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Abstract
Metasurfaces have attracted increasing attention due to their unprecedented capabilities of molding optical fields with exceedingly low losses. Despite significant achievements, most existing metasurfaces are passive and lack dynamic modulation post-fabrication. Here, we propose a tunable phase-change metasurface for switchable vector vortex beam generation in the mid-infrared range. The phase-change meta-molecule, consisting of two coupled Ge2Sb2Te5 (GST) bricks, is firstly designed to perform the switching between a quarter-wave plate and a usual transmissive plate over a wavelength range from 4.95 to 5.05 µm under the amorphous and crystalline phases of GST, respectively. Furthermore, a general method is derived to achieve a switchable vector vortex beam generator at the target wavelength of 5 µm by spatially orienting GST meta-molecules to locally tailor phase and polarization distribution. Under the amorphous phase, radially polarized and azimuthally polarized beams, composed of the co-polarized circularly polarized (CP) component carrying orbital angular momentum (OAM) with a topological charge of l = 0 and cross-polarized CP component carrying OAM with a topological charge of l = ±2 are obtained for the left circularly polarized (LCP) and right circularly polarized (RCP) incident waves, respectively. The mode purity values of the cross-polarized component and the co-polarized component are calculated to be ∼ 0.949 and ∼ 0.955. When GST transits to its crystalline phase, the vector vortex beam disappears, and the incident CP beams pass through directly. Our finding paves the way for advanced applications targeting photonics integration with switchable functionalities.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical metasurfaces, consisting of artificial antennas (often termed as meta-atoms) with subwavelength sizes, have attracted increasing attention and experienced rapid developments due to their ultrathin profiles and outstanding capabilities in controlling transmitted and reflected optical fields. Therefore, optical metasurfaces can be used to realize light-weight, cost-effective, and high-performance flat optics with novel functionalities [1–4]. As the key components of metasurfaces, plasmonic or high-index dielectric meta-atoms are exploited to locally impose abrupt modulation of light through strong light-matter interaction. By elaborately arranging predesigned meta-atoms, numerous promising ultra-compact flat optical components have been developed, such as beam deflectors [5,6], focusing lenses [7,8], optical holograms [9,10], polarimeters [11,12], and wave-plates [13,14]. Despite significant achievements, the functionalities of metasurfaces are generally fixed and lack real-time dynamic modulation post-fabrication. Therefore, it is highly desirable to realize tunable metasurfaces with functionalities actively controlled by applying external stimuli. In recent years, tunable metasurfaces have been studied, where the optical responses can be controlled through light inclination [15,16], mechanical operation [17,18], two-dimensional (2D) materials [19,20], liquid crystals [21,22], and phase-change materials [23–25].
Phase-change materials, such as germanium antimony telluride compounds (GST), are a promising platform for implementing tunable metasurfaces on account of fast switching speed (10 to 100 ns), robust switching ability (up to 1015 cycles), large refractive-index contrast, and relatively low optical losses in the near- and middle-infrared (IR) spectral range [26–29]. Generally, the switching between the amorphous and crystalline phases of the GST can be achieved with appropriate thermal [30], optical [31,32], or electrical stimulus [33], which is non-volatile in nature (as opposed to the alternative phase-change material VO2) [34,35]. With these extraordinary properties, reconfigurable GST metasurfaces have been proposed to realize diversified tunable functionalities, such as thermal emission [36], amplitude modulation [37], polarization control [38–40], resonance tuning [41,42], and wavefront modulation [29,43]. Most of these tunable metasurfaces are realized by placing plasmonic meta-atoms on top of thin GST films, which, however, intrinsically suffer from ohmic losses and limited tunability. Therefore, patterned GST meta-atoms that support multiple Mie resonances have emerged [44–50].
In this work, we propose a tunable GST metasurface for switchable vector vortex beam generation in the mid-IR range. The designed GST meta-molecule, composed of two coupled GST bricks, functions as a quarter-wave plate (QWP) and a usual transmissive plate in a wavelength range varying from 4.95 to 5.05 µm under the amorphous and crystalline phases of GST, respectively. Furthermore, we employ space-variant GST meta-molecules to generate switchable vector vortex beams, which possess spatially varied polarization vectors and carry specified orbital angular momentums (OAMs). Under the amorphous phase of GST, radially polarized (RP) and azimuthally polarized (AP) beams are generated for the left circularly polarized (LCP) and right circularly polarized (RCP) incident waves, respectively. At the crystalline phase, the normal incident circularly polarized (CP) beams transmit through the device directly. The proposed GST metasurface can be used for integrated mid-IR photonics with compact footprints and switchable functionalities.
