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Abstract
We report a quasi-continuous beam splitter with highly efficient equal-power beam splitting in a wide spectral range. It consists of rhombic aluminum antimonide nanorods standing on a silica substrate. Firstly, a beam splitter based on discrete structures is designed, and the structures are optimized to obtain the quasi-continuous beam splitter. The beam splitter achieves a splitting efficiency of over 80% within the region of 675–786 nm (bandwidth = 111 nm), where the splitting angle can vary in the range of 97.2°−121.8°. In particular, the splitting efficiency reaches 93.4% when the wavelength is 690 nm. Overall, the proposed beam splitter potentially paves the way for realizing broadband metasurfaces and high-performance quasi-continuous metasurface-based devices.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Beam splitters play an indispensable role in several optical and photonic applications, such as interferometers, spectroscopy, and optical communications, because they can split light beams based on the polarization, wavelength, or intensity [1–6]. However, traditional beam splitters are bulky, which makes them difficult to be applied to integrated and miniaturized photonic devices. With the rapid development of nanophotonics, heavy optical elements are gradually being replaced by metamaterial elements [7]. For example, H. Xu et al. proposed an on-chip silicon polarization beam splitter with a small footprint, low loss, high extinction ratio, and wide bandwidth by using anisotropic metamaterials [8]. As an ultra-thin metamaterial, metasurfaces can flexibly manipulate the light's polarization, amplitude, phase, and control transmission modes depending on the material selection and structural design [9–15]. Due to these characteristics, metasurfaces have been applied in a wide range of applications, such as anomalous refractors [16,17], metalens [18,19], holography [20,21], polarization modulation [22–24], and so on.
Several studies have been conducted on metasurfaces based on discrete structures, and high anomalous reflection and transmission efficiency have been obtained. For example, X. Zhang et al. used an array of discrete circular gold nanocylinders to achieve efficient reflection beam splitting at a wavelength of 632.8 nm [25]. Further, the splitting angle and power distribution between the two beams could be effectively controlled by changing the incident angle. D. Zhang et al. proposed a gradient metasurface beam splitter based on lithium niobate cylinder arrays by introducing an opposite phase gradient within a unit cell [26]. However, the discrete array structures suffer from the problems of narrow bandwidth, limited aspect ratio, and serious difficulty in precise manufacturing. A quasi-continuous structure can efficiently solve these problems and is expected to be the basic structure for large-scale fabrication. L. Zhang et al. first proposed a quasi-continuous plasmonic metasurface to achieve ultra-wideband anomalous reflection, and only one trapezoidal nanoantenna existed in the unit cell of the metasurface [27]. L. Yang et al. extended this structure to all-dielectric metasurface and realized efficient broadband anomalous transmission [28]. In addition, some researchers have proposed metagratings based on metasurface, which can achieve efficient broadband wavefront manipulation through a continuous structure within the unit cell [29–32]. These structures and design strategies are beneficial for solving the problems of the existing beam splitters, including narrow bandwidth and low efficiency.
In this study, we propose and numerically demonstrate an efficient broadband beam splitter based on a quasi-continuous metasurface. Firstly, an equal-power beam splitter is designed based on discrete nanoantenna arrays. Furthermore, the structure is optimized to obtain the quasi-continuous beam splitter. The simulation results reveal that both splitting efficiency and bandwidth of the quasi-continuous beam splitter are significantly improved after optimization. When the wavelength is 690 nm, the splitting efficiency reaches a high value of 93.4% with a large splitting angle of 100°. Overall, the proposed methods and beam splitter structure provide useful insights into the development of novel quasi-continuous metasurface-based devices.
