Metagrating technologies have attracted great interest and made remarkable progress in a wide range of applications for controlling incoming wavefronts through nanostructures [1–3]. By carefully engineering periodic surface arrays, incident light waves can be redirected to the desired direction. To achieve high efficiency and precision, researchers have designed various building blocks and sophisticated structures that enable near-unitary coupling to a single diffraction channel among the higher orders of diffraction [3].

The concept of metagratings was first introduced by Ra’di et al. [1] in 2017 to overcome limitations of conventional gradient metasurfaces. By incorporating periodic or locally periodic arrays, they demonstrated how propagating higher-order Floquet modes could be aligned with desired directions while suppressing unwanted diffraction orders. Thereafter, a variety of periodic arrays were constructed in the metagratings to achieve multiple functionalities including beam splitting, steering and focusing wavefront control [4–6]. Recently, metagratings have been developed in various areas with integrating [3] and nonreciprocal [7] designs.

In earlier work, Hessel et al. [8], theoretically demonstrated that a rectangular grating surface can produce a single diffracted order (n = −1) with 100% efficiency when satisfying the conjectured Bragg condition. Later, Moharam and Gaylord [9] numerically analyzed various types of grating surfaces to examine their maximum efficiencies of transmitted first diffraction order. Indeed, these prior works serve as fundamental building blocks for designing simple metagrating structures and achieving advanced light control. With the principles of diffraction gratings, this paper presents optimal design and analysis of one-dimensional (1D) metagratings. Despite their simple architecture, these structures demonstrate excellent functionality including negative reflection, unidirectional deflection, beam dividing and concentrating.

2.1. Modelling of 1D Diffraction Metagrating

Figure 1 illustrates a simple 1D metagrating structure that can be designed with key geometric parameters such as grating period (Λ), height (H) and fill factor (F). The grating consists of a high refractive index material (n_H) placed on a substrate with a lower refractive index (n_s). To enhance higher-order diffraction, the first-order transmittance (T₋₁ or T₊₁) was maximized using an optimal set of parameters {Λ, H, F} under TM polarization (i.e. transverse magnetic field, H_y). For precise simulations, a rigorous coupled-wave analysis (RCWA) method [10] was employed using commercial software [11]. By varying the angle of incidence (θ_inc), zeroth- and first-order transmittances (T₀, T_±1) were characterized in the 1D metagrating structure. To achieve nearly unitary T₊₁ or T₋₁, efficient light control is enabled through anomalous transmission at large angles in the desired direction.

Figure 1. Simple 1D metagrating by higher-order diffraction. To enhance first-order transmittance (T₋₁ or T₊₁), the light can be controlled in a large angle of propagation. The geometry parameters include grating period (Ʌ), fill factor (F) and height (H). The n_c, n_g and n_s denote refractive indices of cover, grating and substrate, respectively. Under TM polarization (i.e. H_y), zeroth-order transmittance (T₀) and T_±1 are simulated by rigorous coupled-wave analysis (RCWA) while varying the angle of incidence (θ_inc).

2.2. Angular Properties of Higher-order Transmittance

To investigate the angular properties of higher-order transmittances as presented in Fig. 2, the T₀, T₋₁ and T₊₁ are characterized in the T(θ_inc, λ) color maps. The 1D metagrating is optimized by {Λ = 0.8 μm, H = 0.35 μm, F = 0.6} using a silicon (Si, n_g = 3.48) grating on a glass (n_s = 1.48) substrate in the air (n_c = 1). At θ_inc = ±20°, the grating parameters set was numerically optimized to maximize the efficiency of the T_±1 diffraction orders by using a particle swarm optimization (PSO) method [12]. The three T maps clearly show that the transmission properties are affected by the first-order Rayleigh anomaly (i.e. RA_±1 (n_c or n_s) = Λ[(n_c or n_s) ± sin(θ_inc)]) [13]. Here, the RA_±1 (n_c) and RA_±1 (n_s) indicate the wavelength of the Rayleigh anomaly for reflection and transmission. As shown in the first map, the T₀ exhibits high efficiency within λ > RA_±(n_s) but it shows near-zero efficiency in the range of RA_± (n_a) < λ < RA_± (n_s). This is attributed to the fact that the light is mostly coupled to the T₋₁ or T₊₁ through the 1D metagrating. As seen in the second and third color maps, each higher-order transmittance achieves near-unity efficiency around at θ_inc = ±20°.

Figure 2. Angular properties of higher-order diffraction in the 1D metagrating. The optimal parameter set {Ʌ = 0.8 μm, H = 0.35 μm, F = 0.6} is determined to achieve high efficiency for T₋₁ and T₊₁ under TM polarization. Each color map shows the T₀, T₋₁ and T₊₁ spectra as the θ_inc varies from –90° to 90°. The white and yellow dashed lines indicate the first-order Rayleigh anomalies [RA_±1 (n_c) and RA_±1 (n_s)] in reflection and transmission.

