1. Introduction

Conversion of polarization states is ubiquitous in modern optoelectronic systems, especially in polarization imaging detection and laser communication systems. Conventional methods to control the polarization utilize natural birefringent crystals, which have bulky volume for phase accumulation of ordinary and extraordinary beams [1]. Appropriately designed metamaterials that affect electromagnetic waves with giant anisotropy have been used to realize polarization conversion in infrared and THz spectral region [2,3]. Specially, three-dimensional chiral metamaterials, which possess circular dichroism properties, can generate desired polarization states [4, 5]. However, the difficulty of nanofabrication and the high loss especially in optical regime hinder the application of such an approach. One way to conquer this problem is to use planar metasurfaces. Planar metasurfaces can steer light in a desired manner through introducing abrupt changes of optical properties at the interface, but not depending on the phase accumulation along the optical paths [6]. Metasurfaces are composed of periodic, quasiperiodic or random nanoantenna array with ultrathin thickness by comparison with wavelength, and can function as a two-dimensional smart surface. Considerable efforts focus on developing metasurfaces for arbitrary wavefront engineering [7–9], manipulation of orbital angular momentum [10, 11] and polarization conversion [12–14]. Metasurface-based polarization converters are ultrathin and compact compared with the conventional counterparts. By virtue of elaborate design of the geometric parameters of anisotropic single-layer or multi-layer nanostructures [15–17], one can acquire the expected effects of polarization conversion. For example, single-layer antennas or Babinet-inverted aperture structures [18] have been verified to acquire linear-circular conversion; tri-layer with dielectric or metallic cut-wire array [13, 19] and grating-based metasurfaces [12] have been designed to realize polarization rotation or wave plate for better efficiency and operation bandwidth.

Meanwhile, substantial attention has been drawn to metasurfaces with tunable and reconfigurable functionalities. Several mechanisms for such active metasurfaces are proposed and demonstrated so far, such as mechanical deformation by utilizing plastic substrates [20, 21], photoexcitation of carrier in semiconductors [22, 23], voltage bias for tuning the optical conductivity of graphene [24–27] and thermal excitation of phase change materials [28, 29]. Obviously, utilizing materials with tunable optical properties are crucial for the realization of versatile platforms with reconfigurable functionalities. Specially, the optical properties of phase change materials such as VO₂ and liquid crystals can change dramatically through proper external excitation. Owing to the good stability, high-speed and reversible switching performance, the chalcogenide compound phase change material Ge₃Sb₂Te₆ (GST) is ideally suitable for storing large amounts of information in rewritable optical disk storage technology [30, 31]. GST undergoes a phase change from amorphous state to crystalline state through pumping by ultrafast femtosecond laser beams [32] or by thermal heating [33] with remarkable dielectric property differences between the two states. In particular, the degree of crystallization can be gradually obtained by applying controllable amounts of external excitation [34, 35], giving rise to greater flexibilities to access continuous refractive index control. The combination of these characteristics with specifically designed metasurfaces can provide new functionalities toward active high-performance manipulation of imaging, sensing, wireless communications, electromagnetic perfect absorbers [36], electromagnetically induced transparency (EIT) [28] and even spatial light modulators (SLM) [37].

In this paper, we propose and demonstrate a novel type of active metasurfaces, which can achieve full tunability of the ellipticity of the transmitted light without depending on the incident linear polarization in the mid-infrared (MIR) spectrum. The active metasurface is made of V-shape phased antenna arrays and a dielectric tunable interval modulation layer above the substrate, as shown in Fig. 1. The unit cell consists of two subunits of V-shape antenna arrays with delicate arrangements to generate two co-propagating, orthogonally polarized and equal-amplitude scattering waves. The desired scattering wave bents to the anomalous order with a spatial separation to the ordinary beam, which can eliminate the undesired cross-talk noise. The interval modulation layer is made of periodic silicon strips and GST strips beneath the two subunits to generate the necessary phase delay between the scattering waves from the two subunits. The two waves interfere coherently due to the subwavelength separation of the two subunits. Therefore, we can flexibly modulate the polarization state of the transmitted light. The periodic arranged phase change material modulation layer differs from the widely used homogeneous modulation layers for active metasurfaces. Importantly, such an approach can achieve reversible and dynamic control of polarization conversion without any mechanical stretch or rotation. Our scheme may provide a novel mechanism for a variety of applications such as phase compensators and polarization controllers, especially suitable for flexible, background-free, and compact integrated optical systems.

