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Abstract
Beam splitters play important roles in several optical systems. Due to the growing demand for the miniaturization of optical systems, it is necessary to design beam splitters with nanoscale dimensions to miniaturize the essential components for integrated optical circuits. In this work, we propose and numerically demonstrate a broadband, high efficient, and four-channel beam splitter based on a fishnet-shaped metasurface. The proposed structure is constructed of cruciform AlSb nanoantennas on the PDMS substrate. The simple design can split a beam of light into four beams with equal intensity, it achieves a conversion efficiency above 83%, and an anomalous transmission intensity exceeding 0.8 for the wavelength range of 761-835 nm. In this wavelength range, the beam splitting angle changes from 46.45° to 53.68°. Moreover, the four-channel beam splitter is tunable when the metasurface is designed as a discrete structure. At the wavelength of 874 nm, the beam splitting angle can be adjusted from 56.34° to 46.39° as the period increases from 1050 nm to 1207 nm by stretching the substrate. The presented metasurface might enable promising applications in integrated optical devices, owing to its advantages of multi-channel, wide broadband, high efficiency, and large beam split angle.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
An optical beam splitter can split incident light into two or more beams with pre-designed directions. It has been widely investigated due to its crucial role in many optical systems, such as dual/multi-channel sensing [1], optical communications [2], interferometer [3], and optical spectroscopy [4]. Conventional high-performance beam splitters achieve beam splitting by utilizing various structures and methods, such as diffraction gratings [5,6], waveguides [7–9], multilayer films, etc. However, most conventional beam splitters suffer from the disadvantage of integration into micro-optical circuits because of the bulk and weight. Metasurfaces bring solutions to these problems, manipulating electromagnetic waves in desired ways by changing amplitude, polarization states, and phase at subwavelength scale, and exploiting different nanostructures to achieve new degrees of freedom to manipulate electromagnetic waves from visible light to microwave. So far, the development of metasurface-based applications has yielded fruitful results, such as polarizing devices [10–12], metalens [13–15], and vortex generators [16]. The results of numerous studies have shown that plasmonic metasurface cannot achieve efficient transport due to its inherent metal loss. However, dielectric metasurfaces composed of high dielectric constant materials can achieve efficient transmission in both transmission or reflection modes, such as beam deflectors [17], polarization converters [18,19], and focusing lenses [20]. Based on the antecede of reports, all of geometric metasurfaces [21], coding metamaterials [22,23], and phase gradient metasurfaces [24–26] can achieve the desired high-efficiency beam splitting functions. The phase controlling principles include Fabry−Pérot(F-P) resonance, Pancharatnam−Berry(P-B) resonance, and Mie resonance. Among these three principles, the P-B resonance is only suitable for circularly polarized light, and the bandwidth of the beam splitter obtained by the Mie resonance is narrow, so the F-P resonance is used in this paper to control the phase gradient metasurface.
In general, we can classify phase-gradient metasurface-based beam splitters into discrete metasurfaces [27–31] and continuous metasurfaces [32–34]. Discrete metasurface-based beam splitters are composed of two antenna arrays with opposite phase gradients, and cannot achieve high conversion efficiency and large operating bandwidth. Beam splitters based on continuous metasurfaces can easily achieve high conversion efficiency, large working bandwidth, large beam splitting angles, and fabricating easily. According to the reports so far, the designs of metasurface-based multi-channel beam splitters are all based on discrete metasurfaces, such as Wang et al. [35] proposed a gradient metasurface-based multi-channel beam splitter, which consists of low-loss TiO2 nanopillars. The structure achieved three-channel beam splitting ability. The conversion efficiency of the design exceeds 57%, and the beam split angle reaches 28° over the range of 500-600 nm. Ding et al. [36] used pentamer-based metasurface for designing 1:4 beam splitter, and the beam splitter can achieve the total anomalous transmission intensity above 0.65 covering the wavelength range from 1041 nm to 1073 nm wavelength range. We can clearly see that the design of the previous literature cannot meet the performance requirements of multi-channel beam splitters in practical applications. Therefore, it is necessary and desirable to propose an all-dielectric continuous metasurface beam splitter with high conversion efficiency, large beam splitting angle and wide operating bandwidth.
