The fundamental attributes of phase and polarization in optical fields have demonstrated their remarkable significance in light manipulation, including phase-modulated vortex beams^[1] and polarization-controlled vector beams^[2,3]. Building on the rich polarization diversity of vector beams, vector vortex beams (VVBs) integrate an anisotropic vortex polarization distribution and a helical phase, carrying orbital angular momentum (OAM)^[4,5]. Consequently, vector beams have found widespread applications in optical trapping^[6], ultra-high-capacity optical communication^[7], high-resolution imaging^[8], and various other fields. To date, researchers have proposed numerous methods for generating vector beams, such as using spatial light modulators^[9] and Fourier transform lenses^[2]. However, these traditional methods typically involve bulky optical components, thereby increasing costs and complexity.

In recent years, two-dimensional (2D) subwavelength structures, known as metasurfaces, have attracted widespread attention. Metasurfaces offer high degrees of freedom in controlling the amplitude, phase, and polarization of incident light, providing advantages for miniaturization and integration of optical devices^[10-14]. Consequently, optical metasurfaces have been explored for the realization of novel and cost-effective vector beam generators^[15-24]. However, metasurface-empowered vector beam generators remain static and can only generate one pre-designed structured beam^[25-27].

In our study, a tunable metasurface based on the novel phase-change material Ge2Sb2Se4Te1 (GSST) has been designed to generate tunable vector beams in the mid-infrared wavelength range, owing to the excellent properties of GSST. GSST demonstrates remarkable broadband optical transparency and an exceptionally large figure-of-merit across nearly the entire infrared spectrum. This establishes GSST as a pioneering class of optical phase-change materials, wherein the phase transition induces refractive index modulation without incurring any loss penalty, which can be precisely controlled by the thermal, optical, and electrical stimuli^[28,29]. At the design wavelength of 8.55 µm, the GSST unit structure functions as a quarter-wave plate (QWP) and a half-wave plate (HWP) in response to the transit between the amorphous and crystalline states. When GSST is in the amorphous state, left circularly polarized (LCP) and right circularly polarized (RCP) excitations generate first-order radially polarized (RP) and azimuthally polarized (AP) beams, respectively. Upon the transition of GSST to the crystalline state, the incidences of x- and y-polarized lights on the same metasurface produces second-order AP and RP beams, respectively. This design offers a novel approach for generating dynamic vector beams in the mid-infrared wavelength range by leveraging the tunability of GSST between its amorphous and crystalline states, demonstrating the potential to dynamically manipulate the polarization state and topological charge of structured light. This innovative method contributes to the broader field of structured light manipulation, offering extensive control over the polarization and phase properties of light and opening new frontiers for practical applications involving vector beams and VVBs.

Figures 1(a) and 1(b) depict the GSST unit structure with a rectangular cross-section standing on a barium fluoride (BaF2) substrate, whose refractive index is assumed to be 1.4^[30]. The unit structure has a periodicity of P=3.5μm in both x and y directions, while the GSST block has a height of h=3.78μm, a length of a=2.3μm, and a width of b=1.08μm. The relative permittivities of GSST in its amorphous and crystalline states are set as 11 and 22, respectively, at the wavelength of 8.55 µm^[31]. Meanwhile, the unit structure is rotated on the x−y plane with an angle of θ [Fig. 1(c)]. By appropriately designing the dimensions and orientation of the GSST unit structure, complete and distinct polarization modulation can be achieved in both amorphous and crystalline states, thereby resulting in tunable vector beam generation, as illustrated in Figs. 1(d)–1(g). In the amorphous state, the GSST meta-atoms act as QWPs and produce VVBs under the LCP excitation [Fig. 1(d)], which can be decomposed into the LCP component without OAM and the RCP component with OAM (l=2). Conversely, VVBs can be created when RCP light is incident on the metasurface, where the LCP and RCP components possess the topological charges of l=−2 and 0 [Fig. 1(e)]. When GSST transitions to the crystalline state, the GSST unit structures function as HWPs, which can generate second-order vector beams under linearly polarized excitations. From Figs. 1(f) and 1(g), it can be observed that the second-order AP and RP beams are generated under x- and y-excitations. In this scenario, both AP and RP beams can be represented as different combinations of LCP and RCP vortex beams with topological charges of l=±2.

The GSST unit structure is designed by sweeping the lateral dimensions in the wavelength range of 8 to 9 µm to fulfill the requirement of a QWP and an HWP when GSST transits from the amorphous state to the crystalline state. Figures 2(a) and 2(b) illustrate the transmission amplitudes and phases when GSST is in the amorphous state. At a wavelength of 8.55 µm, both transmission amplitudes, txx and tyy, exceed 0.9 and are nearly equal, while the phase difference Δδ=δxx−δyy approximates π/2, indicating the QWP functionality.