2. Results and discussions
Figure 1 schematically illustrates the working principle of the proposed GST metasurface for switchable vector vortex beam generation under different GST phases. On excitation with CP beams, the polarization and phase of the transmitted waves are simultaneously and independently engineered with GST meta-molecules that function as QWPs at the amorphous state. Therefore, the locally polarized transmitted waves will constructively interfere in the far-field to produce vector vortex beams. In particular, RP and AP vector beams are created under LCP and RCP excitations, respectively. When GST transits to the crystalline state, the generated vector vortex beams disappear. In this case, the designed GST metasurface behaves as a usual transmissive plate and the incident CP beams transmit through directly.
Fig. 1. Working principle of the proposed GST metasurface. (a) LCP/RCP beams are converted into RP/AP beams under the amorphous phase. (b) LCP/RCP beams transmit through directly under the crystalline phase.
In this work, a GST meta-molecule that behaves as a switchable QWP under different GST phases is first considered. As shown in Fig. 2(a) and 2(b), the designed GST meta-molecule consists of two coupled GST bricks standing on the CaF2 substrate that is chosen due to its low refractive index and near-zero absorption in the near- and mid-IR spectral regions. The GST meta-modules are periodically distributed in both the x- and y-directions with a subwavelength periodicity of P = 3.5 µm, which can eliminate unwanted diffraction orders. The height of GST bricks is h = 1.67 µm, ensuring good performance and sufficient phase response at the design wavelength of λ = 5 µm at amorphous and crystalline states. Two GST bricks have equal side lengths of lx and ly and are separated by a distance of d in the x-direction. To optimize the dimensions of the coupled GST bricks (i.e., lx, ly, and d), three-dimensional (3D) full-wave simulations with the commercially available software COMSOL Multiphysics (version 5.5) are conducted, whereas the other geometrical parameters are kept constant. In the simulations, a GST meta-molecule is considered as a unit cell with periodic boundary conditions applied in both the x- and y-directions, while perfectly matching layers (PML) are introduced above and below the structure to truncate the simulation domain. The CaF2 substrate is regarded as a lossless material with a refractive index of 1.399, while the optical properties for both phases of GST are based on measured data [45]. At the target wavelength of 5 µm, the refractive indices of amorphous and crystalline GST are 4.249 and 6.025 + 0.213i, respectively. An x- or y- polarized plane wave is impinging normally from the bottom CaF2 substrate along the z-direction. The optimized dimensions of the coupled GST bricks are determined as lx = 905 nm, ly = 1290 nm, and d = 250 nm. Figure 2(c) and 2(d) show the obtained transmission amplitudes (txx and tyy) and the corresponding phase differences ($\Delta \delta = {\delta _{yy}} - {\delta _{xx}}$) at the wavelength ranging from 4.9 to 5.1 µm at amorphous and crystalline states, respectively. At amorphous state, txx and tyy are found to be 0.593 and 0.621, respectively, with the phase difference $\Delta \delta $ of −88° at the design wavelength of 5 µm, which is basically in line with the expected QWP function that introduces a 90° phase retardation between the transmitted x- and y-polarized components with nearly equal transmission amplitudes. As for the crystalline GST, normally incident x- and y-polarized lights transmit through the structure without introducing any phase retardation ($\Delta \delta $ = −1.4°), and txx and tyy are 0.411 and 0.374, respectively, at the target wavelength of 5 µm, indicating the turn-off of the QWP function. The relatively lower transmission amplitudes are mainly due to the loss of crystalline GST. To further improve the efficiencies of the designed meta-molecule at both amorphous and crystalline states, it is feasible to replace GST with Ge-Sb-Se-Te (GSST) with lower loss in the infrared region [51] or utilize a multilayered meta-atom design with a thinner phase-change material layer embedded [47]. In addition, the designed structure is able to behave as a switchable QWP over a wavelength range from 4.95 to 5.05 µm with relatively good performance under different GST states. As a final comment, it should be emphasized that the potential volume change of the GST meta-molecule at the crystalline state will not affect its performance as a transmissive plate.
