Dynamic Phase‐Change Metawaveplates for Advanced Wavefront Shaping

Abstract

Metasurfaces have recently gained increasing attention and shown great potential in replacing bulk optics with ultracompact flat metadevices, owing to their unprecedented capabilities of molding optical fields with surface‐confined configurations and exceedingly low losses. However, most existing metasurfaces are typically passive and feature well‐defined responses determined by material compositions and configurations, which severely limit the functionalities in intelligent and adaptive nanophotonics. Therefore, it is highly desired to realize active metasurfaces with dynamic modulation postfabrication. Herein, a highly efficient tunable metawaveplate at the telecom wavelength of 1.55 μm by structuring the phase‐change alloy Sb₂Se₃ is designed, which can switch from a half‐waveplate to a quarter‐waveplate once Sb₂Se₃ transits from the amorphous to the crystalline state. Capitalizing on the designed Sb₂Se₃ meta‐atom and the Pancharatnam–Berry phase, two switchable meta‐devices capable of actively shaping the wavefronts of the transmitted waves are proposed, including tunable beam steering and metalens with tailored focal intensity. The presented tunable metasurfaces can open new avenues for adaptive photonics with advanced functionalities.

Introduction

Metasurfaces have recently emerged as one of the most exciting research directions in optics.^{[ ]} Based on the judiciously engineered artificial nanoantennas (often termed meta-atoms), metasurfaces are capable of directly and locally tailoring various properties of light (e.g., amplitude, phase, and polarization) with surface-confined configurations and subwavelength spatial resolutions.^{[ ]} As such, metasurfaces have shown great potential in the implementation of various planar optical devices possessing the advantages of multiple functionalities, planar profiles, lightweight, as well as ease of fabrication and integration, including beam deflectors,^{[ ]} beam splitters,^{[ ]} focusing lenses,^{[ ]} optical holograms,^{[ ]} and polarimeters.^{[ ]} In particular, high-performance optical waveplates, such as quarter- and half-waveplates (QWPs and HWPs), have been successfully demonstrated with metasurfaces, which function as effective wave retarders to manipulate the states of polarization (SoPs) of the incident light.^{[ ]} Despite significant achievements, most existing metasurface-based optical waveplates are passive and feature static responses determined by material compositions and configurations, which cannot meet the requirement of real-time tunability for intelligent and adaptive photonic systems.

Very recently, dynamic waveplates have been explored using tunable metasurfaces, where the optical birefringence can be actively tuned through light inclination,^{[ ]} mechanical operation,^{[ ]} photogenerated hot carriers,^{[ ]} anisotropic nonlinear response,^{[ ]} electrical stimulus,^{[ ]} and phase-change materials.^{[ ]} However, the demonstrated dynamic metawaveplates typically suffer from low-polarization conversion efficiencies.^{[ ]} Although piezoelectric microelectromechanical system-based dynamic metasurfaces have been proven to be good candidates for realizing highly efficient dynamic waveplates, they are constrained to operate in reflection,^{[ ]} which restricts severely the range of potential applications. Therefore, it is highly desired to realize efficient dynamic metawaveplates operating in the transmission mode.

Herein, we propose an efficient dynamic metawaveplate in the near-infrared region by structuring the phase-change material Sb₂Se₃, which exhibits much lower losses (approaching zero) in the near-infrared spectral range compared with Ge₂Sb₂Te₅ (GST) alloy^{[ ]} while maintaining the excellent properties of phase-change materials, such as ultrafast switching speed, robust switching, large refractive-index contrast.^{[ ]} Depending on the state of the Sb₂Se₃ meta-atoms, the designed metawaveplate can switch its function between an HWP and a QWP with high transmission efficiencies, superior to previously reported GST-based tunable waveplates with relatively low efficiencies^{[ ]} or limited functionalities.^{[ ]} Capitalizing on the basic metawaveplate meta-atom, we have numerically demonstrated two dynamic metadevices with advanced and switchable wavefront-shaping capabilities utilizing the Pancharatnam–Berry (PB) phase, including the tunable beam deflector and metalens with tailored focal intensity. The proposed dynamic Sb₂Se₃ metawaveplates have great potential in the application of integrated adaptive photonics with compact footprints and switchable functionalities.