To verify the performance of the GSST QWP, we calculate the degree of linear polarization (DoLP) and angle of linear polarization (AoLP) as a function of the rotation at λ=8.55μm^[32], as shown in Figs. 2(c) and 2(d). When the rotation angle θ increases from 0° to 90°, AoLP follows a linear distribution of θ−45° under LCP incidence while a linear distribution of θ+45° under RCP incidence. Moreover, the DoLPs remain close to 1 under both LCP and RCP incidences, consistent with the theoretical prediction of an ideal QWP that effectively transforms circularly polarized waves into linearly polarized waves regardless of the rotation [Figs. 2(e) and 2(f)]. For instance, the transmitted linearly polarized light has an AoLP of −45° (45°) under the LCP (RCP) excitation when the rotation angle θ is 0°. When the rotation angle changes 45°, the polarization direction of the transmitted linearly polarized light rotates by an additional angle of 45° with respect to the rotation angle, precisely corresponding to the AoLP in Figs. 2(c) and 2(d). Therefore, the transmitted linearly polarized light can achieve an arbitrary polarization angle from 0° to 360° once the GSST unit structure is properly rotated.

When GSST transitions from the amorphous state to the crystalline state, the optimized unit structure acts as an HWP with transmission amplitudes txx and tyy reaching around 0.95 and the phase difference Δδ being ∼π at the targeted wavelength of 8.55 µm, as illustrated in Figs. 3(a) and 3(b). Figures 3(c) and 3(d) illustrate the DoLPs and degrees of circular polarization (DoCPs) of the transmitted beam under circularly polarized light incidence at the wavelength of 8.55 µm as a function of the rotation angle θ. As θ rotates from 0° to 90° for LCP and RCP incidences, the DoCPs of the transmitted beam are essentially +1 and −1, respectively, while DoLPs are consistently smaller than 0.1, indicating well-defined RCP and LCP beams as the output [Figs. 3(e) and 3(f)]. As such, the GSST unit structure can switch between a QWP and an HWP at the target wavelength of 8.55 µm, as GSST undergoes a transit between the amorphous and crystalline states.

Capitalizing on the GSST dynamic wave plate, it becomes possible to achieve tunable vector beams by arranging the elements with proper rotation angles. For the unit cell with an orientation angle of θ, the transmission Jones matrix can be expressed as M=|t|(cosθ−sinθsinθcosθ)(eiϕx00eiϕy)(cosθsinθ−sinθcosθ),(1)where ϕx and ϕy denote the initial phases of the transmitted light for x- and y-polarized incidences, respectively, and |t| represents the transmission amplitude. In our design, the transmission amplitudes for x- and y-polarizations are nearly equal.

When GSST is in the amorphous state, our designed unit cell functions as a QWP with ϕy=ϕx+π2, and its Jones matrix is written as Ma=|t|eiϕx[isin2θ+cos2θ(1−i)sinθcosθ(1−i)sinθcosθsin2θ+icos2θ].(2)

If the incident light is LCP with the electric field represented as Ein=12[1i], the transmitted beam becomes linearly polarized, and its electric field can be expressed as Eout=MaEin=|t|eiϕxeiθ[cos(θ−π4)sin(θ−π4)].(3)

If we set θ−π4 equal to the azimuthal angle φ, the transmitted beam can be expressed as Eout=|t|ei(ϕx+π4)eiφ[cosφsinφ].(4)

As such, the transmitted beam becomes a VVB, which can also be written as the superposition of LCP and RCP components carrying different topological charges: Eout=12|t|ei(ϕx+π4)[(1i)+ei2φ(1−i)].(5)

If the incident light is RCP with Ein=12[1−i], the transmitted beam is also a VVB: Eout=MaEin=|t|ei(ϕx−π4)e−iφ[−sinφcosφ].(6)

Similarly, the above expression can be decomposed into LCP light with OAM (l=−2) and RCP light without OAM: Eout=12i|t|ei(ϕx−π4)[−e−i2φ(1i)+(1−i)].(7)

When GSST transits to the crystalline state, our designed unit cell changes to a HWP with ϕy=ϕx+π: Mc=|t|eiϕx[cos2θsin2θsin2θ−cos2θ].(8)

Since we only change the state of GSST without altering the rotation angle of the unit structure, the relationship between the rotation angle θ and the azimuthal angle φ remains θ−π4=φ. In this case, when an x-polarized light is incident, it will generate a second-order AP beam, and the transmitted beam can be expressed as Eout=McEin=|t|eiϕx[−sin2φcos2φ].(9)

If we express the second-order AP beam as the superposition of two circularly polarized beams, it can be written as Eout=12i|t|eiϕx[−e−i2φ(1i)+ei2φ(1−i)].(10)

In other words, the transmitted beam can be decomposed into the superposition of LCP and RCP vortex beams with topological charges of l=±2, respectively. Similarly, when the y-polarized light is incident, a second-order RP beam is generated: Eout=|t|eiϕx[cos2φsin2φ].(11)

