Hybrid all-dielectric phase-change metasurfaces for tunable waveplate

. Metasurfaces have attracted immense interest across various scientific disciplines due to their ability to manipulate light wave parameters with numerous functionalities. However, these functionalities have historically been static, lacking the capability for dynamic, real-time control. In this study, we introduce a highly efficient, tunable wave-plate by incorporating a thin layer of the phase change material Sb 2 Se 3 into a silicon all-dielectric metasurface. This structure demonstrates the ability to transition from a half-waveplate to a quarter-waveplate as Sb 2 Se 3 shifts from an amorphous to a crystalline state at the telecom wavelength of 1 . 55 μ m. Remarkably, it maintains consistent performance across a range of rotation angles. In addition, we have performed comprehensive electro-thermal simulations to validate the phase change process, confirming the practical feasibility of this technology. This tunable metasur-face represents a significant advancement in adaptive photonics, offering customizable and sophisticated functionalities.


Introduction
7][18] However, most all-dielectric metasurfaces are passive, exhibiting static responses dictated by material compositions and configuration, which prevents them from fulfilling the demand for real-time tunability.
To address the evolving needs of adaptive photonic integrated systems, research has pivoted toward active all-dielectric metasurfaces equipped with dynamic control capabilities.Efforts include integrating Si nanodisk metasurface with liquid crystals, [19][20][21] although the considerable thickness of liquid crystal solutions (i.e., the order of micrometers) often results in a significantly bulkier device.Another approach involves dynamically tuning the all-dielectric metasurface through temperature-dependent changes in the refractive index of Si, 22,23 but this method suffers from a relatively slow tuning speed.Therefore, there is an imperative need for tunable alldielectric metasurfaces that combine high efficiency, rapid tuning, and compactness.
In this work, we introduce a tunable metasurface-based waveplate (meta-WP) operating in the near-infrared region by incorporating a thin layer of phase change material Sb 2 Se 3 within a Si nano-cube.This design allows the meta-WP to alternate functions between a half-waveplate (HWP) and a quarter-waveplate (QWP) at a telecom wavelength of 1.55 μm while maintaining consistent performance across various rotation angles.9][30] Notably, Sb 2 Se 3 has nearly zero loss in both amorphous and crystalline states and undergoes a significant refractive index change (Δn ∼ 1) between these two states at the telecommunication C-band (1.55 μm). 31These characteristics ensure superior performance for our designed meta-waveplate.In addition, we present a detailed Joule heating analysis to confirm the reversible tunability of the meta-WP, where a graphene microheater precisely controls the Sb 2 Se 3 phase transition.Our proposed hybrid nanostructure presents a significant advancement for integrated adaptive photonics, promising high efficiency and versatile switchable functionalities.