Dynamic Metawaveplate

The working principle of the proposed dynamic phase-change metawaveplate with different optical birefringences is illustrated in Figure , where periodic Sb₂Se₃ meta-atoms are on top of a quartz substrate. At the amorphous state, the homogeneous Sb₂Se₃ meta-atoms act as an HWP that converts normally incident circularly polarized (CP) beams into their crosspolarized counterparts with opposite handedness. When Sb₂Se₃ is trigged to the crystalline state, the CP incident beams are transformed into linearly polarized (LP) transmitted beams with the angles of linear polarization (AoLPs) equal to ±45°, mimicking the functionality of a typical QWP.

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From a microscopic perspective, the corresponding optical transmission characteristics of the Sb₂Se₃ meta-atom can be described through the Jones matrix.^{[ ]} 1 $T=\left(\begin{array}{cc}{t}_{xx}& 0\\ 0& t_{yy}\end{array}\right)=\left(\begin{array}{cc}|t_{xx}|e^{i{\delta }_{xx}}& 0\\ 0& |t_{yy}|e^{i{\delta }_{yy}}\end{array}\right)$ where $t_{xx}=|t_{xx}|e^{i{\delta }_{xx}}$ and $t_{yy}=|t_{yy}|e^{i{\delta }_{yy}}$ are the complex transmission coefficients under x- and y-polarized excitations at normal incidence, which are mainly determined by the dimensions of the Sb₂Se₃ meta-atom along x- and y-directions, respectively. Specifically, $|t_{xx}|$ and $|t_{yy}|$ represent the transmission amplitudes, ${\delta }_{xx}$ and ${\delta }_{yy}$stand for the phase delays, and $\Delta \delta ={\delta }_{yy}-{\delta }_{xx}$ is set as the relative phase difference. If the transmission amplitudes are equal (e.g., $|t_{xx}|=|t_{yy}|$) and $\Delta \delta$ equals ±90° or 180°, a QWP or an HWP could be accordingly obtained. To optimize the dimensions of the Sb₂Se₃ brick that functions as a dynamic metawaveplate, 3D full-wave simulations were carried out using the commercially available software COMSOL Multiphysics (version 5.5). In the simulation, periodic boundary conditions are applied to the x- and y- directions of the Sb₂Se₃ meta-atom, and perfectly matching layers (PMLs) 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, while the measured refractive indices of Sb₂Se₃ in the amorphous and crystalline states are 3.306 and 4.3281 + 0.000021i, respectively, at the target wavelength of 1.55 μm (Section S1, Supporting Information). Two orthogonal LP (i.e., x- and y-polarized) plane waves are normally incident from the bottom side of the quartz substrate. The periodicity P of the Sb₂Se₃ meta-atom is set as 790 nm to eliminate any unwanted diffraction orders, and the height h of the Sb₂Se₃ brick is set as 945 nm to ensure sufficient phase retardation under two different states. The length and width of the Sb₂Se₃ brick (i.e., $l_x$ and $l_y$) are varied to realize the expected functionality that switches between an HWP and a QWP when Sb₂Se₃ meta-atoms are in the amorphous and crystalline states. Figure  plots the simulated transmission amplitude and phase distributions of the Sb₂Se₃ meta-atom under x-polarized excitation for the two different states with the side dimensions varied from 100 to 500 nm at a step of 5 nm at λ = 1.55 μm, where the selected metawaveplates are marked. The optimized dimensions of the final Sb₂Se₃ brick are determined to be $l_x$ = 195 nm and $l_y$ = 440 nm. The designed Sb₂Se₃ dynamic meta-atoms could be fabricated by patterning the sputtered Sb₂Se₃ film with the standard electron beam lithography and inductively coupled–plasma reactive ion etching.