2. Design and analysis
A schematic of the rectangular aluminum antimonide (AlSb) nanorods standing on a silica (SiO2) substrate is illustrated in Fig. 1(a). The refractive indices of AlSb and SiO2 can be found in Ref. [33] and Ref. [34], respectively. The transmittance and phase distributions are numerically analyzed using the finite-difference time-domain (FDTD) method. Periodic boundary conditions are adopted in both x- and y-directions, and the boundaries along the z-direction are set as perfect matching layers. An x-polarized light is vertically incident on the bottom surface. The lattice constants in both x- and y-directions are 200 nm. In the simulation, the heights of the rectangular nanorods and the substrate are set to 205 nm and 2000nm, respectively. The phase accumulation can be realized in the metasurfaces through the optical path difference generated by the propagation of electromagnetic waves. These nanorods can be considered as truncated waveguides, whose phases are primarily modulated by the effective refractive index of the fundamental mode [35]. The phase can be expressed as follows:
Fig. 1. (a) Schematic of the rectangular aluminum antimonide nanorods standing on a silica substrate. (b) Variation in the phase and transmittance with the cross-sectional side length w.
Figure 2(a) presents a comparison between the refractive indices of AlSb with Si, a commonly used material in the visible region. The real parts of the refractive index of the two materials are very close, but the imaginary part of the refractive index of AlSb is much smaller than that of Si. Since the absorption of a structure is only governed by the imaginary part of the refractive index, we compare the absorption efficiency of a nanorod with a side length of 170 nm using AlSb and Si, as shown in Fig. 2(b). The absorption efficiency of Si reaches nearly 18% at a wavelength of 650 nm. It is much higher than that of AlSb at the operating wavelengths, which severely limits the structure's transmission performance. By contrast, the absorption of AlSb is almost negligible at wavelengths over 700 nm. Other dielectric materials commonly used in the visible band also exhibit non-negligible absorption loss. Although the imaginary part of the refractive index of titanium dioxide can be ignored, the real part is relatively small, requiring a large height, limiting the precise experimental preparation. Due to its high refractive index and low loss, AlSb is a promising material for the design of devices with high transmission performance.
Fig. 2. (a) Optical parameters of AlSb and Si in the wavelength range of 600–800 nm. (b) Absorption efficiency of a rectangular nanorod using AlSb and Si, respectively.
The incident light beam is divided into two parts due to the phase gradient when it propagates through the beam splitter. According to the generalized Snell's law [38,39], the emergence angles can be expressed as follows:
Fig. 3. (a) Schematic of the discrete beam splitter with six rectangular nanorods in a unit cell, where the spacing d =10 nm. (b) Variation in the transmittance of each diffraction order of the discrete beam splitter with wavelength. (c) Variation in the phase distribution in a unit cell along the x-direction with wavelength.
The phase distribution of discrete structures is not continuous, so it is difficult to achieve perfect phase matching in a wide bandwidth. The linear phase profile is more integrated if the number of nanorods providing phase response in a period increases [40]. However, increasing the number of nanorods in the unit cell can increase the difficulty in precise experimental preparation. To improve the bandwidth, we cancel the spacing of adjacent elements and obtain the continuous structure, as shown in Fig. 4(a). Compared with the discrete structure, only the spacing between adjacent elements is removed, and the other parameters remain unchanged. For comparison, Figs. 4(b) and 4(c) show the transmission intensity of each diffraction order and the phase distributions along the x-direction, respectively. It is clear from Fig. 4(b) that the splitting efficiency reaches 93.2% when the wavelength is 683 nm. Further, the bandwidth over which the splitting efficiency remains higher than 80% increases to nearly 80 nm. Compared with the case of discrete structures, the phase distributions in Fig. 4(c) can ensure a phase difference close to π over a wider bandwidth. These results indicate that the continuous structure is better than the discrete structure for phase matching and bandwidth improvement.
Fig. 4. (a) Schematic of the discrete beam splitter with six rectangular nanorods in a unit cell without spacing. (b) Variation in the transmittance of each diffraction order for the beam splitter with the wavelength. (c) Variation in the phase distributions along the x-direction in a unit cell with the wavelength.