Results and Discussion
The operating principle of the proposed tunable waveplates is illustrated in Fig. 1, where periodic Si − Sb 2 Se 3 − Si sandwich meta-atoms stand on top of a quartz substrate.At the amorphous state, a circularly polarized (CP) incident beam transforms into its cross-polarized counterpart with reversed handedness after transmitting through the Si − Sb 2 Se 3 − Si metasurface, acting as an HWP.Upon triggering Sb 2 Se 3 into its crystalline state, the metasurface functions as a QWP that converts CP incident beams into the AE45 deg oriented linearly polarized (LP) beams.
From a microscopic perspective, the corresponding optical transmission characteristics of the Si − Sb 2 Se 3 − Si meta-atom can be described through the Jones matrix E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 4 ; 4 1 5 where t xx ¼ jt xx je iδ xx and t yy ¼ jt yy je iδ yy are the transmission coefficients under x-and y-polarized excitations, which are mainly determined by the lateral dimensions along x-and y-directions, respectively.Specifically, jt xx j and jt yy j represent transmission amplitudes, whereas δ xx and δ yy stand for the phase delays.If the transmission amplitudes are equal (e.g., jt xx j ¼ jt yy j) and the relative phase difference Δδ ¼ δ yy − δ xx equals AE90 or 180 deg, a QWP or an HWP could be obtained accordingly.
To determine the anticipated meta-atom dimensions, three-dimensional (3D) full-wave simulations were carried out using the commercially available software COMSOL Multiphysics (version 6.0).Throughout simulations, periodic boundary conditions are implemented for the Si − Sb 2 Se 3 − Si unit cell in both x-and y-directions.Perfectly matching layers are introduced above and below the unit cell to truncate the simulation domain.The quartz substrate is assumed as a lossless dielectric material with a constant refractive index of 1.44, whereas the refractive index of amorphous Si is considered 3.6147 þ 0.064753i.Moreover, the measured refractive indices of Sb 2 Se 3 in the amorphous and crystalline states are 3.306 and 4.3281 þ 0.000021i, respectively, at the target wavelength of 1.55 μm. 30The periodicity P of the Si − Sb 2 Se 3 − Si meta-atom is set as 660 nm to eliminate any unwanted diffraction order.The height h of the Si and Sb 2 Se 3 brick is set as 289 and 155 nm, respectively, ensuring sufficient phase response and acceptable transmittance under two different states of Sb 2 Se 3 .Figure 2 presents the simulated transmission amplitudes and phase distributions of the Si − Sb 2 Se 3 − Si meta-atom under x-polarized excitation for the two states.The side dimensions (i.e., l x and l y ) vary from 100 to 600 nm at a 5 nm interval, whereas other geometrical parameters remain constant.The optimized dimensions of the Si − Sb 2 Se 3 − Si meta-atom are determined to be l x ¼ 165 nm, l y ¼ 550 nm, marked in Fig. 2.
Figure 3 shows the transmission amplitudes (jt xx j and jt yy j) and phase differences (Δδ) under x-and y-polarized incidences as a function of wavelength for both amorphous and crystalline Sb 2 Se 3 .In the amorphous state, jt xx j and jt yy j are found to be 0.    E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 7 ; 7 3 6 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 7 ; 6 9 9 DoCP ¼ S 3 ∕S 0 ; Meanwhile, the calculated DoLPs exceed 0.95 for both cases within the wavelength range of 1.53 and 1.57 μm.Moreover, the transmittance and conversion efficiency, defined as the intensity ratio between the transmitted light and incident light and the intensity ratio between the target polarized state light and incident light, exceed 93.7% and 92.8%, respectively, under CP excitations in the HWP mode, whereas in the QWP mode, they are above 90.6% and 88.1%, spanning the wavelengths from 1.53 to 1.57 μm [Figs.4(c) and 4(f)].Notably, at the target wavelength of 1.55 μm, both transmittance and conversion efficiency are nearly equal, reaching up to 95.7% and 94.8% in HWP and QWP modes, respectively.When Sb 2 Se 3 transits to the crystalline state, the DoLPs of transmitted beams stay above 0.975 without obvious changes, as shown in Fig. 5(c).As for the 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 deg (45 deg) to 45 deg (−45 deg) when θ is rotated from 0 to 90 deg for the LCP (RCP) incidence.][3] To dynamically manipulate the Si − Sb 2 Se 3 − Si metasurface, we propose a practical electro-thermal phase control.As illustrated in Fig. 6(a), we analyze a meta-WP consisting of 10 × 10 Si − Sb 2 Se 3 − Si meta-atoms.The Sb 2 Se 3 bricks are uniformly heated by a 10 nm-thick graphene heater possessing excellent thermal and electrical conductivity. 33irect ohmic contact with the graphene layer is achieved via two 50 nm-thick gold electrodes.A coupled Multiphysics model, incorporating the electric currents module that simulates electric current distribution and heat transfer in the solid module that calculates the heating exchange and temperature distribution, was utilized.In the heat transfer module, infinite element domains are set as the side boundaries, and convective heat flux boundary conditions with an ambient temperature of T ¼ 293 K are applied to the bottom surfaces of the model.Material properties essential for the electro-thermal simulation are detailed in Table 1.
With this model, the meta-WP undergoes phase transition with two distinct electrical pulses.Crystallization is initiated by heating Sb 2 Se 3 above the crystalline temperature of T c ¼ 473 K using a long, low-voltage pulse of V c .Specifically, a pulse voltage of 4.46 V and a width of 100 μs are employed in this simulation.Approximately 30 μs into the process, the entire Sb 2 Se 3 array reaches full crystallization [Figs.6(b) and 6(d)].The temperature responses in Fig. 6(d) reveal a remarkably uniform distribution across the top surface, bottom surface, and the entire volume of Sb 2 Se 3 bricks.On the other hand, amorphization requires a short-and high-voltage pulse of V m to heat Sb 2 Se 3 above the melting temperature of T m ¼ 893 K and then rapidly cool it down below the crystalline temperature T c .In this case, a 26.7 V pulse with a 350 ns-long width is adopted.The entire array of Sb 2 Se 3 meta-atoms undergoes rapid annealing above the melting temperature T m , as illustrated in Figs.6(c) and 6(e).6][37] As a result, the processing time for the re-amorphization of the entire array of Sb 2 Se 3 meta-atoms is 1.25 μs, comprising 350 ns for annealing and 900 ns for cooling down.Moreover, by extracting the electric currents for crystallization and re-amorphization (i.e., 2.5 and 15 mA), the estimated energy required for the phase transition is ∼1.115 and 0.1402 μJ, respectively, which provides a valuable reference for future experimental demonstrations.