 

Fig. 1 Schematic of the metasurface for active tunability of the ellipticity of anomalously diffracted beams. There are three layers: the antenna layer, the interval modulation layer and the silicon substrate. The interval modulation layer consists of a silicon strip (blue) and a GST (faint orange) strip underlying the subunit 1 and subunit 2, respectively. The nanoantenna array can generate the necessary phase gradient; therefore deflect the scattered wave away from the original propagation direction. The interval modulation layer can actively control the phase difference between the scattering waves from two subunits.

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2. Design principles

Our design is based on the widely used V-shape antenna, which supports symmetric and antisymmetric eigenmodes [7, 15]. Only the symmetric mode can be excited when the incident light is polarized along the symmetric axis of the antenna and only the antisymmetric mode can be excited when the incident light is polarized perpendicular to the symmetric axis of the antenna. When we use normal illumination with arbitrary polarization angle upon such V-shape antenna arrays on homogeneous substrate, the scattering field of a single antenna in the subunit can be decomposed as follows:

 

Fig. 2 Schematic of a single antenna and a unit cell. (a) Structure parameters of V-shape antenna. $\widehat{s}$and $\widehat{a}$are the unit vectors along the symmetric and antisymmetric axis of the antenna, respectively. (b) Arrangement of the V-shape antennas in one unit. Through rotating clockwise the first four antennas by 90°, the last four antennas are acquired to reverse the phase of (S)_i − (A)_i component. Anomalous beam 1 and 2 are the (2β₁ − α)-polarized and (2β₂ − α)-polarized scattering wave from subunit 1 and subunit 2, respectively. They are spatial overlapped and can interfere coherently to generate the final transmitted beam. E₁ and E₂ denote the polarization of the anomalous beam from subunit 1 and subunit 2 in x’-y’ plane, respectively. And x’-y’ is the local coordinate of anomalous beam, where y’-axis is parallel to the y-axis.

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From Eq. (2), we found that the scattering wave can be decomposed into the combination of (S_i + A_i) and (S_i − A_i) components with polarization angle α and 2β−α from y-axis, respectively. It implies that the (S_i + A_i) and (S_i − A_i) components may possess very different scattering properties by the exact structure design. In addition, the combination of the symmetric and antisymmetric eigenmodes shows a broader phase coverage and a relatively uniform amplitude response between the two resonance frequency ranges [15]. To bend the light trajectory to anomalous refraction order, the structure parameters of the antennas in the subunit can be precisely chosen to satisfy that |S_i − A_i| is approximately equal and the phase difference of (S_i+1 − A_i+1) and (S_i − A_i) is 2π/N, where N is the numbers of antennas in a subunit. Meanwhile, |S_i + A_i| is unequal and the phase response of (S_i+1 + A_i+1) and (S_i + A_i) are approximately equal. As a result, under normal incidence the scattered wave with polarization angle (2β−α) will propagate along the anomalous refractive direction with θ_t = arcsin(λ/D), Fig. 2(b), where λ is the incident wavelength and D is the length of a subunit in x direction [7]; while the rest part of the transmitted wave polarized along α-direction propagate perpendicular to the sample surface as ordinary beam.

The unit cell in the metasurface consists of two subunits with the same antenna parameters and an offset d from each other along x direction. They all produce an anomalous beam propagate along the anomalous refraction θ_t = arcsin(λ/D). The two anomalous beams are spatially coherent because the two subunits are very close to each other (the distance between the two subunits in y-direction is much smaller than the incident wavelength). Meanwhile, the antenna orientation angle β₁ and β₂ satisfy β₂ − β₁ = 45°, namely (2β₂ − α) − (2β₁ − α) = 90°, to produce two orthogonally polarized anomalous beams, Fig. 2(b). The offset d along x-axis controls the phase difference between the two orthogonally coherent polarized wave, leading to Δφ = k₀dsin(θ_t) = 2πd/D. The two nanoantenna arrays with different arrangement in the two subunits can generate a uniform amplitude. Therefore, the transmitted light beam experiences a polarization conversion after composition with the two beams. Note that the preset offset d is used to obtain a desired phase delay between the two subunits.