In this work, we propose and numerically demonstrate a four-channel beam splitter based on an all-dielectric fishnet-shaped metasurface. The properties of multi-channel beam splitting, high conversion efficiency, wide working bandwidth, and large beam splitting angle are achieved, simultaneously. The beam splitter is constructed of cross-shaped aluminum antimonide(ALSB) nanoantennas on a PDMS substrate. The proposed beam splitter can achieve the anomalous transmission intensity above 0.8 over the range of 761-835 nm. The conversion efficiency reaches 83%, and the beam splitting angle exceeds 46.45° over this wavelength range. In addition, we found that since the substrate we used is an elastic material, when the structure size changes, it is no longer a fishnet structure, this time we get a dynamic beam splitter. When the period increases from 1050 nm to 1207 nm, the splitting angle changes from 56.34° to 46.39°. Although this work mainly numerically investigates the design of a four-channel beam splitter, it is possible to obtain an arbitrary channel beam splitter by changing the structure. We believe that our design method can bring more degrees of freedom to design high performance beam splitters.
2. Design and simulation methods
The schematic diagram of our designed four-channel beam splitter based on an all-dielectric metasurface is shown in Fig. 1(a). In the schematic, a fishnet-shaped aluminium antimonide nanoantenna array is placed on a polydimethylsiloxane(PDMS) substrate. Figure 1(b) illustrates the schematic of the structure of one unit cell. As shown in Fig. 1(b), the period along the x-direction is equal to the period in the y-direction set as Px = Py = 1050 nm, and the thickness of the substrate is 1100 nm. The width of the nanoantenna is set as w = 90 nm, and its thickness is h with a vale of 180 nm. Since it is a fishnet structure, the designed arm length is l = (P-w)/2. The time domain finite difference (FDTD) method simulation is performed with a commercial software FDTD Solution to analyze the optical characteristics of the metasurface-based beam splitter. In the simulation, we set periodic boundary conditions both in the x and y directions as periodic boundary conditions, and adopt perfectly matched layers along the z-direction. The refractive index of PDMS is set as 1.4, and the optical parameters of ALSb are taken from Ref [37]. And a normally incident light (the angle between the electric field direction and the x-direction is 45°) linearly polarized wave is incident on the metasurface from the bottom of the substrate, with a wavelength range of 700-900 nm.
Fig. 1. (a) Schematic of the fishnet-shaped metasurface composed of AlSb nanoantennas on the PDMS substrate. (b) Three-dimensional schematic of one unit cell.
We expect that the designed four-channel beam splitter can achieve exceptionally high transmission intensity, large operable bandwidth, and large beam splitting angles. We can use phase gradient metasurfaces to manipulate light according to generalized Snell's law [38]. Generalized Snell's law demonstrates that phase gradient along the horizontal direction at the dielectric interface reaches abnormal refraction or reflection by controlling the propagation of incident light. It defines the anomalous transmission angle as
3. Results and discussion
3.1 Optical response of the four-channel beam splitter
Based on the continuous phase gradient metasurface which is constructed of cross-shaped AlSb nanoantennas, the proposed beam splitter can divide the incident light into four anomalous refracted beams with the same intensity and a beam transmitted light in the normal direction. The total intensity of the anomalous transmission is defined as t = T1 + T2 + T3 + T4, and the conversion efficiency is defined as η= t/(t + T0)*100%. The total abnormal transmission intensity and conversion efficiency of the beam splitter in the wavelength range of 700–900 nm are shown in Fig. 2(a). It can be seen that the anomalous transmission intensity is greater than 0.8 covering the wavelength range from 761 nm to 835 nm, and the highest value reaches 0.87 at the wavelength of 814 nm. And the conversion efficiency in this wavelength range is higher than 83%, maximum value up to 90.8%. The intensities of the four beams of the anomalous refracted light and the normal transmission light are depicted in Fig. 2(b). It can be clearly seen that the intensities of the four beams are equal at any wavelength, so in the following discussion, we will only discuss the (0,−1) order. The light intensity of the (0,0) order is always less than 0.13 when the wavelength is changed from 764 nm to 829 nm. Figure 2(c) demonstrates the angular distribution of the normalized electric field intensity at a wavelength of 776 nm, where the beam splitting angle is 47.65°, and the simulation results are consistent with those calculated by equations (4) and equations (5).
Fig. 2. (a) Total abnormal transmission intensity and conversion efficiency for wavelengths of 700-900 nm. (b) Intensities of T0, T1, T2, T3, and T4 in the same wavelength range. (c) The angular distribution of the normalized electric field intensity of transmitted light at the wavelength of 776 nm.
