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Abstract
Wave plates based on metasurfaces have attracted intensive attention over the past decade owing to their compactness and design flexibility. Although various wave plates have been designed, their working wavelengths are fixed once they are made. Here we present a study on tunable wave plates based on phase-change metasurfaces made of Ge2Sb2Te5 nanopillar structures. The Ge2Sb2Te5 nanopillars can work as a high-efficiency transmissive half- or quarter-wave plate depending on their structural parameters. The working wavelength of wave plate can be tuned via the phase transition of Ge2Sb2Te5. Moreover, the polarization state of the transmitted light at a fixed wavelength can be modified by changing the crystallinity of Ge2Sb2Te5. The features suggest that tunable wave plates may have applications in optical modulators, molecular detection, and polarimetric imaging.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces have made great progress in the past years for realizing planar and miniature optical devices [1,2]. By utilizing subwavelength metallic or dielectric structures to design the local amplitude, phase and polarization of light, metasurfaces have been applied to generate various optical devices, such as metalens, holograms, vortices and wave plates [1,2]. In particular, wave plate is an important component in modern optical systems. Relative to traditional wave plates made of birefringent crystals, the volume of wave plates based on metasurface is reduced remarkably and suitable for integration [3,4]. Various wave plates including half- and quarter-wave plates have been investigated in the wavelength range from microwave to visible spectra [5–13]. However, due to the absorption loss of metal, the high-efficiency wave plates based on metallic structures usually work in the reflection mode [5,8–11,13]. In order to avoid this defect, high-efficiency transmissive wave plates have been proposed by designing the dielectric metasurfaces [12].
Even though various wave plates have been designed, the working wavelengths are fixed once they are made. In realistic application, we expect the working wavelength of wave plate can be tuned dynamically to satisfy different requirements. For example, measuring the circular dichroism spectra of chiral molecular and nanoscale structures needs the quarter-wave plate [14]. Due to different response wavelengths in various chiral molecular and nanoscale structures, quarter-wave plates with various working wavelengths are required. Relative to fabricate multiple passive wave plates, the complexity and cost are decreased based on the tunable wave plates. Recently, active and tunable metasurfaces have attracted widespread attention [15–17]. The functions of metasurfaces can be tuned dynamically by combining metasurfaces with active materials, such as graphene [18], transparent conducing oxides [19], liquid crystals [20], semiconductors [21] and vanadium dioxide [22,23]. Although there are some works discussing the tunable polarizers [18,24–28], two important issues remain to be solved. On the one hand, the existing active polarizers are realized by integrating metallic structures with tunable materials, the transmission efficiency is low due to the absorption loss of metal. On the other hand, wavelength-tunable half- or quarter-wave plates have not been discussed before. To overcome these problems, here, we design active dielectric metasurfaces made of phase-change alloy Ge2Sb2Te5 (GST) to realize tunable half- and quarter-wave plates with high transmission efficiency.
Among various tunable materials, GST is an intriguing material, which is famous for application in rewriteable optical data storage [29,30]. GST is a reversible phase-change material with amorphous and crystalline phases. The amorphous phase can be transformed into the crystalline phase when it is annealed above 160°C, and returns to the amorphous phase by a quick annealing process over 640°C [31]. The phase transition of GST is non-volatile, which is stable in the amorphous and crystalline phases at room temperature. Beside the temperature, the phase transition of GST can also be excited by the voltage and light [29,30]. Based on the large difference in refractive index between the amorphous and crystalline phases, GST films have been combined with metallic metasurfaces to realize tunable optical devices, including tunable antenna [32], bifocal zoom lensing [33], switching of the direction of reflectionless light propagation [34], tunable thermal emission [35], and multistate switching of photonic angular momentum coupling [36]. In addition, due to the high refractive index of GST in the infrared, GST nanostructures can be used to design active dielectric metasurfaces [30]. Active metasurfaces based on GST nanostructures have been proposed to realize reconfigurable zone-plate [37], anomalous reflection angle controlling [38], switchable absorption [39], wavefront switch [40], active control of anapole states [41], dynamical filter [42], and optical programming [43]. Nevertheless, wavelength-tunable wave plates based on GST nanostructures have not been discussed before.
