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Abstract
Metasurfaces have made great progress in the last decade for generating miniature and integrated optical devices. The optical properties of metasurfaces can be tuned dynamically by integrating with phase-change materials. However, the efficiency of tunable metasurfaces remains a bit low, which is a disadvantage for the realistic applications of metasurfaces. Here, we demonstrate the tunable dielectric metasurfaces by structuring the phase-change material Ge2Sb2Te5. The unit cell of metasurface is composed of several Ge2Sb2Te5 nanopillars with different geometric parameters, and the incident light interacts with different nanopillars at diverse phases of Ge2Sb2Te5, leading to various functions. By elaborately arranging the Ge2Sb2Te5 nanopillars, various tunable optical devices have been realized, including tunable beam steering, reconfigurable metalens and switchable wave plate. The refractive direction, focal length and polarization state can be tuned through the phase transition of Ge2Sb2Te5. The phase-change metasurfaces based on Ge2Sb2Te5 nanostructures could be used in cameras, optical microscopy and adaptive optics.
© 2022 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces have attracted widespread attention in the past decade for realizing miniature and integrated optical devices [1–3]. Utilizing subwavelength metallic or dielectric structures to control the local amplitude, phase and polarization of reflected or transmitted light, various planar optical devices have been realized, including beam steering [4], metalens [5], hologram [6], vortex [7] and wave plate [8]. The working wavelength of metasurfaces is also widely ranged from the visible to microwave region. The efficiency is an important factor in realistic application. High-efficiency reflective metasurfaces can be realized by designing metal-insulator-metal structures [9], while high-efficiency transmissive metasurfaces can be achieved by employing low-loss dielectric materials with high refractive indices [10].
Although many optical devices based on metasurfaces have been realized, the functions of these devices are fixed once they are made. Recently, active and tunable metasurfaces have received more and more investigations [11,12]. Various tunable optical devices including spatial light modulators [13–15], reconfigurable metalens [16,17], dynamic holography [18,19], tunable colors [20–22], dynamic beam steering [23,24] and switchable polarizers [25,26] have been designed by combining metasurfaces with active materials, such as graphene [13,25], transparent conductive oxides [15,23], semiconductors [21,24], flexible materials [16–18] and phase-change materials [14,19,20,22,26]. The optical properties of these devices can be tuned by applying voltages, heat, stress or light. However, most tunable metasurfaces are realized by integrating metallic structures with active materials, the efficiencies of these devices are low due to the absorption loss of metal. Although there are a few works discussing the combination of dielectric metasurfaces with active materials [14,16,17], it involves several different materials and complicated fabrication processes. Here, we design a tunable dielectric metasurface by structuring the phase-change material Ge2Sb2Te5 (GST). Instead of combining with other dielectric materials, GST nanostructures themselves can work as active dielectric metasurfaces with tunable optical properties.
Recently, GST has gained intensive attention in nanophotonics [27,28]. It is a reversible phase-change material with amorphous and crystalline states. The phase transition of GST can be excited through multiple methods including temperature [29], light [30] and voltages [31]. The electrical and optical properties of GST make a large change during the phase transition process. In particular, based on the significant variation in the refractive index, GST has been integrated with metallic metasurfaces to realize many tunable optical devices, including switchable absorption [32], bifocal lensing [33], tunable filters [34], reconfigurable beam steering [35,36] and switching of photonic angular momentum [37]. In addition, due to the high refractive index of GST in the infrared, GST nanostructures have also been proposed to design tunable optical devices, including anomalous reflection angle controlling [38], active holograms [39], active anapoles [40,41], reconfigurable metalens [42] and tunable wave plates [43]. Nevertheless, most of the previous studies only consider the amorphous and crystalline phases, and their devices simply exhibit two functions. It is worth noting that there are some intermediate states in GST with a part of amorphous phase transformed into the crystalline phase, as demonstrated in recent experiments by controlling the temperature [37,40] or laser pulse power [44,45]. Therefore, the intermediate phases of GST can be used to realize more functions. Although there are some works employing the intermediate phases of GST to tune the resonant modes of GST nanostructures [38,40], the utilization of intermediate phases of GST to design beam steering, metalens and wave plate with more functions is few. In addition, the efficiencies of previous reported devices are still low and need to be improved.