Conclusion
In this work, we have utilized an array of periodic Si − Sb 2 Se 3 − Si meta-atoms to realize a transmissive tunable metasurface exhibiting the switchable functionalities between an HWP and a QWP under two states of Sb 2 Se 3 at the wavelength of 1.55 μm.The designed tunable meta-WP consistently excels across varied rotation angles, showcasing its versatility in enabling intricate functionalities within diverse designs.In addition, the feasibility of this tunable optical waveplate is convincingly verified through electro-thermal control, which exhibits effective and switchable phase changes of the Sb 2 Se 3 meta-atom array with a graphene heater.The proposed tunable meta-WP could offer fascinating possibilities for developing low-loss and high-performance integrated adaptive photonic devices.

Fig. 1
Fig. 1 Working principle of the proposed tunable meta-WP.(a) The designed metasurface works as an HWP when Sb 2 Se 3 is in the amorphous phase.(b) The designed metasurface works as a QWP when Sb 2 Se 3 is in the crystalline phase.The inset shows the aerial view of the designed unit cell on the quartz substrate.
975 and 0.933, respectively, with a phase difference Δδ of −179.47 deg at the operation wavelength of 1.55 μm.This is consistent with the requirement of conventional HWPs with equal transmission amplitudes and 180 deg phase retardation between two orthogonal LP beams.Upon Sb 2 Se 3 transitioning into the crystalline state, a phase difference Δδ of 86 deg is induced with the corresponding jt xx j of 0.972 and jt yy j of 0.918.Moreover, jt xx j and jt yy j maintain high values of above 0.9 within the wavelength range of 1.53 and 1.57 μm despite the states of Sb 2 Se 3 , whereas the relative phase differences Δδ are found to be 180 deg AE10 deg and 90 deg AE10 deg for the amorphous and crystalline states, respectively, demonstrating the functional switching from an HWP to a QWP for the designed Si − Sb 2 Se 3 − Si metasurface with an operating bandwidth of ∼40 nm centered at 1.55 μm.

Fig. 2
Fig. 2 (a) Simulated and (c) transmission amplitudes and (b) and (d) phase distributions of the Si − Sb 2 Se 3 − Si meta-atom as a function of the lateral dimensions for the incident x -polarized wave at λ ¼ 1.55 μm when Sb 2 Se 3 is at the (a), (b) amorphous and (c), (d) crystalline states.The complex transmission coefficient for the y -polarized incident can be obtained by mirroring the map along the line of l x ¼ l y .

Fig. 3
Fig. 3 Simulated transmission amplitudes (jt xx j and jt yy j) and the relative phase differences (Δδ) under x -and y -polarized excitations at the (a) amorphous and (b) crystalline states.

Fig. 4
Fig. 4 Performance of the tunable meta-WP.(a) DoLPs and (b) DoCPs of the transmitted beams under CP excitations at the amorphous state.(d) DoLPs and (e) AoLPs of the transmitted beams under CP excitations at the crystalline state.(c), (f) The transmittance and conversion efficiency of the transmitted beams in (c) HWP and (f) QWP mode.(g), (h) Polarization state diagrams of the transmitted beams at the (g) amorphous and (h) crystalline states at the design wavelength of 1.55 μm.