In this work, we demonstrate tunable wave plates based on phase-change metasurfaces consisting of GST nanostructures. Firstly, we design periodic GST nanopillars to realize a half-wave plate in the amorphous phase. Then, we change the crystallinity of GST to investigate the variation in the working wavelength of half-wave plate. We also analyze the variation in the polarization state of transmitted light at fixed wavelengths along with the phase transition. Finally, we adjust the geometric parameters of the metasurface to realize a tunable quarter-wave plate, and discuss the variation in the working wavelength at different crystallinities of GST.
2. Design and method
We designed a phase-change metasurface consisting of GST nanopillars to realize tunable wave plates, as shown in Fig. 1(a). The metasurface is composed of GST nanopillars, which are periodic along x- and y-directions. The nanopillar can be regarded as a truncated waveguide, and the rectangle cross-section of the waveguide leads to different effective refractive indices of the waveguide modes polarized along the x- and y-directions [44]. Therefore, there is a phase difference between the transmission of x- and y-polarization. When the incident light is polarized along the 45° relative to the x-direction, it can be divided into the x- and y-directions. The metasurface can work as a half (quarter)-wave plate by designing the phase difference between the x- and y-component of the transmitted light to be π (1.5π).
Fig. 1. (a) Schematic of tunable wave plate based on phase-change metasurface consisting of GST nanopillars. (b) Refractive index and (c) extinction coefficient of GST in the amorphous and crystalline phases. (d) amplitude ratio (|ty|/|tx|) and (e) phase difference (Δφ=φy-φx) between the x- and y-component of the transmitted light with different lengths and widths of nanopillars at the wavelength of 2 µm for GST in the amorphous phase, whereas the height and period of nanopillars were fixed at 1000 and 850 nm, respectively.
Figures 1(b) and 1(c) present the refractive index and extinction coefficient of GST, respectively, as taken from the reference [45]. We can find the GST is a high-index material with low absorption loss in the infrared, and can be tuned through the phase transition. As a result, if we design the amorphous GST nanopillars to realize a wave plate at one wavelength, the working wavelength will shift to another wavelength when it is transformed into the crystalline phase. As schematically illustrated in Fig. 1(a), when a linearly polarized light is incident into a tunable half-wave plate, the polarization state of the transmitted light will be changed to a perpendicular polarization for GST in the amorphous phase. However, when the GST is transformed into the crystalline phase, the working wavelength of half-wave plate will shift and the polarization state of the transmitted light at original wavelength will be same as that of the incident light.
The optical properties of metasurfaces were calculated through the finite-difference-time-domain software (FDTD Solutions) from Lumerical Inc. In the simulation, periodic boundary conditions were applied in both x- and y-directions, whereas perfect matched layers (PML) boundary conditions were used in the z-direction. The glass was selected as the substrate due to the low absorption loss in the wavelength range we considered. It is well-known that there are some intermediate crystallization states for GST between the amorphous and crystalline phases [36,41–43]. The crystallinity of GST can be controlled precisely by changing the temperature [36,41] or laser pulse power [42,43]. In the simulation, the permittivities of the intermediate crystallization states were calculated through [43]:
As explained before, designing the phase difference between the x- and y-component of the transmitted light is critical for realizing a wave plate. The phase difference can be tuned by adjusting the geometric parameters of nanopillars [12,44]. We calculated the transmission coefficient and phase of the amorphous GST nanopillars with different lengths and widths under x- and y-polarized incidence. In the simulation, the height and period of nanopillars were fixed at 1000 and 850 nm, respectively, whereas the length varied from 350 to 440 nm and the width changed from 260 to 350 nm. Figures 1(d) and 1(e) show the calculated amplitude ratio (|ty|/|tx|) and phase difference (Δφ=φy-φx) between the x- and y-component of the transmitted light with different lengths and widths of nanopillars at the wavelength of 2 µm, respectively. It can be observed that the amplitude ratio is around 1, whereas the phase difference can be tuned from 0.5π to 2π by varying the geometric parameters of nanopillars.