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Figure  shows the simulated transmission amplitudes ($|t_{xx}|$and $|t_{yy}|$) and relative phase differences ($\Delta \delta$) of the optimized Sb₂Se₃ meta-atom under x- and y-polarized excitations as a function of the wavelength for both amorphous and crystalline states. When Sb₂Se₃ is in the amorphous state, the obtained $|t_{xx}|$and $|t_{yy}|$ are found to be 0.997 and 0.991, respectively, and the relative phase difference $\Delta \delta$ is 180.77° at the operation wavelength of 1.55 μm, which is essentially consistent with the requirement of conventions HWPs with equal transmission amplitudes and 180° phase retardation between two orthogonal LP beams. As for the crystalline state, a phase difference Δδ of 92.77° is induced with the corresponding amplitudes $|t_{xx}|$ and $|t_{yy}|$ of 0.945 and 0.996 at λ = 1.55 μm, satisfying the condition of a QWP function. Therefore, the designed Sb₂Se₃ metawaveplate composed of periodically distributed Sb₂Se₃ meta-atoms can realize efficient switching between an HWP and a QWP at the target wavelength of 1.55 μm with substantially equal and high transmission efficiencies under two Sb₂Se₃ states. Furthermore, Figure  shows the calculated polarization conversion performance of the designed dynamic metawaveplate within the wavelength range between 1.5 and 1.6 μm. At the amorphous state, the degrees of circular polarization (DoCPs) of the transmitted beams under LCP and RCP excitations are larger than 0.92 or smaller than −0.92 at the wavelength ranging from 1.525 to 1.575 μm, exhibiting acceptable HWP functionality. For the crystalline state, the degrees of linear polarization (DoLPs) of transmitted beams are larger than 0.98 and the AoLPs of the transmitted beams stay close to −45° (45°) under normal LCP (RCP) incidence at the wavelength range of 1.525 and 1.575 μm, indicating good QWP functionality. Therefore, the designed dynamic metawaveplate can work in a wide spectrum with an operating bandwidth of ≈50 nm centered at 1.55 μm.

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Tunable Beam Deflector

Capitalizing on the designed Sb₂Se₃ meta-atom, we further design a tunable beam deflector that enables functional switching between beam steering and beam splitting under two Sb₂Se₃ states (Figure ). As schematically shown in the inset, the tunable metadeflector is made up of identical Sb₂Se₃ meta-atoms with different orientations to form a periodically arranged supercell that supplies a linear phase gradient for the crosspolarized CP component along the x-axis using the PB phase. When the Sb₂Se₃ meta-atom acts as an HWP in the amorphous state, the incident CP beams are first completely converted into their crosspolarized counterparts and then anomalously steered. Specifically, the incident left-handed CP (LCP) beam becomes a right-handed CP (RCP) beam that is anomalously refracted into the +1 diffraction order, while the RCP incident beam is converted into an LCP component directed to the −1 diffraction order, as shown in Figure . When Sb₂Se₃ transits to its crystalline state, the designed metadeflector will switch to a beam splitter capable of splitting the incident CP light into two transmitted beams with equal intensities, namely, the copolarized CP light propagating in the original direction and the deflected crosspolarized CP light (Figure ).