Fig. 2. (a) Aerial View and (b) top view of the designed GST meta-molecule consisting of two coupled GST bricks standing on the CaF2 substrate. Simulated transmission amplitudes (txx and tyy)and the relative phase differences ($\Delta \delta = {\delta _{yy}} - {\delta _{xx}}$) with normally incident x- and y-polarized waves at (c) amorphous state and (d) crystalline state.
Figure 3(a) further shows the degree of linear polarization (DoLP) and the angle of linear polarization (AoLP) of the transmitted beams as a function of the rotation angle θ with respect to the x-axis under LCP and RCP excitations at the design wavelength of 5 µm for amorphous and crystalline GST, respectively. It can be clearly seen that DoLPs are always close to 1 without obvious changes despite the varied rotation angle θ. As for AoLPs, they change linearly with the rotation angle θ, demonstrating the orientation-independent property of the designed QWP. For instance, the AoLP is switched from −45° (45°) to 0° (90°) when the θ is rotated from 0 to 45° for the RCP (LCP) incidence. Figure 3(b) and 3(c) give the corresponding Stokes parameters of generated polarization states with varied rotation angle θ on Poincaré spheres under LCP and RCP excitations at λ = 5 µm. At amorphous state, the retrieved Stokes parameters are all mapped close to the equator of the spherical surface, indicating well-defined linearly polarized (LP) states for both LCP and RCP incidences. When GST transits to the crystalline state, the incident wave transmits through the meta-molecules directly without changing its polarization state, indicated by the relatively low DoLPs and high degrees of circular polarization (DoCPs) that are approaching approximately 0 and ±1, respectively [Fig. 3(d)]. Therefore, the reconstructed Stokes parameters assemble well two CP states on the Poincaré sphere, as shown in Fig. 3(e) and 3(f).
Fig. 3. At amorphous state, (a) simulated DoLP and AoLP of the optimized structure as a function of the rotation angle θ for LCP and RCP waves at normal incidence and Stokes parameters of generated polarization states with varied rotation angle θ on Poincaré spheres under (b) LCP and (c) RCP excitations. At crystalline state, (d) simulated DoLP and DoCP of the optimized structure as a function of the rotation angle θ for LCP and RCP waves at normal incidence and Stokes parameters of generated polarization states with varied rotation angle θ on Poincaré spheres under (e) LCP and (f) RCP excitations.
To realize switchable vector vortex beam generation, we now utilize the aforementioned switchable GST QWP, which can locally tailor the polarization state of the transmitted wave at the amorphous state and finally generate cylindrical vector-beams possessing spatially varied polarization vectors. At the amorphous state, the Jones matrix of the designed GST meta-molecule rotated with an angle of θ from the x-axis can be described as:
Therefore, by locally rotating each GST meta-molecule with an angle of $\theta = \varphi - \frac{\pi }{4} = \textrm{ta}{\textrm{n}^{ - 1}}\left( {\frac{y}{x}} \right) - \frac{\pi }{4}$, an RP beam with additional spiral phase is achieved, which enables vector vortex beam generation carrying a specific OAM with a topological charge of $l = 1$. Similarly, if the incident beam is switched to RCP with ${E_{in}} = \frac{1}{{\sqrt 2 }}\left( {\begin{array}{c} 1\\ { - i} \end{array}} \right)$, the transmitted beam is:
Once GST transits to the crystalline state, the Jones matrix of the designed GST meta-atom rotated with an angle of θ from the x-axis can be described as:
For the amorphous GST, the transmitted light can also be considered as a superposition of two CP components, one has the same handedness as the incident CP light (co-polarized, Eco) without additional phase delay while the other has the opposite handedness (cross-polarized, Ecr) with additional phase delay. The additional phase delay is known as the Pancharatnam-Berry phase with a value of 2σθ, where $\sigma = 1$ for LCP light and $\sigma ={-} 1$ for RCP light. Therefore, the transmitted light can be expressed as:
After theoretical discussion, the designed switchable vector vortex beam generator, which is composed of identical GST meta-molecules with spatial-variant orientations, is verified through numerical simulations based on the 3D finite-difference time-domain (3D-FDTD) method. Figure 4 plots the simulated far-field intensity profiles and phase distributions of two CP components at the design wavelength of 5 µm when GST is in its amorphous state. Under LCP and RCP excitations, the doughnut-shaped intensity distributions [Fig. 4(c) and 4(e)] confirm the existence of vortex beams, which corresponds to the cross-polarized CP components. The spiral phase distributions in the intensity regions possess 2-fold 2π phase variation along the azimuthal direction with opposite signs [Fig. 4(d) and 4(f)], identifying the topological charges of l = ±2 for the cross-polarized OAMs. On the other hand, the co-polarized CP components exhibit Gaussian distribution in intensity [Fig. 4(a) and 4(g)] and the corresponding phases [Fig. 4(b) and 4(h)] are constant in the intensity region.