In this work, we realize several tunable optical devices based on phase-change metasurfaces made of GST nanostructures. The phase-change metasurfaces can exhibit diverse optical properties at different phases of GST. Firstly, we discuss the design principle of phase-change metasurfaces. Then, we design an array of GST nanostructures to realize a tunable beam steering, and study the direction of transmitted light at different phases of GST. Next, we design a special distribution of GST nanostructures to realize a reconfigurable metalens, and discuss the variation in the focal length through the phase transition. Finally, we design a periodic array of GST nanostructures to realize a switchable wave plate, and analyze the change in the polarization state of transmitted light.
2. Design and simulation
The phase-change metasurface is composed of an array of GST nanopillars on a glass substrate, as schematically illustrated in Fig. 1. The unit cell is made of two GST nanopillars with different geometric parameters, which are defined as A and B, respectively. The structural parameters of A and B nanopillars are carefully adjusted so that the working wavelength of A nanopillar in the amorphous phase is same as that of the B nanopillar in the semicrystalline phase. In this work, the working wavelength of A nanopillar in the amorphous phase is chosen as 2.5 µm, where the absorption loss of GST at this wavelength is small. As the absorption loss of GST in both amorphous and crystalline phases is low in the wavelength ranging from 2.5 to 10 µm [46], we can also tune the working wavelength to other wavelengths at mid-infrared by adjusting the geometric parameters of GST nanopillars. The mid-infrared spectral region is important in many biomedical, military, and industrial applications [47]. When the GST is in the amorphous phase, at the wavelength of 2.5 µm, the incident light mainly interacts with A nanopillars and displays one function. When the GST is transformed into the semicrystalline phase (crystallinity of 50%), the working wavelength of B nanopillars is identical to the wavelength of incident light, while the working wavelength of A nanopillars shifts to another wavelength due to the variation in the refractive index of GST. Hence, the incident light mainly interacts with B nanopillars and presents another function. When the GST is transformed into the crystalline phase completely, both the working wavelengths of A and B nanopillars are shifted away from the wavelength of incident light, therefore both A and B nanopillars do not work anymore. As shown in Fig. 1, under the incidence of right-handed circularly polarized (RCP) light, the transmitted light is converted into the left-handed circularly polarized (LCP) light and deflects along one direction for GST in the amorphous phase, while deflects along another direction for GST in the semicrystalline phase. When the GST is transformed into the crystalline phase completely, the polarization state and direction of transmitted light are the same as that of the incident light. As a result, the functions of metasurfaces can be tuned through the phase transition of GST.
Fig. 1. Schematic of tunable beam steering based on phase-change metasurfaces composed of two kinds of GST nanopillars with different geometric parameters. When a circularly polarized light is normally incident on the sample, the transmitted light will be deflected to different directions for GST in the amorphous, semicrystalline and crystalline phases.
