. [23] Combining integrated photonics and terahertz technology may enable the fabrication of compact, efficient, and high-performance devices for future terahertz photonic applications. [24,25] The fabrication of high-performance photonic devices may enable the emergence of metamaterial functionalities for applications in the technologically difficult terahertz-frequency regime. One of the fundamental directions is the advancement of optical wavefront engineering for application in the free-space interconnection of terahertz waves. [26,27] Recently, a type of metallic or plasmonic biparticle [28] or metagrating [29] has shown significant electromagnetic wave-manipulation functionalities, including abnormal scatterings, in the radio frequency band and optical region. [30][31][32][33] Compared with conventional phase-gradient metasurfaces, metagratings do not require a rapidly varying impedance profile, which requires high-resolution fabrication processes. Therefore, metagratings can be fabricated using methods that are more cost-effective and scalable. [34] Furthermore, metagratings can achieve high beam steering in unitary efficiency by exploiting periodicity, rather than surface phase-gradient distribution, to reroute an incident wave to a propagating highorder diffractive mode. [35] In contrast, the overall efficiency of metasurfaces in beam steering is fundamentally restricted owing to physical bounds on conversion and nonunitary efficiencies.
Abnormal terahertz beam engineering may be demonstrated efficiently by simply modulating the scattering of a few discrete particles in a plasmonic array structure operating in terahertz wavelengths. [34][35][36] However, resonant-particle-enhanced Ohmic damping in plasmonic metasurfaces significantly restricts the performance of plasmonic metagratings in the optical region, including the terahertz band. [37] Metasurfaces with periodic complex unit cells [38,39] composed of high-index dielectric materials such as ceramics, [40] titanium dioxide, [41,42] perovskite, [43] and silicon [44] have been demonstrated to be effective for overcoming the loss in plasmonic structures and achieve high performance. [45] In this study, we experimentally demonstrate that appropriately designed metagratings composed of a silicon cuboid complex lattice can control abnormal terahertz beams with highefficiency, including retroreflection for oblique incidence and one-way diffraction for normal incidence, by coherently suppressing unnecessary orders. The synergy of multiple particles per supercell is shown to optimize the performance of anomalous reflections rather than building phase gradients. In addition, abnormal reflection can operate in the broadband region and shows a spatially dispersive response, which is promising for dispersive terahertz optics because the broadband and high-efficiency spatial separation of terahertz signals may have applications in compact spectrometers for measuring the spectra of terahertz and far-infrared signals. [46]

Results and Discussion
A common method for manipulating beam steering via gradient metasurfaces is to design the continuous gradient impedance of local meta-atoms, which enables the desired local momentum to reroute an impinging wave in a nonspecular radiation direction. However, the overall efficiency of gradient metasurfaces in wavefront manipulation is fundamentally restricted owing to physical bounds on the conversion and nonunitary efficiencies. Metagratings employing a periodicity k g = 2 n∕p, rather than adding transverse momentum d ∕dy, to redirect an incident wave to one of the propagating high-order diffractive modes, have demonstrated great capability for extreme beam steering with unitary efficiency. This class of metagratings can be modeled as an effective surface electric current density [29] J e (x, y, z) = ⃖⃖ ⃗ e z I x e (x − m where (x) is Dirac's delta function and I x e = j xx ee E x ext is the induced electric current on each particle. Figure 1a shows the designed bipartite metagrating, which can redirect an oblique incident wave into a nonspecular direction with unitary efficiency in a broadband manner. To design this metagrating the period must be p y = p 1 and p x = p 1 /2 to ensure that only two scattered propagating modes (N = 2) are radiated into the far field under oblique incidence over a certain frequency regime, i.e., diffractive mode for 0 and −1 order. Dual silicon cuboids located over the ground plane constituted the metagrating. Every bipartite silicon cuboid with a different size makes up a supercell ( Figure 1b) with a periodic dimension of p 1 × p 1 /2 to fold the diffraction cone into the working frequency range from 0.39 to 0.78 THz (Note S5, Supporting Information). The dual silicon cuboid scatterers were designed (Note S2, Supporting Information) to create asymmetric scattering and eliminate the undesired specular propagating mode (0 order), thereby redistributing the energy flow to the retroreflection direction (−1 order), as shown in Figure 1c. Note that the coupling of individual particles is not negligible, particularly when the particle size is comparable to the period. We prove that although a tailored individual alldielectric scatterer per supercell is sufficient to achieve complex diffraction scenarios, the performance can be further optimized by introducing another properly perturbative synergetic scatterer into the bipartite metagrating system, and the generated system exceeds their combined advantages (Note S3, Supporting Information).