Figure 3(a) shows the anomalous transmitted intensity and phase response of the beam splitter for the (0, −1) order in the wavelength range of 700–900 nm. It can be found that the abrupt changes in the phase correspond to each other where the abnormal transmission intensity abruptly occurs. The variation of the splitting angle at wavelengths from 700 nm to 900 nm can be seen in Fig. 3(b). The angle changes from 46.45° to 52.68°, and the wavelength increases from 761 nm to 835 nm. It can be seen that when the structural parameters are constant, the beam splitting angle changes with the wavelength. The total transmission and reflectivity are shown in Fig. 3(c). In the wavelength range from 761 nm to 835 nm, the total transmission intensity reaches a maximum of 0.98 at the wavelength of 817 nm, while the reflectance reaches minimum with a vaule of 0.02. At the wavelength of 778 nm, the total transmission intensity has a minimum value of 0.9, and the reflectance has a maximum value of 0.10 at a wavelength of 779 nm. The maximum absorbance obtained by 1-T-R is also less than 0.02. The total transmission and the transmission of the ALSb layer are shown in Fig. 3(d). It is obvious that the two lines are almost identical. Since the imaginary part of the refractive index of ALSb is very small as plotted insert Fig. 3(d), the absorption can be almost ignored. Therefore, the loss is mainly caused by reflection.
Fig. 3. (a) Simulated intensity of the (0, −1) order transmission light and phase response for wavelengths of 700-900 nm. (b) Beam splitting angle covering the same wavelength range. (c) Total anomalous transmission and reflection intensities. (d) The transmission intensity of each layer and total transmission intensity.
Since the variation of the structural parameters is not negligible in a practical exercise, in order to make our proposed beam splitter highly robust. We simulated the effect of three structural parameters on the optical performance of the beam splitter. We define the anomalous transmission intensity of order (0,−1) as greater than 0.2 to indicate that the metasurface exhibits efficient beam splitting and define the corresponding wavelength as the working wavelength. Figures 4(a) and 4(b) show the anomalous transmission intensity and transmission phase shift of the (0, −1) order as a function of w. It is clear that as w increases, the bandwidth of the operating wavelength also increases. In Fig. 4(c), it can be observed that the (0, −1) order has a range of working wavelengths at different w values and the maximum and minimum values of the beam splitting angle within the working wavelength. We can see that when w = 74 nm, its working bandwidth is 71 nm; however, when w = 90 nm, the working bandwidth increase to 76 nm. When w is set as 90 nm, and the operating wavelength changes from 760 nm to 836 nm, the beam splitting angle also increases from 46.37° to 52.77°.
Fig. 4. (a) The anomalous transmission intensity of (0, −1) order at different w values in the wavelength range of 700-900 nm. (b) The corresponding transmission phase shift for diferent structural parameter w. (c) Operating wavelength and range of the beam splitting angle at different w values.
In Figs. 5(a) and 5(b), we can observe anomalous transmission intensity and phase shifts of the (0, −1) order anomalous transmission light at different h values. It can be clearly seen that the red-shift of the end wavelength of the working wavelength. In the case of increasing h, a phase shift of 2π can still be achieved in the wavelength range of 700-900 nm. Figure 5(c) shows the range of working wavelengths and the variation splitting angle within the working wavelength for different h values. When h = 176 nm and 178 nm, respectively, the operating bandwidths are 72 nm and 74 nm, respectively, and for the condition of h = 180 nm, 182 nm, and 184 nm, respectively, the bandwidths are the same with a value of 76 nm. When h equals to180 nm, the beam splitting angle changes from 46.37° to 52.77°. It can be found that the change of h has little effect on the performance of the beam splitter.
Fig. 5. (a) The anomalous transmission intensity of (0, −1) order at different h values covering the wavelength range from 700 to 900 nm. (b) The corresponding transmission phase shift. (c) Operating wavelength and range of the beam splitting angle at different h values.
To investigate the effect of the size of the period on the performance of the beam splitter, we scanned the anomalous transmission intensities and phase shifts of the (0, −1) order as the period increased from 1000 nm to 1100 nm, as shown in Figs. 6(a) and (b). It can be clearly found that the onset wavelength of the working wavelength takes place red-shifted. Through Fig. 6(c), we find that the bandwidths at 1010 nm and 1030 nm are relatively small, which are 48 nm and 53 nm, respectively. When the period increases to 1050 nm, the bandwidth becomes 76 nm, and the angle increases from 46.37° to 52.77°. When the period keeps increasing to 1070 nm and 1090 nm, it still maintains a large bandwidth of 71 nm and 64 nm, respectively. It can be seen that the change of the period had a great impact on optical performance. From these results, we can find that the proposed four-channel beam splitter has high robustness.