To further facilitate precision fabrication and improve the performance, we simplify the original serrated edge to obtain a continuous rhombic nanoantenna. As shown in Fig. 5(a), the beam splitter's height h1, length of the long side L1, and length of the short side L2 are 205, 760, and 168 nm, respectively. Figure 5(b) shows the transmission intensity of each diffraction order as a function of wavelength. It can be seen that due to the symmetry of the structure, the proposed beam splitter can still achieve equal-power beam splitting. Moreover, owing to the continuity of the structure, the performance of the beam splitter (which includes splitting efficiency and bandwidth) is significantly improved compared with the discrete structure. The splitting efficiency is 93.4% when the wavelength is 690 nm. Meanwhile, the beam splitter achieves a splitting efficiency of over 80% in the wavelength range of 675–786 nm, which corresponds to a bandwidth of 111 nm. The proposed quasi-continuous beam splitter can suppress the zero-order transmission better, and its transmission intensity is almost negligible in the wavelength range of 700–780 nm.
Fig. 5. (a) Schematic of the proposed quasi-continuous beam splitter. The lattice constants in the x- and y-directions are 900 nm and 200 nm, respectively. (b) Variation in the transmittance of each diffraction order for the proposed quasi-continuous beam splitter with the wavelength.
Using FDTD simulation for the proposed quasi-continuous beam splitter, the deflection angle and transmission intensity of each diffraction order are obtained as a function of wavelength, which are shown in Fig. 6(a). The broadband zero-order suppression is more intuitively reflected in Fig. 6(a). The transmitted light is mainly concentrated in the ±1 diffraction orders. Moreover, the transmittance of the ±1 diffraction orders always remains above 40% when the deflection angle varies from 48.6° to 60.9°. Figure 6(b) shows the total transmittance, reflectance, and absorptivity of the beam splitter. The total transmittance is higher than 80% in the wavelength range of 669–792 nm, and it reaches 97.3% when the wavelength is 687 nm. When the wavelength is above 675 nm, the absorption of the structure is almost negligible, indicating that the AlSb is an effective material for the fabrication of a beam splitter. Moreover, the total transmission efficiency decreases significantly with the increase in reflectance when the wavelength is under 670 nm and over 800 nm.
Fig. 6. (a) Deflection angle and transmittance of each diffraction order as a function of wavelength. (b) Total transmittance, reflectance, and absorptivity as functions of wavelength.
To reveal the high-efficiency, wideband beam splitting mechanism of the proposed quasi-continuous beam splitter, Fig. 7(a) shows the variation in the phase distributions along the x-direction in a unit cell with the wavelength. It is clear from Fig. 7(a) that the phase difference between the two sides and the center is approximately π in the wavelength range of 670–800 nm. The broadband phase difference is the basis to ensure the realization of beam splitting over a wide bandwidth. Due to the interaction between neighboring elements, the discrete structures can only achieve phase matching in a very narrow bandwidth. By contrast, owing to the continuity of the structures, the quasi-continuous structures can realize wideband phase matching. Figure 7(b) displays the phase distribution of electromagnetic waves in the y = 0 plane at a wavelength of 690 nm. The auxiliary lines connecting equiphase planes are also shown in Fig. 7(b). For clarity, the phase distribution of two unit cells are plotted. It can be seen in the figure that the normal incident light is divided into two beams at the same angle of 50.1° after passing through the beam splitter.
Fig. 7. (a) Variation in the phase distributions along the x-direction in a unit cell with the wavelength. (b) Phase distribution of electromagnetic waves in the y = 0 plane at a wavelength of 690 nm.