To analyze the working performance of the bipartite metagrating, we performed full-wave numerical simulations using the commercial simulator COMSOL Multiphysics. In the simulations, the silicon cuboids were simulated as loss-free materials owing to their high resistivity (>5 kΩ) and refractive indices of 3.45. Periodic boundary conditions were set along the x and y directions to simulate an infinite periodic array. A plane wave illuminated the metagrating at an angle i with an x-polarized electric field, which can be written as follows where E 0 is the incident amplitude, 0 is the free-space wave impedance, and k 0 = 2 ∕ is the wave vector in free space. The reflected fields can be represented as an infinite sum of the Floquet harmonic diffraction modes as follows where A n denotes the complex amplitude of the nth harmonic. The corresponding reflected magnetic fields can be written as The transverse wavevector of the n th diffraction with period p satisfies k r,y = k i + nk g = k 0 sin i + 2 n∕p, and the correspond- r,y , which is evanescent and does not contribute to the far field when k r,y > k 0 . For a completely controllable nonspecular reflection, the reflected field is represented using only one propagating harmonic n = −1 with an integral electric field amplitude with an angle of r = sin −1 ( k r,y k 0 ). In a reflective-type system, the number of allowed diffraction orders N is governed by the following equation [28] where ⌊.⌋ is a round down operation. Substituting k 0 , k i , and k g into (6) yields the following To achieve perfect anomalous reflection, at least N metaelements are required in a supercell to suppress undesired reflected propagating leaky modes. Notably, within a specific range of i and fp/c, N is limited to 2, which implies that there exist only two leaky modes, including a specular reflection mode (0 order) and a diffraction mode (−1 order). This is beneficial for simplifying metagrating designs to achieve broadband and high-efficiency metagratings, because as long as the specular reflection is suppressed, the incident waves can only be redirected to the anomalous direction, with a diffraction angle of If the period p is fixed, Equation (7) is a function related only to the incident angle i and working frequency f (Note S1, Supporting Information). Figure S1 in the Supporting Information shows the relationship between these two attributes, with i ranging from 0°to 90°and f from 0.4 to 0.7 THz, when p = p 1 = 385 μm (see the Supporting Information). Only N = 1 and N = 2 exist in the frequency of interest, and there is a dividing line between these two regions, which is called a diffraction cone. Below the diffraction cone, only the specular mode can propagate, whereas above the diffraction cone, both the specular and diffraction modes (−1 order) can propagate. All higher-order modes are evanescent waves that cannot radiate energy into the far field.
We plotted the scattered power reflected into the specular (Figure 2a) and anomalous ( Figure 2b) directions with the incidence angle ranging from 0°to 89°and the green line yielded by Equation (7) is the diffraction cone. Perfect anomalous reflection can be maintained in a broadband manner above the diffraction cone. For example, between 0.48 and 0.62 THz under i = 50°planewave illumination, the anomalous reflection carries more than 99% of the incident power, indicating a broadband anomalous reflector with high efficiency. Moreover, a nearly perfect anomalous reflection can be achieved over a wide incidence-angle range. For example, with an incidence angle range of 17°to 71°, the anomalous reflection at 0.63 THz carries more than 95% of the incident power, demonstrating the capability of rerouting the input light to the desired direction with high efficiency over a broad incident angle.
Instead of adding a transverse surface phase gradient to engineer the wavefront, periodicity is applied to align the direction of one of the propagating high-order diffractive modes with the desired direction in unitary efficiency. In addition, the simulated electric fields for incident ( Figure 2c) and scattered (Figure 2d) waves at 0.5 THz with 50°incidence confirm the near-perfect anomalous reflection performance. The calculated anomalous reflection angle was −52°, which is in good agreement with the simulated field distribution.
The appearance of reflected power in the −1 order can also be explained as the result of Brillouin zone folding. [47] We assume that the scattered power in Figure 2a,b can be interpreted as a function of both the incident angle and frequency, i.e., P = P(f, i ). Because the wavevector component k r,y = k 0 sin i + 2 n∕p is also a function of f and i , there exists a certain projection such that P = P(k r,y ) = P(k 0 sin i + 2 n∕p). If we denote the reflected power function as P 0 for the unperturbed case (a 1 = b 1 = 125 μm, p = p 1 /2), then for the 0 order P 0 = P(k 0 sin i ). When the structural symmetry is broken (Note S4, Supporting Information), the unit cell size will increase to p = p 1 . Owing to the periodicity of the grating, the behavior of the reflected power should be the same across different Brillouin zones. Therefore, P(k r,y ) = P(k r,y + 2 ∕p 1 ). Substituting the expression of k r,y and setting n = −1, we obtain With a small perturbation, the approximation P(k 0 sin i ) ≈ P 0 (k 0 sin i ) may be applied. Therefore, the reflected power is redirected to the −1 order through the folding of the Brillouin zone.