Further, by introducing the interval modulation layer composed of periodic arranged phase change materials between the antenna layer and the homogeneous substrate, we can achieve active control of the scattering properties. We utilize silicon and GST beneath subunit 1 and subunit 2, respectively, as shown in Fig. 2(b). GST possesses a transparency window located from 2.8μm to 5.5μm, where the absorption of both amorphous and crystalline phase are negligible [38]. Therefore, we choose the working wavelength at 4μm. At this wavelength, the refractive index of GST can change from n_a ≈3.58 + 0.01i to n_c ≈6.5 + 0.06i by the spatial averaging effects of the mixture amorphous state and crystalline state when heated at about 160° with controllable amount [39]. The process can be reversed by cooling and using proper optical and electrical methods [32]. While the silicon properties sustain nearly stable for the thermal temperature change. It is well known that the resonance of plasmonic structures is very sensitive to the surrounding dielectric environment. By actively controlling the optical property of GST while keeping the silicon section unchanged, one can cause a redshift or blueshift of the antenna resonance in subunit 2, and effectively change the accumulated phase among the multi-layer system. In general, such effect can affect the scattering amplitude and phase simultaneously. Nevertheless, on account of the double spectral resonances of the V shape antenna, the amplitude can undergo small fluctuation with such dielectric environment changing. In contrast, the scattering property from subunit 1 keeps unchanged. Consequently, we can manipulate the phase delay between the two waves while maintain the scattering amplitude still uniform to achieve active control of polarization conversion of the transmitted light.

3. Simulations and discussion

For the proof of the concept, we carry out full wave numerical simulations by using the finite differential time domain (FDTD) method. Firstly, we design the geometric parameters of gold V-shape antennas on a homogenous silicon substrate. The refractive index of the silicon substrate is set as n = 3.4. The V-shape antennas have a fixed width w = 120nm and thickness of 50nm, with a square lattice set as 937.5nm, by considering the possible fabrication capabilities. For simplicity of simulation, the orientation angle of all antennas are fixed as β = 45°. Hence, when illuminating with a x-polarized wave with α = 90° from the substrate, the (2β−α)-polarized scattering component is exactly along the y-axis. The permittivity of gold is described by the Drude model $\epsilon (\omega )={\epsilon }_{\infty }-{\omega }_p^2/({\omega }^2+i\gamma \omega )$, with plasma frequency ω_p = 1.366 × 10¹⁶ rad/s and damping frequency γ = 1.2 × 10¹⁴ rad/s. Calculated amplitude and phase of the (2β−α)-polarized scattering component with various arm lengths L and opening angles θ are shown in Figs. 3(a) and (b). We choose four antenna parameters as listed in Table. 1 to satisfy that |S_i − A_i| is approximately equal and the phase difference of (S_i+1−A_i+1) and (S_i−A_i) is 2π/8 = 45°. The last four antennas in a subunit can be obtained by rotating the first four antennas by 90° to achieve negative phase response with respective to the first four antennas, Fig. 2(b). With such arrangement, the (2β−α)-polarized scattering component of a subunit propagates along the anomalous refraction direction θ_t = arcsin(λ/D) ≈32°.

 

Fig. 3 Calculated scattering amplitude (a) and phase shift (b) of a single antenna with various arm lengths L and opening angles θ on a homogeneous silicon substrate. The inset in (a) shows the schematic of the simulated V-shape antenna with β = 45°. The four circles in (a) and (b) indicate the value of L and θ used for further simulation.

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To verify the tunable phase-delay effect by manipulating the refractive index of the GST layer, we carry out numerical simulation to demonstrate the amplitude and phase modulation properties of a single V-shape antenna in subunit 2. The schematic structure is shown in the inset of Fig. 4(a). The structural parameters of each V-shape antenna can be found in Table 1 and the orientation angle of all antennas are fixed as β_i = 45° in the simulation. The antennas are placed on top of a 500nm-thick GST layer. The thickness of GST layer is delicately chosen to induce sufficient phase shift but limited resonance shift to maintain the scattering efficiency. The loss of the modulation layer and substrate are ignored in the simulation. We proved in the following that tiny loss of GST within the limited thickness has negligible effects towards the transmitted polarization states. It is noteworthy that the refractive index is set from 3 to 4.5 for the conceptual demonstration of our scheme.