Fig. 4. Numerical simulation results of the designed GST metasurface at amorphous state. Far-field (a) intensity profile and (b) phase distribution of the transmitted LCP component and (c) intensity profile and (d) phase distribution of the transmitted RCP component under LCP excitation. Far-field (e) intensity profile and (f) phase distribution of the transmitted LCP component and (g) intensity profile and (h) phase distribution of the transmitted RCP component under RCP excitation.
For the crystalline GST, it can be clearly seen that nearly all the incident CP beams transmit through the device directly without polarization conversion [Fig. 5(a) and 5(g)]. However, due to the imperfection of the designed transmissive plate, the cross-polarized component does exist with an extremely intensity, 3 orders of magnitude smaller than its co-polarized counterpart, as shown in Fig. 5(c) and 5(e). Therefore, spiral phases can still be seen for the cross-polarized components [Fig. 5(d) and 5(f)]. Anyway, all these results indicate the disappearance of the vector vortex beam generation.
Fig. 5. Numerical simulation results of the designed GST metasurface at crystalline state. Far-field (a) intensity profile and (b) phase distribution of the transmitted LCP component and (c) intensity profile and (d) phase distribution of the transmitted RCP component under LCP excitation. Far-field (e) intensity profile and (f) phase distribution of the transmitted LCP component and (g) intensity profile and (h) phase distribution of the transmitted RCP component under RCP excitation.
To verify the OAM emission of amorphous emission in a quantitative way, we have projected the decomposed cross- and co-polarized CP components to the OAM basis by encoding different spiral phases corresponding to specific topological charges. Then the OAM mode purity can be determined, which is defined as the relative central intensity of the beam after demodulation by the spiral phase with an opposite topological charge [52]. The calculated mode purities of two CP components for LCP and RCP incidences at the design wavelength of 5 µm are shown in Fig. 6. Impressively, the mode purities of the cross-polarized components with topological charges of $l ={\pm} 2$ are determined to be ∼ 0.949. For the co-polarized components carrying no OAMs, the mode purity values are ∼ 0.955.
3. Conclusions
In this work, we have utilized GST meta-molecules to realize a transmissive active metasurface for switchable vector vortex beam generation in the mid-infrared range. The designed GST meta-molecule could switch between a QWP and a usual transmissive plate in a wavelength range from 4.95 to 5.05 µm when GST transits from the amorphous state to the crystalline state. In addition, a switchable vector vortex beam generator is achieved by spatially orienting GST meta-molecules. At the amorphous state, RP and AP beams that are decomposed of the co-polarized component carrying OAMs with topological charges of $l = 0$ and cross-polarized component carrying OAMs with topological charges of $l ={\pm} 2$ are generated effectively with high mode purities around 0.955 and 0.949, for the LCP and RCP incidences, respectively. As amorphous GST transits to its crystalline state, the generated RP and AP beams disappear, and the incident CP beams transmit directly. Considering the thickness of the GST meta-molecule in our design, it is feasible to conduct the phase transition of GST through a thermal stimulus. The proposed tunable GST metasurface enables reconfigurable structured beam generation and thereby offers new fascinating possibilities for multifunctional intelligent meta-devices.
Funding
National Natural Science Foundation of China (61774015, 62074015); 111 Project (B14010); Villum Fonden (00022988, 37372); China Scholarship Council (202106030165).
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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