Based on the above analysis, how to design the A and B nanopillars is the key issue to realize the tunable metasurfaces. As the design of the phase response of nanostructures is critical for metasurfaces, therefore, it is important to design the phase response of A and B nanopillars. The phase response of nanostructures can be designed by many approaches, including resonant phase, geometric phase and propagation phase [1,2]. In particular, the geometric phase (Pancharatnam-Berry phase) is very useful [48,49], because the phase can be designed by simply rotating the nanostructures without changing the structural parameters, and it can work in a broad wavelength range. Therefore, we choose the geometric phase to design the phase response of the two kinds of nanopillars. To realize high-efficiency metasurfaces, it is important to optimize the geometric parameters of nanostructures to enable them to work as half-wave plates [5,6]. We can adjust the geometric parameters of A and B nanopillars to realize half-wave plates, where the working wavelength of A nanopillars in the amorphous phase is equal to the working wavelength of B nanopillars in the semicrystalline phase. At the designed wavelength (2.5 µm), the phase distribution of metasurface is mainly determined by the A nanopillars for GST in the amorphous phase, while the phase distribution of metasurface is mainly determined by the B nanopillars for GST in the semicrystalline phase. When the GST is transformed into the crystalline phase completely, both A and B nanopillars cannot function as half-wave plates at the original wavelength of incident light, therefore both A and B nanopillars do not work anymore. As a result, if we design two different arrays for A and B nanopillars, the metasurface will generate distinct functions through the phase transition of GST.
In order to demonstrate previous ideas, we designed the phase-change metasurfaces and calculated their optical properties by the finite-difference-time-domain software (FDTD Solutions) from Lumerical Inc. In the simulation, the complex refractive index data of GST in the amorphous and crystalline phases were taken from the Ref. [46]. Beside the familiar amorphous and crystalline phases of GST, recent experiments indicate that some intermediate phases can also exist [37,40,44,45]. In the simulation, the permittivities of the intermediate phases of GST were calculated through [45]:
3. Geometric parameters of Ge2Sb2Te5 nanopillars
Figure 2(a) shows the unit cell of A nanopillars, which are periodic along x- and y-directions. The length, width and height of GST nanopillars were chosen as 500, 370 and 1200 nm, respectively. Both periods along x- and y-directions were set as 1200 nm. We calculated the transmission spectra of the structure at different crystallinities of GST, when the incident light was polarized along the 45° direction relative to the x-direction. Figure 2(b) presents the transmission spectra of the A nanopillar array for GST in the amorphous phase. We define that the transmission component polarized parallel to that of the incident light as T‖, whereas the transmission component polarized perpendicular to that of the incident light as T┴. As presented in Fig. 2(b), when the GST is in the amorphous phase, T┴ is around 0.9 while T‖ is approaching 0 at the wavelength of 2.5 µm. Therefore, the A nanopillars can work as a half-wave plate at 2.5 µm for GST in the amorphous phase. When the GST is transformed into the semicrystalline and crystalline phases, the working wavelength of half-wave plate is red-shifted, due to the increase in the refractive index of GST, as shown in Figs. 2(c) and 2(d), respectively. Therefore, the A nanopillars cannot work as a half-wave plate at the wavelength of 2.5 µm for GST in the semicrystalline and crystalline phases.
Fig. 2. (a) Schematic of the structural unit of A nanopillars. (b), (c) and (d) are calculated transmission spectra of the A nanopillar array for GST in the amorphous, semicrystalline and crystalline phases, respectively, when the incident light was polarized along the 45° direction relative to the x-direction. The transmission component polarized parallel to that of the incident light is defined as T‖, whereas the transmission component polarized perpendicular to that of the incident light is defined as T┴. (e) Schematic of the structural unit of B nanopillars. (f), (g) and (h) are calculated transmission spectra of the B nanopillar array for GST in the amorphous, semicrystalline and crystalline phases, respectively, when the incident light was polarized along the 45° direction relative to the x-direction. (i) Schematic of the structural unit of C nanopillars. (j), (k) and (l) are calculated transmission spectra of the C nanopillar array for GST in the amorphous, semicrystalline and crystalline phases, respectively, when the incident light was polarized along the 45° direction relative to the x-direction.