Figure 3(a) represents the transmittance spectra of the T₀, T₋₁ and T₊₁ at θ_inc = 20° where the 1D grating structure is the same as for Fig. 2. When the λ locates between RA₋₁ (n_s) = 0.91 μm and RA₊₁ (n_s) = 1.457 μm, the T₋₁ efficiency is significantly enhanced. In fact, in this spectral region, the T₊₁ becomes zero because it propagates evanescent waves above the RA₋₁ (n_s) = 0.91 μm. In contrast, the T₋₁ continues to propagate in the substrate until it reaches RA₊₁ (n_s) = 1.457 μm. Consequently, incident light can only be coupled to the T₀ and T₋₁ directions when the input wavelength is between RA₋₁ (n_s) and RA₊₁ (n_s). With numerical optimization of the grating structures, incident light can be predominantly coupled to T₋₁ diffraction among these two remaining channels. Notably, at λ = 1.2 μm, the T₋₁ reaches its maximum efficiency of 0.992. Due to its symmetric structure, the T₊₁ is also expected to achieve the same efficiency 0.992 at θ_inc = −20°. As illustrated in the schematic, the light is mostly transmitted in the T₋₁ direction. Figure 3(b) demonstrates the T₋₁ light propagation by simulating the tangential component of magnetic field (H_y) distribution from the finite-difference time-domain (FDTD) simulation. When the 1D metagrating is illuminated, the light undergoes negative refraction with the large diffraction angle of the T₋₁ (i.e. θ₋₁), which can be derived from the grating equation, sin⁻¹ {[sin θ_inc − λ / Λ] / n_s}. At θ_inc = 20°, the light is refracted with a high angle, θ₋₁ = −51.48°.

Figure 3. Negative refraction in the 1D metagrating. (a) Transmittance spectra of T₀, T₋₁ and T₊₁ at θ_inc = 20° in the 1D metagrating. (b) Distribution of H_y (y-component of the magnetic field) simulated using the finite-difference time-domain (FDTD) method.

2.3. Asymmetric Structure for 1D Metagrating Deflector

As depicted in Fig. 4(a), the asymmetric 1D structure enables light deflection. When light passes perpendicularly through the asymmetric grating, it can be coupled into a unidirectional channel if one desired diffraction order retains unity efficiency. For the normal incidence operation, the asymmetric 1D structure can be tailored by modifying the 1D grating structure from Fig. 1. In a simple way, as seen in the schematic, an additional component of the same material is aligned with the right edge of the grating. Then the structure is properly decided by its height (H₁) and fill factor (F₁). Figure 4(b) shows the T₁ spectra as a function of the H₁ where the grating parameter set is {Λ = 0.8 μm, H = 0.34 μm, F = 0.68, F₁ = 0.2} at normal incidence. As the H₁ increases from 0.02 μm, the T₁ is significantly enhanced as it forms the asymmetry structure.

Figure 4. Asymmetric structure for 1D metagrating. (a) Schematic of the asymmetric grating where the H₁ and F₁ are height and the fill factor of the additional component from Fig. 1. (b) The T₁ map as a function of the H₁ for the asymmetric structure {Ʌ = 0.8 μm, H = 0.34 μm, F = 0.68, F₁ = 0.2} at normal incidence.

Figure 5(a) represents the T₀, T₋₁ and T₊₁ spectra of the asymmetry grating with H₁ = 0.08 μm under normal incidence. At λ = 0.948 μm, it clearly shows that the light is coupled to the T₊₁ diffraction with high efficiency of 0.988. In Fig. 5(b), the H_y distribution demonstrates the light deflection when the diffraction angle θ₊₁ = 53.19° is derived from the grating equation. As displayed in the inset, the right-side asymmetric grating induces rightward deflection with the θ₊₁. Conversely, the left-side asymmetric grating is also valid for leftward deflection.

Figure 5. Light deflection in 1D asymmetric grating. (a) The T₀, T₋₁, and T₊₁ spectra at H₁ = 0.08 μm. (b) The H_y distribution of the right-side asymmetric grating. The grating parameter set is {Ʌ = 0.8 μm, H = 0.34 μm, H₁ = 0.08 μm, F = 0.68, F₁ = 0.2}.

2.4. Light Control by 1D Asymmetric Metagrating

The integration of left- and right-side (L and R) asymmetric gratings enables precise control of light, effectively functioning as a beam divider and concentrating element. Figure 6(a) shows the simulated H_y distribution of a combined array where the L and R asymmetric gratings occupy the left and right halves of the region, respectively. The parameter set of both L and R are the same as for {Λ = 0.8 μm, H = 0.34 μm, H₁ = 0.08 μm, F = 0.68, F₁ = 0.2}.

Figure 6. Light control of the combined 1D array with left- and right-side (L and R) asymmetric grating. Schematic and H_y distribution for (a) the beam dividing and (b) the concentrating element where the grating parameter set is the same as for Fig. 5. For beam dividing (a), the L and R asymmetric gratings are located in the left and right halves of the region. For concentrating (b), their positions are reversed. To avoid disruption in the focal area in (b), 6 periods of gratings at the center are removed.

As presented in Fig. 6(a), the incident light beam is divided into T₋₁ and T₊₁ diffraction orders with a high deflection angle. When the positions of the L and R asymmetric gratings are reversed, as shown in Fig. 6(b), the beam can be concentrated due to the switching of each deflection direction. To prevent interference in the focal area, six periods of the gratings at the center are removed. The H_y distribution demonstrates that the beam is concentrated at z = −7.5 μm, which serves as the focal plane.

In this study, a simple 1D grating demonstrates various types of metagratings such as negative reflection, unidirectional deflection, beam dividing and concentrating elements. By optimizing the 1D grating structure, one higher-order diffraction is significantly enhanced, which can be a desired radiation channel for the metagrating. In the symmetric 1D structure based on a Si grating-on glass substrate, it achieved a high efficiency of the T₋₁ diffraction and demonstrated negative refraction with a large diffraction angle. For normal incidence operation, the 1D structure can be modified by incorporating an asymmetric grating with an additional component. With optimal parameters, it enabled unidirectional light deflection when light is incident perpendicular to the surface. Furthermore, by combining left- and right-side asymmetric gratings, it demonstrated beam dividing and concentrating elements. This innovative metagrating technology, based on diffraction optics, will be useful for a wide range of applications.

The author received no financial support for the research, authorship, and/or publication of this article.

The author declares that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The data that support the findings of this study are available from the corresponding author upon reasonable request.