Design of Multifunctional Polarization Waveplates Based on Thermal Phase-Change Metasurfaces

Abstract

The switching function of traditional waveplates necessitates mechanical replacement or the superimposition of multiple waveplates, which gives rise to a complex system and a large volume. We have devised a multifunctional micro-waveplate based on the COMSOL simulation platform (v5.6), which concurrently integrates the compact nature of metasurfaces and the dynamic regulatory features of phase-change materials. When the phase-change material is in the crystalline phase, the metasurface possesses the functionality of a half-waveplate (HWP) and is capable of performing chirality inversion of circularly polarized light within the wavelength range of 1.45 μm to 1.52 μm and 1.56 μm to 1.61 μm. When the phase-change material is in the amorphous phase, the metasurface serves as a quarter-waveplate (QWP) and can achieve the conversion between linear and circular polarization through a 90° phase delay. The phase-change metasurface breaks through the constraint of fixed functions of traditional optical waveplates, facilitating the development of optical systems towards miniaturization, intelligence, and low power consumption and providing a crucial technical route for the next generation of photonic integration and dynamic optical applications.

1. Introduction

Traditional waveplates (such as quartz, mica, or polymer waveplates) are fundamental polarization control components in optical systems [1]. Through the thickness design of birefringent materials [2,3] (such as quartz), the functional regions of waveplates can cover the ultraviolet to infrared bands. Taking reflective waveplates as an example, in the case of 45-degree linearly polarized light incidence, the amplitudes of the projected components of the reflected light in the x-axis and y-axis directions will be equal, and the phase difference will typically be 90 degrees (corresponding to the QWP [4]) and 180 degrees (corresponding to the HWP [5]). Traditional waveplates possess advantages such as stable optical performance, high phase retardation precision, and low influence from the environment (temperature, humidity) [6]. Nevertheless, they also encounter drawbacks such as fixed functions, volume and weight limitations, and low design freedom. In addition, the photoelastic modulator (PEM) is also a powerful tool for achieving phase delay, and it can function over a wide range of wavelengths. However, it cannot be ignored that it still faces the predicament of being expensive at present.

Metasurfaces [7,8,9,10,11] are two-dimensional planar optical devices composed of subwavelength structures (such as nanoantennas and resonators), capable of flexibly manipulating the amplitude, phase, polarization, and other properties of light waves. Through ultrathin structures, multifunctional integration, and low-cost manufacturing, metasurface technology has significantly improved the performance and application range of optical waveplates. Over the past decade or so, a large number of outstanding metasurface structure designs have emerged, with a focus on optimizing the efficiency [12,13,14,15,16] and bandwidth [17,18,19,20,21] of compact optical waveplates. Phase-change metasurfaces [22,23] are intelligent optical devices that combine phase-change materials (PCMs) and metasurfaces and can dynamically regulate the multi-dimensional characteristics of light waves through external stimuli (such as heat [24], light [25], and electricity [26]). By designing waveplates using phase-change metasurfaces, one can not only possess the ultrathin structural characteristics of metasurfaces but also overcome the defect of the single functionality of traditional waveplates.

In this paper, we have designed an optical metasurface based on the dynamic regulation property of the phase-change material Sb₂Se₃ [27,28]. The activation and quenching of the phase-change material are proposed to be accomplished by employing thermoelectric cooler (TEC) technology [29]. When Sb₂Se₃ is in the amorphous state, the metasurface possesses the functionality of a quarter-waveplate, which can transform linearly polarized light into circularly polarized light. When Sb₂Se₃ is in the crystalline state, the metasurface presents the characteristic of a half-waveplate, allowing for the rotation of the polarization direction of linearly polarized light or the chirality inversion of circularly polarized light. Furthermore, we have analyzed the attenuation effect of potential process errors on the performance of the metasurface.