Figure 2(e) shows the unit cell of B nanopillars, where the length and width of GST nanopillars were changed to 340 and 295 nm, respectively, while the height and period of GST nanopillars were same as that of A nanopillars. We calculated the transmission spectra of the structure at different crystallinities of GST, when the incident light was polarized along the 45° direction relative to the x-direction. Figure 2(g) presents the transmission spectra of the B nanopillar array for GST in the semicrystalline phase. When the GST is in the semicrystalline phase, T┴ is around 0.72 while T‖ is approaching 0 at the wavelength of 2.5 µm. Therefore, the B nanopillars can work as a half-wave plate at 2.5 µm for GST in the semicrystalline phase. The working wavelength of B nanopillars in the semicrystalline phase is equal to the working wavelength of A nanopillars in the amorphous phase. When the GST is in the amorphous and crystalline phases, the working wavelength of half-wave plate shifts to other wavelengths, due to the variation in the refractive index of GST, and cannot function as a half-wave plate at 2.5 µm, as shown in Figs. 2(f) and 2(h), respectively.
In addition to the A and B nanopillars, we also design the C nanopillars to realize a half-wave plate working at 2.5 µm for GST in the crystalline phase. Figure 2(i) shows the unit cell of C nanopillars, where the length and width of GST nanopillars were changed to 275 and 250 nm, respectively, while the height and period of GST nanopillars were same as that of A and B nanopillars. Figures 2(j)-(l) shows the calculated transmission spectra of the C nanopillar array at different crystallinities of GST, when the incident light was polarized along the 45° direction relative to the x-axis. As presented in Fig. 2(l), when the GST is in the crystalline phase, T┴ is around 0.55 while T‖ is approaching 0 at the wavelength of 2.5 µm. Therefore, the C nanopillars in the crystalline phase can work as a half-wave plate at 2.5 µm, which is same as the working wavelength of B nanopillars in the semicrystalline phase and A nanopillars in the amorphous phase. When the C nanopillars are in the amorphous and semicrystalline phases, the working wavelength of half-wave plate is blue-shifted, due to the decrease in the refractive index of GST, as shown in Figs. 2(j) and 2(k), respectively. Therefore, the C nanopillars cannot work as a half-wave plate at the wavelength of 2.5 µm for GST in the amorphous and semicrystalline phases.
In the previous simulations, the permittivities of the intermediate phases of GST were acquired by the linear interpolation, which can match well with the experimental results [45]. It should be noted that the permittivities of the intermediate phases of GST can also be calculated through the Lorentz-Lorentz relation [40]:
We also calculated the transmission spectra of the A, B and C nanopillar arrays with GST in the semicrystalline phase, where the permittivity of semicrystalline phase was acquired by the formula (2). As shown in Figs. 3(a)–3(c), the transmission spectra are different from the previous results of Figs. 2(c), 2(g) and 2(k), which is attributed to the difference in the permittivity of the semicrystalline phase of GST. In particular, the B nanopillars cannot work as a half-wave plate at 2.5 µm for GST in the semicrystalline phase, which is required in the design. Instead, the semicrystalline B nanopillars can work as a half-wave plate at 2.5 µm by adjusting the geometric parameters of B nanopillars. Figures 3(d)–3(f) show the calculated transmission spectra of the B nanopillars at different crystallinities of GST, where the length and width of B nanopillars were changed to 385 and 320 nm, respectively, while the height and period of B nanopillars were same as that of A and C nanopillars. We can find that the semicrystalline B nanopillars with modified geometric parameters can work as a half-wave plate at 2.5 µm. Since both linear interpolation and Lorentz-Lorentz relation used to acquire the permittivities of the intermediate phases of GST by different groups can get consistent results between experiments and simulations [40,45], the permittivities of the intermediate phases of GST are dependent on the quality of GST samples. In realistic applications, the permittivity of the semicrystalline phase of GST should be obtained by the direct experimental measurement, as done in a recent work [37]. In the following, all the results for GST in the semicrystalline phase were calculated by using the linear interpolation, and similar results can be obtained by using the Lorentz-Lorentz relation with modified geometric parameters of B nanopillars.