3. Tunable half-wave plate
To demonstrate the idea of active wave plates, we designed the geometric parameters of the metasurfaces and calculated their optical properties at different crystallinities of GST. Firstly, we adjusted the geometric parameters of GST nanopillars to generate the tunable half-wave plate. As shown in Fig. 1(e), when the length and width of nanopillars were set as 410 and 285 nm, respectively, the phase difference between the transmission of x- and y-polarization is around π at the wavelength of 2 µm, satisfying the condition of half-wave plate. Figure 2(a) shows the calculated transmission coefficient under the x- and y-polarized incidence with the GST in the amorphous phase. The transmission coefficient is approaching 1 because of the low absorption loss of GST in the infrared, as presented in Fig. 1(c). The suppression of reflection is attributed to interference between dipole- and higher-order multipoles [12]. The phase difference between the x- and y-component of the transmitted light is around π at 2 µm, as shown in Fig. 2(a). Therefore, when the incident light is polarized along the 45° direction, the transmitted light will be rotated to the 135° direction. We also calculated the transmission of the structure with the incident light polarized along the 45° direction, as presented in Fig. 2(c). We define 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┴. It can be observed that T┴ is around 0.96 at 2 µm, while T‖ is around 0 at this wavelength. As a result, the structure can work as a transmissive half-wave plate with high conversion efficiency.
Fig. 2. Calculated transmission coefficient and phase difference of the half-wave plate under the x- and y-polarized incidence with the GST in the amorphous phase for (a) and crystallinity of 50% for (b), where the length, width, height and period of nanopillars were 410, 285, 1000 and 850 nm, respectively. Transmission of two orthogonal polarizations with the incident light polarized along the 45° direction with the GST in the amorphous phase for (c) and crystallinity of 50% for (d). (e) Variation of the working wavelengths of half-wave plate along with the crystallinity of GST. (f) Transmission with polarization perpendicular to that of the incident light at the two working wavelengths with different crystallinities of GST.
Next, we calculated the optical properties of the metasurface with different crystallinities of GST. Figure 2(b) shows the calculated transmission coefficient under the x- and y-polarized incidence with the crystallinity of 50%. The transmission coefficient is decreased relative to that of the amorphous phase because of the increased absorption loss in the infrared, as presented in Fig. 1(c). There is a dip in the curve of phase difference similar to that of the amorphous phase. However, the wavelength of dip shifts to 2.55 µm, and the phase difference at this dip is decreased to 0.8π, due to the increase in the refractive index of GST, as shown in Fig. 1(b). The phase difference of π occurs at the wavelengths of 2.44 and 2.67 µm, and the transmission coefficient of the x-polarized light is close to that of the y-polarized light at the two wavelengths. Therefore, the structure can work as a half-wave plate at 2.44 and 2.67 µm. Further, we calculated the transmission of the structure with the incident light polarized along the 45° direction, as presented in Fig. 2(d). We can find that T┴ at 2.44 and 2.67 µm are 0.81 and 0.76, respectively, while T‖ is around 0 at the two wavelengths. Consequently, when 50% of GST has been changed to the crystalline phase, the structure is still a high-efficiency transmissive half-wave plate with a different working wavelength.
We also simulated the optical properties of the metasurface with other crystallinities of GST, and extracted the working wavelengths of the half-wave plate, as illustrated in Fig. 2(e). Similar to the results with the crystallinity of 50%, two working wavelengths occur when the crystallinity is larger than 10%. We define the short working wavelength as λ1, while the long working wavelength as λ2. The λ1 and λ2 almost shift linearly with the increase of crystallinity. When the GST has been transformed into the crystalline phase completely, the λ1 and λ2 are changed to 2.8 and 3.1 µm, respectively. The wavelength tunable range relative to the original wavelength (Δλ/λ) can reach 50%. Figure 2(f) shows the transmission of T┴ at the wavelengths of λ1 and λ2. We can observe that T┴ decreases with the increase of crystallinity, resulting from the increased absorption loss of GST. Nevertheless, T┴ is larger than 50% at all crystallinity. Compared to the previous experimental device demonstrations, the transmissivity of wave plates in reference [6] and [7] are 10% and 50%, respectively. Therefore, the wave plate with such reduced performance in our work is still useful. In previous works, the efficiency of active transmissive polarizer is around 30% [25], and the efficiency of active reflective polarizers is around 40% [18]. Therefore, the efficiency (larger than 50%) of our tunable transmissive wave plate is higher relative to the existing works. As a result, we can realize a wavelength-tunable transmissive half-wave plate with high efficiency.