To demonstrate the advantages of the proposed quasi-continuous beam splitter, a quantitative comparison between the proposed beam splitter and the previously reported metasurface-based beam splitters is presented in Table 1. Specifically, we have compared the materials used in each work, maximum splitting efficiency, and the bandwidth in which splitting efficiency over 80% is achieved. The discrete beam splitter designed by D. Zhang et al. [26] could only achieve the maximum efficiency when the wavelength was 800 nm, and the transmittance was less than 60%. In the polarization beam splitter designed by S. Tian et al. [41], the anomalous transmittances of x- and y-polarized light reached 71% and 76%, respectively. Guo et al. [42] proposed a polarization beam splitter based on discrete GaN nanorods. The transmittance in x- and y-directions reached 42.5% and 44.7%, respectively, with a polarization angle of 45°. Compared to these three discrete beam splitters that could only work in a narrow bandwidth, the beam splitter proposed by He et al. [43] can achieve more than 80% splitting efficiency in a bandwidth close to 50 nm. Ozer et al. [44] achieved efficient beam splitting by using two TiO2 nanorods with a π phase difference. The splitting efficiency reached 90% at a wavelength of 532 nm and could be higher than 80% over a bandwidth of nearly 60 nm. However, due to the low refractive index of TiO2, the height of nanorods in the above two works was 600 nm. The highest aspect ratio was closer to 10, which greatly limited the precise manufacturing. Li et al. [45] realized dual-band beam splitting by using two opposite trapezoidal antennas. Compared with the previously reported discrete structures, the quasi-continuous beam splitter proposed by Li et al. exhibited significantly improved bandwidth. Further, the transmittance of y-polarized incident light remained above 65% in the wavelength range of 687–710 nm, while that of x-polarized incident light remained above 74% in the wavelength range of 969–1054 nm. However, due to the non-negligible absorption loss of silicon material, the bandwidth with splitting efficiency over 80% was still less than 30 nm. Overall, compared to the previously reported beam splitters, the proposed quasi-continuous beam splitter displays substantially improved splitting efficiency and bandwidth.
Table 1. Performance comparison between the proposed and previously reported beam splitters.
Compared with the discrete structures, the proposed quasi-continuous beam splitter has the advantage of fewer control parameters. To obtain the optimal transmission performance, the influence of geometric parameters on the splitting efficiency and bandwidth of the beam splitter is analyzed. When a parameter sweep is performed on one variable, the remaining parameters take the values mentioned in Fig. 5(a). Benefitting from the symmetry of the proposed structure, T−1 and T+1 remain the same at any wavelength. Consequently, the transmittance of the +1 diffraction order is used for subsequent analysis. Figure 8(a) shows the variation in the transmittance with the height h1 of the beam splitter in the wavelength range of 650–850 nm. There are two dark regions in this figure. As the height h1 increases, the transmission peak has an obvious redshift. The blue area at short wavelengths and above 750 nm corresponds to the transmittance decrease due to the increase in reflectivity, which severely limits the transmittance and bandwidth of the beam splitter. To select the appropriate height h1, the variations in the peak transmittance (black axis) and the bandwidth with transmittance over 40% (red axis) as a function of height h1 are shown in Fig. 8(b). As the height h1 increases, the transmittance peak redshifts. It may be noted that the transmittance curve shows two peaks. Although the transmittance is 47.8% when the height h1 is 200 nm, the bandwidth is only 85 nm. The transmittance slightly drops to 46.6% at a height h1 of 205 nm, but the bandwidth reaches 111 nm. To achieve high transmittance and wide bandwidth simultaneously, the height h1 is set to 205 nm.
Fig. 8. (a) Variation in the +1 order transmittance with the height h1 of the quasi-continuous beam splitter. (b) Variation in the peak transmittance and the bandwidth with transmittance over 40% as a function of height h1.
Figure 9(a) shows the transmittance of the proposed beam splitter with different lengths L1 in the range of 600–900 nm. Similar to the effect of height h1, the transmittance is limited by the increased reflectivity at short wavelengths and wavelengths greater than 750 nm. It can be seen that the maximum intensity is achieved when the length L1 is in the range of 740–780 nm. Figure 9(b) shows the effect of length L1 on the peak transmittance and the bandwidth with transmittance over 40%. Both the curves show an increasing trend initially, followed by a decreasing trend, reaching the maximum value simultaneously when the length L1 becomes 760 nm. When the length L1 is 600 nm, the bandwidth with transmittance greater than 40% is 52 nm. However, when the length L1 exceeds 880 nm, more than 40% transmittance cannot be obtained. Therefore, the value of length L1 should be set to 760 nm.
Fig. 9. (a) Variation in the +1 order transmittance with the length L1 of the quasi-continuous beam splitter. (b) Variation in the peak transmittance and the bandwidth with transmittance over 40% as a function of length L1.