Fig. 3. (a), (b) and (c) are calculated transmission spectra of the A, B and C nanopillar arrays with GST in the semicrystalline phase, respectively, where the permittivity of semicrystalline phase was acquired by the Lorentz-Lorentz relation. (d), (e) and (f) are calculated transmission spectra of the B nanopillar array for GST in the amorphous, semicrystalline and crystalline phases, respectively, where the length and width of B nanopillar were changed to 385 and 320 nm, respectively, and the permittivity of semicrystalline phase was acquired by the Lorentz-Lorentz relation.
Now, we have optimized the geometric parameters of A, B and C nanopillars, and we can further design the phase of transmitted light based on the three kinds of nanopillars. According to the theory of geometric phase, under the incidence of circularly polarized light, the phase of transmitted light with opposite circular polarization is determined by: Φ=2σφ, where φ is the angle between the long side of nanopillar and x-direction, and σ=+1 (-1) corresponds to the incidence of right-handed (left-handed) circularly polarized light [48,49]. We changed the direction of A nanopillars as schematically illustrated in Fig. 4(a), and calculated the transmittance and phase of left-handed circularly polarized light under the incidence of right-handed circularly polarized light with GST in the amorphous phase at the wavelength of 2.5 µm. As shown in Fig. 4(b), the phase of transmitted light is nearly proportional to the rotated angle of nanopillars, consistent with the result of theory. The transmittance of left-handed circularly polarized light is around 0.9, almost independent of the rotated angle of nanopillars. We also changed the direction of B nanopillars as schematically illustrated in Fig. 4(c), and calculated the transmittance and phase of left-handed circularly polarized light under the incidence of right-handed circularly polarized light with GST in the semicrystalline phase at the wavelength of 2.5 µm. Similar to the results of A nanopillars, the phase of transmitted light can cover the 2π range by rotating the nanopillars, and the transmittance of left-handed circularly polarized light is around 0.7, as presented in Fig. 4(d). We also changed the direction of C nanopillars as schematically illustrated in Fig. 4(e), and calculated the transmittance and phase of left-handed circularly polarized light under the incidence of right-handed circularly polarized light with GST in the crystalline phase at the wavelength of 2.5 µm. As shown in Fig. 4(f), the phase of transmitted light can be tuned by rotating the nanopillars, and the transmittance of left-handed circularly polarized light is around 0.53. As a result, we can design the phase of transmitted light with high transmission efficiency by changing the rotating direction of nanopillars.
Fig. 4. (a) Schematic of the direction of A nanopillar. (b) Transmittance (T) and phase (Φ) of left-handed circularly polarized light in A nanopillars under the incidence of right-handed circularly polarized light with GST in the amorphous phase at the wavelength of 2.5 µm. (c) Schematic of the direction of B nanopillar. (d) Transmittance (T) and phase (Φ) of left-handed circularly polarized light in B nanopillars under the incidence of right-handed circularly polarized light with GST in the semicrystalline phase at the wavelength of 2.5 µm. (e) Schematic of the direction of C nanopillar. (f) Transmittance (T) and phase (Φ) of left-handed circularly polarized light in C nanopillars under the incidence of right-handed circularly polarized light with GST in the crystalline phase at the wavelength of 2.5 µm.
4. Tunable beam steering
Based on the design of the phase response of GST nanopillars, we can further realize tunable optical devices by reasonably designing the phase distribution. Firstly, we realize the tunable beam steering by elaborately arranging the GST nanopillars. According to the generalized Snell's law for anomalous refraction, the direction of transmitted light depends on the phase gradient along the interface through [48,49]:
Fig. 5. (a) Schematic of the unit cell of metasurface to generate the tunable beam steering. (b) and (c) are the calculated phase distribution and far-field intensity of left-handed circularly polarized light with GST in the amorphous phase, respectively. (d) and (e) are the calculated phase distribution and far-field intensity of left-handed circularly polarized light with GST in the semicrystalline phase, respectively. (f) and (g) are the calculated phase distribution and far-field intensity of right-handed circularly polarized light with GST in the crystalline phase, respectively.