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For the Sb₂Se₃ meta-atom rotated with an angle of θ from the x-axis, the corresponding Jones matrices under two different states become 2 $T_{\mathrm{a}\_\text{θ}}=R(\theta )T_{\mathrm{a}}R(-\theta )$ 3 $T_{\mathrm{c}\_\text{θ}}=R(\theta )T_{\mathrm{c}}R(-\theta )$ where $R\left(\theta \right)=\left(\begin{array}{cc}\cos \theta & -\text{sin\hspace{0.17em}}\theta \\ \text{sin\hspace{0.17em}}\theta & \cos \theta \end{array}\right)$ represents the rotation matrix, and $T_{\mathrm{a}}$ and $T_{\mathrm{c}}$ are the Jones matrices of the Sb₂Se₃ meta-atom without any rotation at two different states. As the designed Sb₂Se₃ meta-atom functions as an HWP and a QWP at amorphous and crystalline states, $T_{\mathrm{a}}$ and $T_{\mathrm{c}}$ can be expressed as 4 $T_{\mathrm{a}}=|t_{\mathrm{a}}|e^{i{\delta }_{\mathrm{a}\_xx}}\left(\begin{array}{cc}1& 0\\ 0& e^{i\pi }\end{array}\right)=|t_{\mathrm{a}}|e^{i{\delta }_{\mathrm{a}\_xx}}\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)$ 5 $T_{\mathrm{c}}=|t_{\mathrm{c}}|e^{i{\delta }_{\mathrm{c}\_xx}}\left(\begin{array}{cc}1& 0\\ 0& e^{i\frac{\pi }{2}}\end{array}\right)=|t_{\mathrm{c}}|e^{i{\delta }_{\mathrm{c}\_xx}}\left(\begin{array}{cc}1& 0\\ 0& i\end{array}\right)$ where $|t_{\mathrm{a}}|$ and $|t_{\mathrm{c}}|$ represent the transmission amplitudes of the Sb₂Se₃ meta-atom under amorphous and crystalline states, respectively, while ${\delta }_{\mathrm{a}\_xx}$ and ${\delta }_{\mathrm{c}\_xx}$ stand for the phase delays under the x-polarized excitation. Here we assume that the transmission amplitudes along the fast and slow axes are equal. Considering a CP incident beam $E_{\text{in}}=\frac{\sqrt{2}}{2}\left(\begin{array}{c}1\\ \sigma i\end{array}\right)$ with σ = 1 for LCP light and σ = −1 for RCP light, the transmitted beam passing through the rotated Sb₂Se₃ meta-atom under the amorphous state is calculated as 6 $E_{\mathrm{a}\_\text{out}}=\frac{\sqrt{2}}{2}|t_{\mathrm{a}}|e^{i{\delta }_{\mathrm{a}\_xx}}{e}^{i\left(2\sigma \theta \right)}\left(\begin{array}{c}1\\ -\sigma i\end{array}\right)$

For the crystalline state, the transmitted beam becomes 7 $E_{\mathrm{c}\_\text{out}}=\frac{|t_{\mathrm{c}}|e^{i{\delta }_{\mathrm{c}\_xx}}}{2\sqrt{2}}(E_{\text{out}\_\text{cross}}+E_{\text{out}\_\text{co}})$ 8 $E_{\text{out}\_\text{cross}}=\left(1-i\right)\left(\begin{array}{c}1\\ -\sigma i\end{array}\right)e^{i2\sigma \theta }$ 9 $E_{\text{out}\_\text{co}}=(1+i)\left(\begin{array}{c}1\\ \sigma i\end{array}\right)$

Therefore, the incident CP beam is converted into the crosspolarized CP light with additional PB phase modulation of $2\sigma \theta$ when Sb₂Se₃ is at the amorphous state. In contrast, the incident CP light becomes linearly polarized with its AoLP rotated.^{[ ]} Meanwhile, the transmitted LP light can be decomposed into two CP components with equal intensities, where one is the copolarized CP light without any phase modulation while the other is the crosspolarized CP light with an additional phase delay of $2\sigma \theta$. To verify the performance of the metawaveplate with different orientations, we simulated the DoLPs and the DoCPs of the transmitted beams as a function of the rotation angle θ with respect to the x-axis under normal LCP and RCP excitations at the design wavelength of 1.55 μm for two different states, as shown in Figure . At the amorphous state, the incident CP beams are converted into their crosspolarized lights with high conversion ratios, indicated by the relatively low DoLPs and high DoCPs that approach ≈0 and ±1, respectively (Figure ).