 

Fig. 4 Full-wave simulation for each single V-shape antenna positioned above GST and substrate layer. (a) Amplitude distribution and (b) phase distribution of the (S)_i − (A)_i component by changing the refractive index of GST from 3 to 4.5. The antenna 9 is the same as antenna 1. The inset in (a) shows the simulation structure.

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Table 1. Structure parameter of antennas in a subunit

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The scattering properties of such V-shape antennas by changing the refractive index of the GST interval modulation layer is elucidated in Figs. 4(a) and (b). The scattering amplitude of each antenna (i = 1, 2…8) almost keeps the same with small fluctuation as the refractive index of the GST changes from 3 to 4.5. The reason is that the antennas possess a broad resonance bandwidth with the combination of the symmetric and antisymmetric eigenmodes so that the amplitude is not very sensitive to the resonance shift. However, antenna 4 and antenna 8 have an opening angle θ = 180°, as a result, the amplitude modulation from the two antennas degenerate because such single-arm antennas are more sensitive to the surrounding dielectric environment. It should be noticed that the small fluctuation of scattering amplitude will not cause remarkable efficiency degeneration. The phase responses for each i^th antenna are quite smooth and linear with the gradual changes of refractive index, as shown in Fig. 4(b). As a result, the subunit 2 containing eight antennas will simultaneously sustain the consistent amplitude and possess an initial phase increment added onto the constant phase gradient with the growing of refractive index of GST. Such phase gradient can bend the light trajectory to the anomalous refraction order with θ_t = arcsin(λ/D). Note that by increasing the refractive index of GST larger than 4.5, the scattering amplitude from each antenna would undergo significant decrease and cannot satisfy the approximately equal condition anymore. Therefore, the GST layer can induces the desired active phase control at the refractive index range from 3 to 4.5.

For further demonstration, we implement simulations by integrating the two subunits with both GST and silicon in an interval modulation layer, as shown in Fig. 2(b), with the incident polarization angle α = 45°. The orientation angles of the antennas in subunit 1 and subunit 2 are β₁ = 67.5° and β₂ = 112.5°, respectively. The offset between the two subunits is set as d = D/4. Notably, there is negligible coupling between the two neighboring subunits for generating the required phase gradient as well as the required amplitude. Each single antenna can be viewed as an independent pixel. With the increase of refractive index of GST, the scattering properties of subunit 1 with the silicon strip beneath is fixed, meanwhile the anomalous beam from subunit 2 experience a gradual increase of phase delay. As a result, the polarization state of the coherently interfered transmitted beam can be controlled. The degree of circular polarization (DOCP) of the output beam with the increase of refractive index is shown in Fig. 5(a). Here the DOCP is defined as |I_LCP - I_RCP| / |I_LCP + I_RCP|, where I_LCP and I_RCP denote the intensity of left and right-handedness circular polarization component of the anomalous beam, respectively. The DOCP reaches the maximum value of 99.9% at n ≈3.4 and then drops to the minimum 0.01% at n ≈4.2. That is, a purely circularly polarized beam and purely linearly polarized beam can be achieved at these two refractive indices. In addition, we calculated the normalized intensity of the output anomalous beam, Fig. 5(a). The scattering intensity reaches a peak value at n ≈3.75 because of the small variation of scattering amplitude of each antenna. The corresponding polarization ellipses are plotted in Fig. 5(b) at five refractive indices n = 3, 3.4, 4, 4.2, and 4.5 of GST. As discussed above, when the refractive index of GST is equal to silicon (n = 3.4), such a metasurface functions as a quarter-wave plate and the output anomalous beam is right circularly polarized. The polarization state gradually turns to linear polarization as the refractive index of GST gradually approach n = 4.2. All the intermediate elliptical polarization states can be reached. Even take the loss of GST into consideration by setting Im(n) ≈0.03i, there is only negligible trajectory shift of the polarization on the Poincaré sphere. Therefore, the lossless assumption of GST is suitable to guide design of such active wave plate and will reveal the underlying physics faithfully.