As we discussed previously, when GST is in the amorphous phase, the A nanopillars work as a half-wave plate, and the phase gradient of metasurface is determined by the arrangement of A nanopillars. Figure 5(b) shows the calculated phase distribution of left-handed circularly polarized light in the XZ plane with GST in the amorphous phase. The deviation angle is around -15°, which is consistent with the theoretical value calculated by the formula (3). Further, we also calculated the far-field intensity of left-handed circularly polarized light, as presented in Fig. 5(c). The deviation angle is in agreement with the result in Fig. 5(b). When GST is transformed into the semicrystalline phase, the B nanopillars work as a half-wave plate, and the phase gradient of metasurface is determined by the arrangement of B nanopillars. The calculated phase distribution and far-field intensity of left-handed circularly polarized light with GST in the semicrystalline phase are shown in Figs. 5(d) and 5(e), respectively. We can observe that the deviation angle is around 15°, which is consistent with the theoretical value calculated by the formula (3). When the GST is transformed into the crystalline phase completely, neither A or B nanopillars can function as a half-wave plate at 2.5 µm, and T┴ is around 0 at 2.5 µm, as shown in Figs. 2(d) and 2(h). Therefore, under the incidence of right-handed circularly polarized light, the transmitted light is still right-handed circularly polarized, and the transmission component of the left-handed circularly polarized light is around 0. In this case, neither A or B nanopillars can be used to design the geometric phase, thus there is no phase gradient in the metasurface. As a result, the direction of transmitted light is same as that of the incident light. Figures 5(f) and 5(g) present the calculated phase distribution and far-field intensity of right-handed circularly polarized light with GST in the crystalline phase. We can find that there is no variation in the direction of the transmitted light. As a result, we can tune the polarization state and direction of transmitted light by the phase transition of GST. We also calculated the efficiency of tunable beam steering, which was defined as the intensity ratio of the anomalously refracted light to the incident light [33]. The calculated efficiencies are 84% and 54% for amorphous and semicrystalline phases, respectively. Although the active beam switching has been realized by combining metallic metasurfaces with GST film [33], the efficiency is approximately 5% due to the absorption loss of metal. Instead of metal nanostructures, a recent work demonstrates the tunable beam steering can be realized by design GST nanostructures [39]. However, the transmitted light is dominated by the normally refracted light and the intensity of anomalously refracted light is low. Therefore, relative to the previous works [33,39], the efficiency of tunable beam steering is improved remarkably by elaborately designing the GST nanostructures.
5. Reconfigurable metalens
Besides the tunable beam steering, the GST nanostructures can also be used to generate the reconfigurable metalens. In the tunable beam steering demonstrated before, we designed two kinds of GST nanopillars to realize two different functions in the amorphous and semicrystalline phases, and the two functions were switched off when the GST was transformed into the crystalline phase. In fact, the metasurface can also realize three different functions by designing three kinds of GST nanopillars in the unit cell. Here, we demonstrate the reconfigurable metalens with three different focal lengths by designing three kinds of GST nanopillars in the unit cell, as shown in Fig. 6(a). In the simulation, the geometric parameters of A, B and C nanopillars were the same as the structures in Figs. 2(a), 2(e) and 2(i), respectively. As discussed before, the C nanopillars in the crystalline phase can function as a half-wave plate working at 2.5 µm, which is same as the working wavelength of B nanopillars in the semicrystalline phase and A nanopillars in the amorphous phase.
Fig. 6. (a) Schematic of reconfigurable metalens based on phase-change metasurfaces composed of three kinds of GST nanopillars with different geometric parameters. (b), (d) and (f) are the calculated intensity distributions of left-handed circularly polarized light in the XZ plane with GST in the amorphous phase, semicrystalline, and crystalline phases, respectively. (c), (e) and (g) are the calculated intensity distributions of left-handed circularly polarized light in the XY plane with GST in the amorphous phase, semicrystalline, and crystalline phases, respectively.