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When Sb₂Se₃ transits to the crystalline state, the DoLPs of transmitted beams are always close to 1 without obvious changes despite the varied rotation angle, as shown in Figure . 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° (45°) to 0° (90°) when θ is rotated from 0 to 45° for the LCP (RCP) incidence. In addition to the robust polarization conversion, the metawaveplates exhibit stable and linear-phase modulation under different orientations. Figure  shows the transmittance and phases of LCP and RCP components under two CP excitations when Sb₂Se₃ is at the amorphous phase. Under normal LCP or RCP excitation, the incident light is totally converted into the crosspolarized CP light with the crosspolarized transmittance larger than 0.9, and the copolarized transmittance close to 0, which is independent of the rotation angle θ, revealing the negligible near-field coupling between neighboring elements. At the same time, the phase of the crosspolarized CP transmitted light varies from 0° (360°) to 360° (0°) when θ is rotated from 0 to 180° under the LCP (RCP) incidence, consistent with the theory of PB phase. When it comes to the crystalline state, the transmitted light consists of two CP components with approximately equal intensities (Figure ). Similarly, the phases of the crosspolarized CP component vary linearly with respect to the rotation angle.

Based on the dynamic metawaveplate unit cell and PB phase, we design a tunable beam deflector with a supercell composed of ten spatially oriented elements that are gradually rotated with a constant angle step of 18° to form a linear phase gradient. At the amorphous state, the incident CP wave is completely converted into its crosspolarized counterpart. Meanwhile, the transmitted crosspolarized CP light experiences different phase delays upon the interaction with meta-atoms, finally forming a titled wavefront, as shown in Figure . To retrieve the intensity distributions of two CP beams in different directions, the 3D far-field simulations were conducted using the finite-difference time-domain method (FDTD) with a commercial software package (Lumerical), where the near-field distributions have been projected into the far field. As shown in Figure , only one dominant intensity peak appears at the angle of ±11.2° under LCP and RCP excitations, respectively, which are in good agreement with the theoretical values of ±11.3° from the generalized Snell's law. In addition, the intensity of the crosspolarized CP component coincides well with the total transmitted intensity while the copolarized CP component is suppressed. The absolute transmission efficiency and deflecting efficiency, defined as the intensity ratio between the transmitted light and incident light and the intensity ratio between the diffracted crosspolarized light and incident light, respectively, are above 94% and 92.7% under CP excitations when Sb₂Se₃ is at the amorphous state.

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As for the crystalline state, the co-polarized CP transmitted waves propagate along the original direction wherein the corresponding crosspolarized CP components are deflected to the angles of ±11.3° (Figure ), which are also in line with the theoretically calculated values. For the far-field intensity distributions shown in Figure , the dominating intensity peaks of the co- and crosspolarized CP components appear at the angle of 0° and ±11.3°, respectively. More importantly, the co- and crosspolarized CP beams share nearly equal intensities, indicating the potential application as a beam splitting. The corresponding absolute transmission efficiency and deflecting efficiency are above 93.2% and 47.2%, respectively, under CP excitations. In addition, the tunable beam deflector shows good performance at other wavelengths (Section S2, Supporting Information).

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2D Focusing with Tailored Focal Intensity

In addition to the tunable beam deflector, the designed Sb₂Se₃ meta-atom can be utilized to realize 2D focusing with tailored focal intensity, as shown in Figure . For the amorphous state, the RCP incident beam is totally converted into the LCP beam confined in the focal spot (Figure ). When it comes to the crystalline state, the transmitted light contains two orthogonal CP components with equal power, where the LCP component is tightly focused into a tiny spot as that in the amorphous state case, while the RCP component still propagates in the normal direction, as shown in Figure . Thus, the intensity of the focal spot varies with the phase transition of Sb₂Se₃.