Fig. 6. (a) The anomalous transmission intensity of (0, −1) order at different p values for wavelengths range of 700-900 nm. (b) The corresponding transmission phase shift. (c) Operating wavelength and range of the beam splitting angle at different p values.
3.2 Design of the dynamic beam splitter
Because the optical characteristics of metasurfaces come from the morphology of the nanostructure array and the preparation materials, tunable metasurfaces provide a way to manipulate optical response in real time. Here, we analyze the tunability of the optical properties for the proposed four-channel beam splitter. Since we used a mechanically stretchable polydimethylsiloxane (PDMS) substrate, it can be changed into a dynamic beam splitter by applying an external mechanical stimulus on the elastic substrate. Experimentally, in order to fabricate fishnet metasurfaces, we can use existing nanofabrication techniques described by various experimental dynamic metasurfaces [39–41]. We can use a flexible technique based on the “metal-assisted transfer" [42] strategy. Firstly, the fishnet-structure was formed on a silicon substrate with a silver film (named the Ag-coated silicon substrate) through electron beam lithography (EBL), evaporation, and the lift-off process. Next, we bonded the Si/Ag/fishnet-structures on the PDMS slab and then separated the silicon from the PDMS slab. The benefit of the weak adhesion between the entire layer of the Ag film and silicon is that the fishnet-structures and Ag film clung tightly to the PDMS slab. After etching the Ag layer using phosphorous acid, nanostructures were left behind on the PDMS substrate. Finally, yielding the designed fishnet-shaped continuous metasurface. Assuming that the localized phase transition is independent of substrate deformation, we apply a diagonal stretch to the substrate along the x and y-axes at a uniform rate, with a stretch ratio 1+ɛ. Setting the initial period Pa to 1050 nm, the period P under diagonal stretching can be described as P = Pa*(1+ɛ). We re-determined the parametric dimensions of the structure by parametric sweep; the width w became 85 nm, the thickness h became 240 nm, and the arm length l no longer changes with P and w, and its value is 480 nm. At this time, the beam splitter is no longer a fishing net structure. As ɛ increased to 17.14%, the period increased from 1050 nm to 1230 nm, and scanned the variation of the anomalous refractive intensity of the (0, −1) order in the wavelength range of 700–900 nm, as shown in Fig. 7(a). It can be found that the anomalous transmission intensity is higher in the wavelength range of 800-900 nm. In Fig. 7(b), the red dashed line indicates that the anomalous transmission intensity value of order (0, −1) is 0.16. The wavelength at this time is 874 nm, and it can be found that the abnormal transmission intensity can be kept above 0.16 in the range of the period from 1050 to 1207 nm. The beam splitting angle in this period range varies from 56.34° to 46.39°, as shown in Fig. 7(c). It can be seen that after the structural parameters are determined, a dynamic beam splitter can be obtained by applying external mechanical stimulation.
Fig. 7. (a) The intensity of (0,−1) order anomalous transmission light at different values of p with the wavelength range of 700-900 nm. (b) The intensity of (0,−1) order anomalous transmission ligth at different values of p at a wavelength of 874 nm. (c) The beam angle from period 1050 nm to 1230 nm.
4. Conclusions
In summary, we propose and numerically demonstrate a high efficient, ultra-broadband, and four-channel beam splitter based on a continuous metasurface. The proposed beam splitter is constructed of a fishnet-shaped AlSb nanoantenna array on a PDMS substrate. In the wavelength range of 761-835 nm, the total anomalous transmission intensity exceeds 0.8, the lowest conversion efficiency reaches 83%, and the splitting angle also varies from 46.45° to 52.68° at this wavelength range. Furthermore, we further investigate a four-channel dynamic beam splitter based on the proposed structure, which utilizes the stretchability of the substrate. It is shown that the beam splitting angle of the (0, −1) order at 874 nm can be adjusted from 56.34° to 46.39° by stretching the period from 1050 nm to 1230 nm. These merits, including broad bandwidth, high efficiency, and tunable, compared with traditional optical components, render the proposed continuous metasurface a good candidate to be applied in photonic integrated optical systems.
Funding
National Natural Science Foundation of China (61805051); Natural Science Foundation of Guangxi Province (2020GXNSFAA297192); Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing, Guilin University of Electronic Technology (GXKL06220105).
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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