E 4 )
Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 1 1 7 ; 6 8 1 AoLP ¼ tan −1 ðS 2 ∕S 1 Þ∕2: (To further validate the polarization conversion performance of the designed Si − Sb 2 Se 3 − Si meta-WP, Fig. 4 presents the DoLPs and the DoCPs of the transmitted beams for amorphous Sb 2 Se 3 and the DoLPs and the AoLPs for crystalline Sb 2 Se 3 under LCP and RCP excitations at the operation wavelength ranging from 1.5 to 1.6 μm.At the amorphous state, the transmitted beams exhibit high DoCPs approaching 1 and −1 under left and right CP (LCP and RCP) excitations, respectively, with relatively low DoLPs smaller than 0.195, within the wavelength range of 1.53 and 1.57 μm [Figs.4(a) and 4(b)].Specifically, the DoLPs are ∼0.024 at the target wavelength of 1.55 μm, manifesting a well-distributed circular polarization [Fig.4(g)].Once Sb 2 Se 3 transits into the crystalline state, the LCP and RCP incident beams are converted into −45 deg-oriented and 45 deg-oriented LP beams correspondingly [Figs.4(d), 4(e) and 4(h)].

Fig. 5
Fig. 5 Performance of the tunable meta-WP with different rotations relative to the x -axis.(a) DoLPs and (b) DoCPs of the transmitted beams under CP excitations at the amorphous state.(c) DoLPs and (d) AoLPs of the transmitted beams under CP excitations at the crystalline state.

Figure 5
Figure 5 shows the DoLPs and DoCPs of the transmitted beams for amorphous Sb 2 Se 3 and the DoLPs and AoLPs of the transmitted beams for crystalline Sb 2 Se 3 as a function of the rotation angle with respect to the x-axis at λ ¼ 1.55 μm.At the amorphous state, the incident CP beams are converted into their cross-polarized lights with high conversion ratios despite the rotation angle, indicated by the relatively low and high DoCPs (>0.925) [Figs.5(a) and 5(b)].When Sb 2 Se 3 transits to the crystalline state, the DoLPs of transmitted beams stay above 0.975 without obvious changes, as shown in Fig. 5(c).As for the 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 deg (45 deg) to 45 deg (−45 deg) when θ is rotated from 0 to 90 deg for the LCP (RCP) incidence.Therefore, the Si − Sb 2 Se 3 − Si metasurface maintains consistent performance for different rotation angles, indicating its versatility for accomplishing more intricate functionalities.[1][2][3]To dynamically manipulate the Si − Sb 2 Se 3 − Si metasurface, we propose a practical electro-thermal phase control.As illustrated in Fig.6(a), we analyze a meta-WP consisting of 10 × 10 Si − Sb 2 Se 3 − Si meta-atoms.The Sb 2 Se 3 bricks are uniformly heated by a 10 nm-thick graphene heater possessing excellent thermal and electrical conductivity.33Direct ohmic contact with the graphene layer is achieved via two 50 nm-thick gold electrodes.A coupled Multiphysics model, incorporating the electric currents module that simulates electric current distribution and heat transfer in the solid module that calculates the heating exchange and

Fig. 6
Fig. 6 Electro-thermal control of the Si − Sb 2 Se 3 − Si meta-WP.(a) A schematic view of the tunable meta-WP driven by the electro-thermal control.(b) Simulated temperature profiles under a crystallization pulse with a bias voltage of 4.46 V and a pulse width of 100 μs.(c) Simulated temperature profiles model under an amorphization pulse with a bias voltage of 26.7 V and a pulse width of 350 ns.Temperature responses of the bottom surface, the top surface, and the entire volume of Sb 2 Se 3 bricks during the (d) crystallization and (e) amorphization processes.

Table 1
Material properties used in electro-thermal simulation.
• K −1 )d is the thickness of graphene, R s is the sheet resistance of 1936 Ω. a