To realize a spherical lens, the phase profile Φ(r) of the metalens is required through [5]:
Figures 6(b) and 6(c) show the intensity distributions of left-handed circularly polarized light with GST in the amorphous phase in the XZ and XY planes, respectively. We can find that the transmitted light is focused well at a distance of 20 µm. As discussed previously, when GST is in the amorphous phase, the A nanopillars work as a half-wave plate, and the phase distribution of metasurface is determined by the arrangement of A nanopillars. The simulated focal length is consistent with the designed focal length of A nanopillars. The calculated intensity distributions of left-handed circularly polarized light with GST in the semicrystalline phase in the XZ and XY planes are presented in Figs. 6(d) and 6(e), respectively. When GST is transformed into the semicrystalline phase, the B nanopillars work as a half-wave plate, and the phase distribution of metasurface is determined by the arrangement of B nanopillars. Therefore, the focal length of metasurface has been changed to 30 µm. When the GST is transformed into the crystalline phase completely, C nanopillars can function as a half-wave plate, and the phase distribution of metasurface is determined by the arrangement of C nanopillars. Therefore, the focal length of metasurface has been changed to 40 µm, as shown in Figs. 6(f) and 6(g). As a result, we can tune the focal length of metalens through the phase transition of GST. We also calculated the efficiency of the reconfigurable metalens, which was defined as the focused intensity divided by the incoming intensity [33,42]. The calculated focusing efficiency is 54% for the amorphous phase, 50% for the semicrystalline phase and 14% for the crystalline phase. Even though reconfigurable metalens has been realized by integrating metasurfaces with GST film [33], the focusing efficiencies in the amorphous and crystalline phase are 10% and 5%, respectively. Very recently, the focusing efficiencies in the amorphous and crystalline phase has been increased to 39.5% and 25.4% through designing GST nanostructures [42]. Comparing to previous studies [33,42], the focusing efficiencies in this work has been improved remarkably by elaborately designing the GST nanostructures. In addition, the previous works simply realize two different focal lengths exploiting the phase transition of GST [33,42], the tunable metalens demonstrated in our work can generate three different focal lengths.
6. Switchable wave plate
Finally, we can also realize a switchable wave plate based on the similar method. As schematically illustrated in Fig. 7(a), the metasurface is composed of A and B nanopillars, and the A and B nanopillars are periodic along x- and y-direction. In the simulation, the period along x- and y-direction was set as 1200 nm. Both directions of A and B nanopillars were along the x-direction, and the spacing between A and B nanopillars in both x- and y-direction was 600 nm. The distances between A and B nanopillars were chosen to decrease the interaction between A and B nanopillars. The length, width and height of A nanopillars were same as the structure in Fig. 2(a), while the length and width of B nanopillars were changed to 324 and 280 nm, respectively. The geometric parameters of B nanopillars were adjusted to realize a quarter-wave plate working at 2.5 µm for GST in the semicrystalline phase. We calculated the transmission spectra of the metasurface with the incident light polarized along the 45° direction relative to the x-direction. Figure 7(b) shows the transmission spectra with the GST in the amorphous phase. We can find that the metasurface can work as a half-wave plate at 2.5 µm. As discussed in Fig. 2(b), the amorphous A nanopillars are half-wave plate working at 2.5 µm, therefore, the optical property of metasurface at 2.5 µm is mainly determined by the A nanopillars. To describe the polarization state of transmitted light quantitatively, we also calculated the Stokes parameters of the transmitted light. The Stokes parameters were calculated through [50]:
Fig. 7. (a) Schematic of switchable wave plate based on phase-change metasurfaces composed of two kinds of GST nanopillars with different geometric parameters. (b), (d) and (f) are the calculated transmission spectra with GST in the amorphous, semicrystalline and crystalline phases, respectively, when the incident light was polarized along the 45° direction relative to the x-direction. (c), (e) and (g) are the calculated Stokes parameters of transmitted light with GST in the amorphous, semicrystalline and crystalline phases, respectively, where S1, S2 and S3 are normalized with respect to S0. (h) Schematic of the polarization state of transmitted light at different phases of GST.