Figure 10(a) shows the variation in the transmittance as a function of the length L2 of the quasi-continuous beam splitter in the wavelength range of 650–850 nm. Similar to the previous cases, there are still reflection regions that limit the bandwidth, and the red area becomes very narrow as the length L2 approaches 80 nm. It is obvious that the highest transmittance can be obtained when the length L2 is in the range of 120–160 nm. Further, as the length L2 increases, the red area becomes wider. In addition, when the wavelength is close to 730 nm, there are some light-colored regions in the figure, where the transmittance is less than 40%, limiting the bandwidth. Figure 10(b) depicts the peak transmittance and the bandwidth with transmittance over 40% as a function of the length L2. When the length L2 is 144 nm, the transmittance reaches a maximum of 48.2%. However, affected by the light-colored regions in Fig. 10(a), the bandwidth can only reach 79 nm. As the length L2 increases, the transmission intensity of the light-colored regions gradually increases. When the length L2 is 168 nm, the bandwidth reaches 111 nm, though the peak transmittance drops to 46.6%. To recapitulate, the optimal parameters of the proposed equal-power quasi-continuous beam splitter are h1 =205 nm, L1 =760 nm, and L2 = 168 nm.
Fig. 10. (a) Variation in the +1 order transmittance with the length L2 of the quasi-continuous beam splitter. (b) Variation in the peak transmittance and the bandwidth with transmittance over 40% as a function of the length L2.
Figure 11(a) shows the variation in the splitting efficiency with the polarization angle of incident light. The beam splitting efficiency and bandwidth decrease with the increase in the polarization angle of incident light. It can be seen that when the polarization angle is less than 20°, the beam splitting efficiency can be maintained at a high level. For further clarity, the splitting efficiencies at the polarization angles of 0°, 20°, 45° and 90° are depicted in Fig. 11(b). When the polarization angle is 0°(x-polarized), the bandwidth with beam splitting efficiency over 80% can reach 111 nm. The bandwidth with splitting efficiency over 80% can still reach 60 nm when the polarization angle becomes 20°. When the polarization angle increases to 45°, the splitting efficiency becomes lower than 70%. When the incident light is y-polarized, the maximum splitting efficiency can only reach 60%. This is because the phase gradient of the originally designed beam splitter is along the x-direction, and it is excited by the x-polarized incident light. As the polarization direction of the incident light changes, the initial phase matching is no longer satisfied. However, when the polarization angle is less than 20°, the proposed quasi-continuous beam splitter still achieves high splitting efficiency and large bandwidth.
Fig. 11. (a) Variation in the splitting efficiency with the polarization angle of the incident light. (b) Splitting efficiency at the polarization angles of 0°, 20°, 45°, 90°.
3. Conclusions
We numerically demonstrated a quasi-continuous beam splitter with highly efficient, wide bandwidth equal-power beam splitting, which consisted of AlSb rhombic nanorods standing on a Si substrate. Firstly, a beam splitter with six discrete rectangular nanorods in a unit cell was designed. To resolve the issues of narrow bandwidth and difficulty in the precise fabrication of discrete structures, we further developed the quasi-continuous beam splitter. The beam splitter based on discrete structures could achieve a splitting efficiency above 80% only over a bandwidth of 42 nm. On the other hand, the proposed quasi-continuous beam splitter achieved a splitting efficiency over 80% within the wavelength region of 675–786 nm, corresponding to a bandwidth of 111 nm, where the splitting angle could be varied in the range of 97.2–121.8°. In particular, the splitting efficiency reached 93.4% when the wavelength was 690 nm. We believe that the design methods and structure of the proposed beam splitter can boost the development and practical applications of quasi-continuous, ultra-broadband metasurface-based devices.
Funding
National Natural Science Foundation of China (61805051); Natural Science Foundation of Guangxi Province (2018GXNSFBA281145, 2018JJA170021, 2020GXNSFAA297192, AD18281047); Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing, Guilin University of Electronic Technology (GXKL06160102, GXKL06180104, GXKL06180203, GXKL06190118).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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