The fabricated bipartite metagrating was characterized using fiber-based angular resolved terahertz time-domain spectroscopy (THz-TDS). A simplified schematic of the experimental setup for angular scanning is shown in Figure 3a. A collimated, vertically polarized terahertz beam illuminates the fabricated metagrating at several oblique incident angles. Subsequently, the metagrating deflects the beam in different directions depending on the wavelength. The deflected beams are captured using a linearly polarized detector attached to a rotating mount. To measure the radiation across an angular scanning range, the emitter is fixed at a certain angle and the detector is rotated over the scanning range with pulse increments of 1°. Figure 3b shows a side view of the fabricated bipartite metagrating via scanning electron microscopy (SEM), where the supercell is highlighted and denoted by a dashed yellow rectangle.
The specular reflection amplitude was first measured with an incident angle ranging from 10°to 70°, as shown in Figure 3c. In the range of the frequency of interest, the reflection amplitude was maintained at a small value, indicating its capability to suppress the 0-order specular mode. To verify the high-efficiency and broadband characteristics of the metagrating, the diffraction spectra over a frequency range of 0.4-0.7 THz under 20°, 25°, 30°, 50°, 55°, and 60°illumination were also measured over a broad angular range, as shown in Figure 3d-i. The reflected amplitude is significantly enhanced around the reflection angle of the −1 diffraction order, where a single leaky mode can be clearly observed; this is in good agreement with the previously simulated results shown in Figure 2b. In the measurement system, because the angle between the emitter and detector should be larger than 18°to prevent their contact, some reflection angles with highefficiency anomalous reflection cannot be measured. Under 30°i llumination, the measured reflection amplitude at 0.635 THz with a reflection angle of −48°reaches a maximum of 75%, revealing the capability of high-efficiency wavefront control. For all Laser Photonics Rev. 2023, 17, 2200975 these experiments, the measured diffraction angles are in good agreement with the theoretically calculated diffraction angles obtained using Equation (8) (red dashed lines in Figure 3d-i) over a broad bandwidth range.
Many applications require anomalous reflections with normal incidence. Therefore, we propose the design of a tripartite metagrating (Figure 4a), which can reroute a normally incident wave in a nonspecular direction with unitary efficiency over a broad bandwidth. To design this metagrating, we first set the period p y = p 2 and p x = p 2 /3 to ensure that only three diffraction orders (N = 3) were radiated into the far field under normal incidence in the frequency band of interest. Triple silicon cuboids of various sizes were fabricated into a supercell (Figure 4b) with periodic dimension p 2 × p 2 /3 to fold the diffraction cone from 1.2 to 0.4 THz (Note S6, Supporting Information). For the normal incidence case, three leaky propagating modes existed over a certain frequency regime, i.e., diffraction modes 0, −1, and +1. These silicon cuboids were designed to create asymmetric scattering and they broke both periodic and mirror symmetry (Notes S7-S9, Supporting Information) to suppress the undesired leaky modes 0 and +1 and redirect the normally incident wave in the direction of diffraction mode −1, as shown in Figure 4c.
We validated this concept by performing full-wave numerical simulations. Figure 5a shows the simulated reflection spectra with diffraction orders of 0, −1, and +1. At ≈0.49 THz, more than 95% of the incident power is redirected into the −1 order, while less than 5% of the incident power is scattered in the direction of the diffraction order of 0 and +1, indicating the high-efficiency anomalous reflection of the metagrating. The electric field distributions at 0.49 THz of the incident (Figure 5b) and scattered (Figure 5c) waves also show that the incident wave is reflected  in a near-perfect manner. The reflection angle of −55°coincides with the value theoretically calculated using the diffraction law.
In addition to fabricating the tripartite metagrating, we characterized its performance using THz-TDS. Figure 6a shows a simplified schematic of the experimental setup used for the angular scanning. The fabricated sample and emitter are fixed, while the detector is rotated over the scanning range between +23°to +87°and −23°to −87°with pulse increments of 1°. A side view of the fabricated tripartite metagrating using SEM is shown in Figure 6b, where a supercell is highlighted by a dashed yellow rectangle.