Figure 7(d) presents the transmission spectra with the GST in the semicrystalline phase. We define that the transmission components of the left-handed and right-handed circularly polarized light as TL and TR, respectively, which can be retrieved according to the transmission coefficient and phase [43,52]. At the wavelength of 2.5 µm, the TL is 0.75 and TR is around 0. Therefore, the metasurface is changed to a quarter-wave plate, when GST is transformed into the semicrystalline phase. As the working wavelength of semicrystalline A nanopillars is away from 2.5 µm, while the semicrystalline B nanopillars are quarter-wave plate working at 2.5 µm, therefore, the optical property of metasurface at 2.5 µm is mainly determined by the B nanopillars. We also calculated the Stokes parameters of the transmitted light when GST is in the semicrystalline phase, as presented in Fig. 7(e). The S1 / S0, S2 / S0 and S3 / S0 at the wavelength of 2.5 µm are -0.189, 0.042 and -0.981, respectively, which indicates the transmitted light is approximately a left-handed circularly polarized light. We also calculated the degree of circular polarization (DOCP) of the transmitted light, defined as |ILCP-IRCP|/ |ILCP+IRCP|, where ILCP and IRCP denote the intensity of transmission components of the left-handed and right-handed circularly polarized light, respectively [53]. The DOCP of the transmitted light at the wavelength of 2.5 µm is around 1, when GST is in the semicrystalline phase. When the GST is transformed into the crystalline phase completely, neither A or B nanopillars can function as a wave plate working at 2.5 µm. Therefore, the polarization state of transmitted light at 2.5 µm is close to that of the incident light, as shown in Fig. 7(f). We also calculated the Stokes parameters of the transmitted light when GST is in the crystalline phase, as presented in Fig. 7(g). The S1 / S0, S2 / S0 and S3 / S0 at the wavelength of 2.5 µm are 0.181, 0.834 and -0.522, respectively, which indicates the transmitted light is approximately polarized along the 45° direction relative to the x-direction. The DOLP of the transmitted light at the wavelength of 2.5 µm is around 0.85, when GST is in the crystalline phase. As a result, when the incident light is polarized along the 45° direction, the transmitted light at the wavelength of 2.5 µm will experience a variation from a perpendicular polarization to a circular polarization, and finally become a parallel polarization across the phase transition of GST, as schematically illustrated in Fig. 7(h).
7. Conclusion
In conclusion, we have demonstrated various tunable optical devices based on GST nanostructures. The refractive direction, focal length and polarization state can be tuned through the phase transition of GST. Although the active metasurfaces were designed to work in the transmission mode, the GST nanostructures can also be adjusted to work in the reflection mode. In addition, the phase-change metasurfaces could also be utilized to generate tunable holograms and vortex based on similar methods. Since there are multiple intermediate phases in GST between amorphous and crystalline phases, the phase-change metasurface can display more functions by reasonably designing GST nanostructures. Even though we discussed the tunable metasurfaces through numerical simulations, the GST nanostructures can be fabricated experimentally and the phase transition of GST could be excited by changing the temperature, voltage and light intensity. We expect the tunable metasurfaces based on GST nanostructures could be used in cameras, optical microscopy, adaptive optics and LiDAR scanning systems.
Funding
National Natural Science Foundation of China (12004362, 12004361, 61875179, 61727816, 11874332); Natural Science Foundation of Zhejiang Province (LY22A040006, LQ21A040012, LY20F050007, LZ21A040003); Fundamental Research Funds for the Provincial Universities of Zhejiang (2021YW20).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results represented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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