The equation above can be expressed as the superposition of LCP and RCP vortex beams with topological charges l=±2: Eout=12|t|eiϕx[e−i2φ(1i)+ei2φ(1−i)].(12)

We conducted numerical simulations based on the finite-difference time-domain (FDTD) method to validate the feasibility of the designed vector beam generator. In the simulation, a metasurface array with 20×20 units was calculated, where each unit structure rotates at an angle of θ=π4+φ. Additionally, perfect matching layers were applied in the x, y, and z directions. Two Gaussian beams with orthogonal polarizations, phase retardation of π/2, and beam waists of 40 µm were incident with the circularly polarized excitation. A 2D monitor was placed in the x–y plane to observe the near-field electric fields. Figure 4 illustrates the simulated field intensity distributions and electric field vectors of the VVBs, along with the far-field intensity and phase distributions of the LCP and RCP components, when GSST is in an amorphous state under circularly polarized incidence at a target wavelength of 8.55 µm. Figures 4(a), 4(b), 4(g), and 4(h) present the intensity distributions and electric field vectors of the VVBs. It is observable that the intensity distributions of the beams exhibit a ring-like pattern, and the electric field vectors correspond to the beams carrying an optical vortex with a helical phase factor of e±iφ. As evident from Figs. 4(c) and 4(d), under LCP excitation, the intensity distribution of the LCP component follows a Gaussian pattern, with a constant phase. Figures 4(e) and 4(f) illustrate that the intensity distribution of the RCP component is toroidal in shape, exhibiting a 4π helical phase change. The case of RCP light incidence is analogous, as shown in Figs. 4(i)–4(l), with the LCP component exhibiting a toroidal intensity distribution and a helical 4π in the reverse direction. Therefore, the cross-polarized transmitted waves exhibit excellent vortex properties, carrying OAM with topological charges of l=±2 under both LCP and RCP incidences, while the co-polarized components display typical Gaussian distributions without any vortex properties. Impressively high mode purity values of 0.92 and 0.93 are obtained for the cross-polarized components with topological charges of l=±2, while for the co-polarized components carrying no OAM, the mode purity values are approximately 0.99, indicating a high degree of purity in the generated VVBs.

Having examined the transmission characteristics of the metasurface with GSST in the amorphous state, we now investigate the case when GSST is in the crystalline state. At the same target wavelength of 8.55 µm, x- and y-polarized lights are normally incident on the GSST metasurface. Figure 5 shows the simulated field intensity distributions and electric field vectors of the second-order vector beams, along with the far-field intensity and phase distributions of the transmitted LCP and RCP lights in the far field. Figures 5 (a), 5(b), 5(g), and 5(h), respectively, illustrate the electric field intensity profiles and electric field vector orientations for the second-order AP and RP beams. The ring-like pattern is evident in the intensity distribution of both types of beams, with the electric field vectors aligning consistently with the characteristic polarization structures of second-order AP and RP beams. As seen in Figs. 5(c), 5(d), 5(i), and 5(j), the intensity distributions of the transmitted circularly polarized components form toroidal shapes under both x- and y-polarized incidences, indicating that the outgoing circularly polarized components are vortex beams. By examining the phase distributions [Figs. 5(e), 5(f), 5(k), and 5(l)], it is evident that the phase of the transmitted LCP light undergoes counterclockwise 4π helical phase change, while the phase of the transmitted RCP light undergoes clockwise 4π helical phase change. This implies that, when linearly polarized light is incident on the meta-surface, the transmitted beam is composed of an LCP vortex beam with a topological charge of −2 and an RCP vortex beam with a topological charge of 2. In the crystalline state, mode purity values of LCP and RCP vortex beams obtained under x-polarized incidence are 0.70 and 0.71, respectively. When y-polarized light is incident, the purity values of LCP and RCP vortex beams become 0.85 and 0.73, respectively.

In conclusion, we have explored the design of an anisotropic phase-change unit cell with tunable phase retardation at the wavelength of 8.55 µm when GSST transits between two different phase states, specifically targeting the transit between a QWP and an HWP. By rotating the GSST unit structure with a defined orientation angle θ, we have realized a transmissive metasurface capable of generating switchable vector beams. Specifically, VVBs are generated under LCP and RCP incidences when GSST is in the amorphous state, which can be decomposed into co-polarized components without OAM and cross-polarized OAM waves with topological charges of l=±2. In the crystalline state, the second-order AP and RP beams are under x- and y-polarized excitations, which can be decomposed into RCP and LCP vortex beams with topological charges of l=±2, respectively. Our work introduces a novel phase-change metasurface that marks a significant advance in the generation of dynamic structured light beams. The implications of this technology extend far beyond its immediate applications, opening new avenues in integrated polarization optics and potentially revolutionizing fields reliant on precise light manipulation.