The diffraction spectra over a frequency range from 0.4 to 0.7 THz under normal incidence are shown in Figure 6c,d. The diffraction order can be clearly observed in Figure 6c, while it is significantly suppressed in Figure 6d, indicating that the metagrating can reshape the wavefront in the −1-order direction with high efficiency. The measured diffraction angles are in good agreement with the theoretically calculated diffraction angles (red dashed lines in Figure 6c,d) over the measurement frequency range. Figure 6e shows the reflection amplitude spectra with diffraction orders of 0, −1, and +1 for a reflection angle r of |46°|. The reflection of the 0 order is approximately measured via specular reflection with a 10°incidence. The measured reflection  amplitude reaches a maximum of 85% at 0.55 THz with a reflection angle of −46°, while it is almost eliminated in the cases of the 0 and +1 diffraction orders. Note that metagrating can also operate at broadband frequency. Figure 6f,g shows the measured reflection amplitudes for diffraction order of −1 and +1, respectively, with five discrete frequencies from 0.45 to 0.65 THz, where prominent suppression of the +1 order and enhancement for the −1 order can be observed, implying the broadband working performance of the metagrating. Note that both the bandwidth and efficiency show a certain decrease in the experiments, which may be attributed to unexpected fabrication errors and the influence of the silicone oil between the silicon cuboids and substrate.

Conclusion
In conclusion, we have demonstrated all-dielectric terahertz metagratings composed of a silicon cuboid complex lattice that can achieve high-efficiency abnormal terahertz beam control by coherently suppressing undesired propagating leaky modes. Under wide-angle oblique incidence, bipartite metagrating enables broadband retroreflection above the diffraction cone because of Brillouin zone folding. In particular, a perturbative synergetic scatterer is important for slightly tailoring the array coupling to further improve the performance of the bipartite system. In addition, a tripartite metagrating can achieve highly efficient oneway diffraction under normal incidence by breaking both periodic and mirror symmetries. Compared with conventional gradient metasurfaces, the proposed metagratings are easier to design and fabricate, with far less complexity and considerable robustness. All-dielectric metagrating designs can be extended to other frequency bands. High-performance, broadband, and wide-angle wavefront shaping via metagratings pave the way for diffractivecontrolled photonic devices, which may have advanced applications in beam steering and extreme wave manipulation.

Experimental Section
Microfabrication of the Sample: A 4 in. silicon wafer was cleaned with solvents and dried using compressed nitrogen. A 200 nm film of aluminum was deposited on the wafer, along with a 5 nm chromium adhesion layer. The two metal thin films were deposited via electron beam evaporation (FU-12PEB) at a rate of 0.2 nm s −1 after pumping down to a base pressure of 1 × 10 −6 Torr. In addition, another 3 in. high resist (HR) silicon wafer with a thickness of 100 μm and resistivity of >5 kΩ cm was spin-coated with a layer of SPR-220 at 3000 rpm to achieve a film thickness of 3 μm. Subsequently, laser direct writing (Heidelberg; DWL 66+) was performed to define the patterns corresponding to the diameter of the terahertz dielectric cuboids. Before plasma-enhanced deep reactive ion etching (Oxford PlasmaPro 100 Cobra), the 3 in. HR silicon was bonded to a 4 in. metal-coated silicon wafer with silicone oil. The etching process consisted of two steps: deposition and etching. In the deposition step, a gaseous mixture of C 4 F 8 (100 sccm) and SF 6 (1 sccm) with an inductively coupled plasma (ICP) power of 700 W and radio frequency (RF) power of 10 W was used for 6 s. The etching step employed a gaseous mixture of C 4 F 8 (1 sccm) and SF 6 (100 sccm) with an ICP power of 700 W and an RF power of 25 W for 7 s. Thus, an approximate etching rate of 0.67 μm per cycle was obtained for the HR Si. The required 100 μm deep etch was obtained over 150 cycles. The photoresist was stripped off using a reactive ion-etching system (Oxford NGP 80).
Measurement of the Sample: Two fiber-coupled terahertz antennas were employed as the emitter and detector. The fabricated metagrating, which was placed at the center of a rotator, was illuminated by a collimated vertically polarized terahertz beam from the emitter at various incident angles and the reflected beams were scattered in wide directions, depending on their wavelengths. A linearly polarized detector was attached to a rotating mount to measure spatially dispersed scattered terahertz beams. In the measurement, the emitter had a fixed angle while the detector was rotated over the scanning range with pulse increments of 1°to measure the spatial dispersive radiation across an angular scanning range.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.