 

Fig. 5 Calculated output polarization state and intensity. (a) Calculated degree of circular polarization and intensity of the anomalous beam as a function of refractive index under α = 45°. (b) The polarization ellipse for the anomalous beam at n = 3, 3.4, 4, 4.2 and 4.5, respectively. The arrows denote the handedness of the elliptical beam. Ex and Ey denote the amplitude of electric field in x’-y’ coordinate in Fig. 2(b). (c) Polarization state of the anomalous beam along the main axis of Poincaré sphere under α = 45°.

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The electric field of the output anomalous beam can be expressed as$\text{J}={[\begin{array}{cc}{E}_x& E_y{e}^{-j\delta }\end{array}]}^T$in x’-y’ coordinate, Fig. 2(b), where δ is the phase difference between E_x and E_y. In our scheme, we have E_x ≈E_y. Note that δ_{n = 3} < π/2 and δ_{n = 4,4.2,4.5} > π/2, which can determine the orientation of the polarization ellipse. The corresponding Stokes parameters of these polarization states along the main axis of Poincaré sphere under normally incidence with α = 45° linear polarization are shown in Fig. 5(c). The Stokes parameters are defined as

It is worth mentioning that such metasurface is able to work at a broad bandwidth from 4μm to 5μm. We found that in this wavelength range, all the selected V-shape antennas possess relatively flat resonances and the amplitude fluctuations are within the tolerance. Meanwhile the phase modulations are quite linear with the changement of refractive index at this bandwidth. It is noteworthy that for a larger incident wavelength, the accumulation of optical path will be smaller as the refractive index of GST increase, leading to a relatively narrower tunable ellipticity range. From simulations we proved that the ellipticity χ ranges from 0.92 to −0.16 at 4.5μm, and 0.89 to −0.07 at 5μm. Meanwhile ψ switches from 152° to 50° at 4.5μm, and 153° to 53° at 5μm. While for the incident wavelength outside this bandwidth, the amplitude fluctuation deteriorate away from the tolerance scope, which will result in imperfect modulation of ellipticity.

Furthermore, we have numerically verified that the full ellipticity tunability of the output anomalous beam is independent of the incident linear polarization orientation, as shown in Fig. 6. Three linear incident polarization angles α = 0°, 45°, and 90° with a GST refractive index increment of 0.25 are numerically simulated and the Stoke’ parameters of the anomalous beam are plotted on the Poincaré sphere. The azimuthal angle of polarization state on the Poincaré sphere is defined as φ = 2ψ. The rotation of incident polarization causes the rotation of the polarization ellipse, as a result, leading to azimuthal rotation on the surface of Poincaré sphere. The azimuth angle of the polarization states on the Poincaré sphere turns from 0° to 180° as α changes from 0° to 90°, as shown in Fig. 6. The simulation results are in good consistence with such tendency except that the case when the incident light is polarized along α = 90°. The deviation of the polarization ellipse orientation is approximately 7.5°. It can be explained by the near-field coupling of the localized surface plasmon resonance when illuminating with linear polarization parallel to the periodic arrangement of the interval modulation layer. Such tiny disturbance can cause the fluctuation of scattering amplitude from subunit 1 and subunit 2, resulting in the rotation of the polarization ellipses. Nevertheless, the entire behavior of such active metasurface possess very flexible tunability of the transmitted ellipticity.

 

Fig. 6 The polarization state of anomalous beam along the main axis of Poincaré sphere under α = 0°, 45°, and 90°.

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4. Conclusions

In summary, we have reported a novel active plasmonic metasurface which can gradually tune the ellipticity of light and reach all intermediate elliptical polarization states in the MIR region. Our approach involves a periodically arranged phase change material GST as a dielectric reconfigurable interval modulation layer to achieve dynamical control of the scattering phase delay without any mechanical movement. The broad resonance of the combination of symmetric and anti-symmetric modes plays a key role in our approach. The inexpensive, non-volatile phase change material GST is very well suitable for flexible functional applications due to its large amounts of reversibility cycles and high-speed, continuous refractive index control with remarkable dielectric adjustable range. Therefore, our work may open up a potential avenue for ultrathin, compact and reversible polarization manipulation and can be extremely beneficial for applications such as polarization sensitive detection or thermal-imaging.