We also analyze the variation in the polarization state of the transmitted light along with the crystallinity of GST at fixed wavelengths. Figure 3(a) show the transmission coefficient and phase difference of the tunable half-wave plate with different crystallinities at the wavelength of 2 µm. The phase difference varies from π to 2π with the increase of crystallinity. Therefore, when the incident light is polarized along the 45° direction, the transmitted light will experience a variation from a perpendicular polarization to an elliptical polarization, and finally become a parallel polarization. Figure 3(b) show the transmission coefficient and phase difference of the tunable half-wave plate with different crystallinities at the wavelength of 2.2 µm. Due to the variation in the refractive index of GST, the phase differences change with the increase of the crystallinity. The phase differences at the crystallinity of 0 and 10% are 1.5π and π, respectively, and the transmission coefficient of the x-polarized light is close to that of the y-polarized light at the two crystallinities. Therefore, the structure can work as a quarter-wave plate at the wavelength of 2.2 µm for GST in the amorphous phase, and will be switched to a half-wave plate working at the same wavelength when 10% of GST is transformed to the crystalline phase.
Fig. 3. Transmission coefficient and phase difference of the tunable half-wave plate with different crystallinities at the wavelength of 2 µm for (a) and 2.2 µm for (b), where the length, width, height and period of nanopillars were 410, 285, 1000 and 850 nm, respectively.
It is worth noting that the size and shape of the nanopillars may also change when the GST transforms from amorphous to crystalline states [39,41]. However, it is not clear how such a change would behave and evolve in GST nanostructures at different crystallinities. A recent experimental work indicates that a 5% height reduction between amorphous and crystalline GST nanostructures without any noticeable changes in their lateral sizes or surface topology [41]. We also discuss the effect of the geometric parameters of GST nanopillars on the optical properties of wave plate. Figures 4(a) and (b) shows the transmission of the half-wave plate with different heights of nanopillars for GST in the crystalline phase, where the incident light is polarized along the 45° direction. We can find that the subtle change in the height of GST nanopillars has a little influence on the working wavelength and transmission of wave plate. Figures 4(c) and (d) shows the transmission of the half-wave plate with different lengths of nanopillars for GST in the crystalline phase. It can be observed that the small change in the length of GST nanopillars will shift slightly the working wavelength of wave plate. Figures 4(e) and (f) shows the transmission of the half-wave plate with different widths of nanopillars for GST in the crystalline phase. The effect of width of GST nanopillars on the working wavelength of wave plate is more obvious than that of length and height.
Fig. 4. Transmission of the half-wave plate with different heights of crystalline GST nanopillars for (a) with polarization parallel to that of the incident light and for (b) with polarization perpendicular to that of the incident light, whereas the length, width and period of nanopillars were fixed at 410, 285 and 850 nm, respectively. Transmission of the half-wave plate with different lengths of crystalline GST nanopillars for (c) with polarization parallel to that of the incident light and for (d) with polarization perpendicular to that of the incident light, whereas the height, width and period of nanopillars were fixed at 1000, 285 and 850 nm, respectively. Transmission of the half-wave plate with different widths of crystalline GST nanopillars for (e) with polarization parallel to that of the incident light and for (f) with polarization perpendicular to that of the incident light, whereas the height, length and period of nanopillars were fixed at 1000, 410 and 850 nm, respectively.
Although the tunable wave plates in our work are discussed through the numerical simulations, the GST nanopillars could be fabricated by magnetic sputtering of GST film, then structured by combining E-beam lithography and inductively coupled plasma-reactive ion etching, as demonstrated experimentally in a recent work [40]. Similar etching method has been used to fabricate 1.5-µm-thick Si nanofins [46]. However, the etching process will induce a slightly tapered shape of the pillars [46]. Therefore, we also calculated the optical properties of the wave plate with a tapered shape. We supposed the top length, top width, base length and base width of GST nanopillars were 410, 285, 460 and 335 nm, respectively, and the height and period of GST nanopillars were same as the structure in Fig. 2. Figure 5 shows the calculated transmission of the structure with different crystallinities of GST. The working wavelength of wave plate shifts slightly relative to the realistic results in Fig. 2, and still can be tuned by the phase transition of GST.
Fig. 5. Transmission of two orthogonal polarizations with the incident light polarized along the 45° direction with the GST in the amorphous phase for (a), crystallinity of 50% for (b), and crystalline phase for (c), respectively. The shape of GST nanopillars is slightly tapered, where the top length, top width, base length and base width, height and period of nanopillars were 410, 285, 460, 335, 1000 and 850 nm, respectively.