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To realize 2D focusing, the hyperbolic phase profile $\text{Φ}(x,y)$ should be imposed on the metalens that enables the transformation between an incident planar wavefront into a spherical wavefront in transmission. 10 $\text{Φ}(x,y)=-\frac{2\pi }{\lambda }(\sqrt{x^2+y^2+f^2}-f)$ where λ is the operation wavelength in free space, f is the desired focal length of the designed metalens, and x and y are the coordinates of each Sb₂Se₃ meta-atom. Specifically, each meta-atom is spatially rotated with an angle of $\frac{\text{Φ}(x,y)}{2}$ to impart the PB phase on the crosspolarized CP component of the transmitted beam. Then, the designed Sb₂Se₃ metalens was numerically studied by conducting 3D FDTD simulations, where the metalens with a diameter of 32.39 μm and a focal length of 20 μm, corresponding to a numerical aperture is 0.63, is normally excited by an RCP Gaussian beam with waist radius of 9.936 μm from the bottom side of the quartz substrate. Figure  shows the decomposed intensity distributions of the transmitted light in the CP basis in both x–z and x–y planes under two Sb₂Se₃ states. It is clearly observed that the transmitted light is well focused at z = 19.5 μm, which mainly consists of the LCP component with the RCP counterpart greatly suppressed when Sb₂Se₃ is at the amorphous state. In particular, the power ratio between the LCP and RCP components in the focal plane reaches 17.3. Once trigged to the crystalline state, the Sb₂Se₃ metalens only focuses the LCP light at the designed location. In the focal plane, the LCP and RCP beams carry 51.8% and 48.2% of the total transmitted power, respectively. The designed Sb₂Se₃ metalens can work equally well for 2D focusing with tailored focal intensity at other wavelengths (Section S2, Supporting Information).

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To further study the focusing performance of the designed Sb₂Se₃ metalens with tailored focal intensity, the absolute transmission efficiency and focusing efficiency under different crystalline fractions, defined as the ratio of the light intensity of the transmitted light from the focal plane to the incident intensity and the ratio of the light intensity of the transmitted LCP component from the focal spot to the incident intensity respectively, are shown in Figure . At the amorphous state, the focusing efficiency is 83.6%, which changes to 46.4% when Sb₂Se₃ fully transits to the crystalline state, indicating the intensity switching of 2D focusing. With the increased crystalline fraction, the absolute transmission efficiency remains larger than 80%, except for the case of 51% crystalline Sb₂Se₃, in which the y-polarized incident light is mostly reflected by the designed Sb₂Se₃ meta-atom, resulting in low transmittances of the designed Sb₂Se₃ meta-atoms with different rotation angles under CP excitations and affecting the absolute transmission efficiency of the designed Sb₂Se₃ metalens (Section S3, Supporting Information). To further increase the absolute transmission efficiency of the metalens and make it approach the transmittances of the designed dynamic metawaveplate, especially at two states of Sb₂Se₃, a larger metalens could be designed, which can decrease the influence from the near-field coupling between elements and the phase deviation at the boundary of the metalens. As for the corresponding focusing efficiency, it does not show a linear change with the increased crystalline fraction, which is mainly ascribed to the nonlinear transition in the phase retardation. When Sb₂Se₃ transits from the amorphous to the crystalline state gradually, the introduced relative phase difference $\Delta \delta$ does not decrease linearly from 180° to 90° (Section S3, Supporting Information). Therefore, the metawaveplate cannot gradually switch from an HWP to a QWP with decremental phase retardation.

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Conclusion

In this work, we have utilized low-loss phase-change material Sb₂Se₃ to realize an efficient dynamic metawaveplate at the telecom wavelength of 1.55 μm, which enables the switchable functionality between an HWP and a QWP with high transmission efficiencies under two different states of Sb₂Se₃. Based on the basic metawaveplate unit cell and the PB phase, we further design two switchable metadevices with advanced and tunable wavefront-shaping capabilities, including a tunable beam deflector and a metalens with tailored focal intensity. The designed tunable Sb₂Se₃ metasurfaces could offer fascinating possibilities for multifunctional adaptive near-infrared photonics. More importantly, similar concepts can be utilized to implement dynamic waveplates in visible frequencies utilizing the phase-change material Sb₂S₃ with a wider bandgap of 1.70–2.05 eV, which moves absorptance band edge to the visible spectrum at 600 nm.^{[ ]}

Acknowledgements

This work was funded by the National Natural Science Foundation of China (62074015 and 61774015); 111 Project of China (B14010); State Scholarship Fund of China Scholarship Council (202106030165); Villum Fonden (37372); and Danmarks Frie Forskningsfond (1134-00010B).

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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