Experimentally, the phase transition of GST from amorphous phase to crystalline phase can be realized by annealing above 160°C, and the crystalline GST can return to the amorphous phase by a quick annealing process over 640°C [31]. Although the phase transition of GST can also be induced optically [37,42,43], light-induced switching leverages precisely tailored short laser pulses and is very challenging to optically switch GST layers of more than around 100 nm thickness. As a result, it is preferred to induce the phase transition of GST in our samples by changing the temperature.
4. Tunable quarter-wave plate
Beside the tunable half-wave plate, we can also realize the tunable quarter-wave plate by adjusting the geometric parameters of the metasurface. As shown in Fig. 1(e), when the length and width of nanopillars were set as 365 and 315 nm, respectively, the phase difference between the transmission of x- and y-polarization is around 1.5π at the wavelength of 2 µm, satisfying the condition of quarter-wave plate. Figure 6(a) shows the calculated transmission coefficient under the x- and y-polarized incidence with the GST in the amorphous phase. We can find that the transmission coefficient is approaching 1, and the phase difference between the x- and y-component of the transmitted light is around -0.5π at 2 µm. Therefore, when the incident light is polarized along the 45° direction, the transmitted light will be changed to a right-hand circularly polarized light. Due to the symmetry of the structure, if the incident light is polarized along the 135° direction, the transmitted light will be changed to a left-hand circularly polarized light. The simulated transmission coefficient and phase can be used to retrieve the circular polarization states through [13]:
Fig. 6. Calculated transmission coefficient and phase difference of the quarter-wave plate under the x- and y-polarized incidence with the GST in the amorphous phase for (a) and crystallinity of 50% for (b), where the length, width, height and period of nanopillars were 365, 315, 1000 and 850 nm, respectively. Transmission of the circular polarization states with the GST in the amorphous phase for (c) and crystallinity of 50% for (d), when the incident light is polarized along the 45° direction. (e) Variation of the working wavelengths of quarter-wave plate along with the crystallinity of GST. (f) Transmission of the right-hand circularly polarized light at the two working wavelengths with different crystallinities of GST.
Figure 6(b) shows the calculated phase difference between the x- and y-component of the transmitted light with the crystallinity of 50%. There is a dip in the curve of phase difference similar to that of the amorphous phase. However, the wavelength of dip shifts to 2.56 µm, and the phase difference at this dip is decreased to -0.66π. The phase difference of -0.5π occurs at the wavelengths of 2.48 and 2.64 µm, and the transmission coefficient of the x-polarized light is close to that of the y-polarized light at the two wavelengths. Therefore, the structure can work as a quarter-wave plate at 2.48 and 2.64 µm. Further, we retrieved the circular polarization states when the incident light is polarized along the 45° direction, as indicated in Fig. 6(d). We can find that TR at 2.48 and 2.64 µm are 0.76 and 0.67, respectively, while TL is around 0 at the two wavelengths. Consequently, when 50% of GST has been changed to the crystalline phase, the structure is still a high-efficiency transmissive quarter-wave plate with a different working wavelength.
We also simulated the optical properties of the metasurface with other crystallinities of GST, and extracted the working wavelengths of the quarter-wave plate, as illustrated in Fig. 6(e). Similar to the results of the crystallinity of 50%, two working wavelengths occur when the crystallinity is larger than 10%. The two working wavelengths shift remarkably, when the crystallinity of GST is increased. With the increase of crystallinity, the change in the refractive index of GST leads to the variation of the phase difference, therefore the working wavelength of wave plate shifts well. Due to the same mechanism in tunability, the variation of working wavelengths in quarter-wave plate as a function of crystallinity of GST is similar to that of the half-wave plate. Figure 6(f) shows the transmission of TR at the two working wavelengths. Although the TR decreases with the increase of crystallinity, it remains to be larger than 40% at all crystallinity. As a result, we can realize a wavelength-tunable transmissive quarter-wave plate with high efficiency.
5. Conclusion
We have demonstrated tunable half- and quarter-wave plates by designing phase-change metasurfaces composed of GST nanopillars. The working wavelength of wave plates can be tuned through controlling the crystallinity of GST. The polarization state of the transmitted light at a fixed wavelength can also be tuned by the phase transition of GST. Even though we realize tunable wave plates in a transmissive mode, the structure can be adjusted to work in a reflective mode. We anticipate that tunable wave plates based on the GST nanopillars will be applied in optical modulators, molecular detection, and polarimetric imaging.
Funding
National Natural Science Foundation of China (12004362, 12004361, 51771175, 11847002, 11904008).
Disclosures
The authors declare no conflicts of interest.
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