2. Materials and Methods

Sb₂Se₃ is a typical phase-change material, presenting significant disparities in optical properties (such as refractive index, extinction coefficient, band gap, etc.) between the amorphous (a-Sb₂Se₃) and crystalline (c-Sb₂Se₃) states. Figure 1a depicts the functional diagram of the phase-change metasurface based on Sb₂Se₃. The metasurface is composed of a TEC, a metal reflector, and a periodic array of Sb₂Se₃ cubic cells from bottom to top. Figure 1b shows the three-dimensional structure of the TEC, which mainly comprises N-type and P-type semiconductor thermocouple pairs (BiTe), metal current collectors, a ceramic substrate, and electrodes. Based on the Peltier effect [30,31], energy transfer takes place at the junction of N-type and P-type semiconductors. When a direct current passes through the TEC in the forward direction, it absorbs heat (cooling effect), while in the reverse direction, the TEC releases heat (heating effect), thereby achieving active heat transfer from the cold end to the hot end, resulting in cooling or heating outcomes. When electrons flow from the P-type to the N-type semiconductor, the top surface of the TEC is the cold side, and Sb₂Se₃ is in the amorphous state. The metasurface demonstrates the functionality of a quarter-waveplate, which can convert linearly polarized light into circularly polarized light. When the current reverses, the top surface of the TEC becomes the hot side, and the metasurface with crystalline Sb₂Se₃ behaves as a half-waveplate. Figure 1c,d describe the material attributes and structural dimensions of the metasurface. The optical refractive index parameters of Sb₂Se₃ in the two distinct states are derived from Reference [32]. The refractive index data of the gold are sourced from Reference [33]. The optical model for calculating the efficiency and phase of the metasurface’s reflection spectrum is established on the COMSOL platform. Periodic boundary conditions are applied to the four lateral interfaces to converge the computational domain, and perfect matching layers are added to the top and bottom interfaces. The phase and amplitude information of the incident and reflected light are obtained through port modes. The thickness h2 of the gold reflector is significantly greater than the skin depth of the gold (~20 nm), ensuring the absence of photons in the transmission domain. Furthermore, only a gold film with a thickness of 600 nm needs to be grown on the ceramic substrate of the TEC, followed by physical deposition of an Sb₂Se₃ film. After the electron beam lithography process for patterning the electron glue and etching, the metasurface can be fabricated.

3. Results

Figure 2a presents the reflection spectra and phase-difference spectra of the amorphous phase-change metasurface within the 1.4 μm to 1.65 μm wavelength range. The light blue line corresponds to the reflection spectrum of the TM mode, featuring only one reflection valley, a, with typical asymmetry characteristics. With the exception of the redshift of the central wavelength corresponding to reflection valley b, the spectral profile of the reflection spectrum in the TE mode is analogous to that of the TM mode. Additionally, disregarding the effect of the reflection valleys, it can be discerned that the average reflection efficiency exceeds 85%, and the efficiencies of the TM and TE modes are proximate. The red line represents the phase difference, whose graph exhibits irregular oscillations. The purple region encompasses the phase space ranging from −100 degrees to −80 degrees. The phase-difference spectrum and the purple region have three overlapping locations. The first overlapping band contains reflection valley a, while the latter two overlapping bands lack reflection valleys. Consequently, in accordance with the definition of a quarter-waveplate, the phase-change metasurface can manifest the functionality of a reflective QWP in the latter two overlapping bands. Figure 2b displays the reflection spectra and phase-difference spectra of the metasurface in the crystalline state. The reflection spectrum of the TM mode has two reflection valleys, and the TE mode exhibits two reflection peaks. The average reflection rates of the TE and TM modes are similar, and the oscillation amplitudes are not significant. The phase-difference spectrum also has extensive overlap with the phase space from −170 degrees to −190 degrees, signifying that within the wavelength bands represented by these overlapping regions, the phase metasurface assumes the function of a half-waveplate.

In addition to employing the conventional reflection spectra and phase-difference spectra to evaluate the quality of waveplates, their polarization control characteristics can also be exploited to measure the function of waveplates. A quarter-waveplate possesses a phase delay of π/2 (an optical path difference of 1/4 wavelength), and thereby its main function is to convert linearly polarized light into circularly polarized light (or vice versa). Figure 3a depicts the polarization conversion function of the amorphous metasurface. Here, $LTC=\sqrt{{\left(t_1-n_1\right)}^2+{\left(t_2-n_2\right)}^2+{\left(t_3-n_3\right)}^2+{\left(t_4-n_4\right)}^2}$, where ($t_1,t_2,t_3,t_4$) are the theoretical Stokes parameters of the reflected light, which are (1, 0, 0, 1) for RCP and (1, 0, 0, −1) for LCP when the incident light is 45° linearly polarized and −45° linearly polarized, respectively. ($n_1,n_2,n_3,n_4$) are the simulated Stokes parameters directly obtained from COMSOL 5.6. The smaller the value of LTC, the better the conversion from linearly polarized light to circularly polarized light. As presented in Figure 3a, the LTC spectra for the 45° linearly polarized light and −45° linearly polarized light are consistent. The values of LTC are less than 0.25 near the wavelengths of 1.5 μm and 1.58 μm, corresponding to the light blue rectangles. Figure 3b shows the polarization conversion function of the metasurface under the incidence of circularly polarized light. The definition of CTL here is the same as that in Figure 3a, but it quantitatively assesses the ability to convert circularly polarized light into linearly polarized light. The blue rectangles at the wavelengths of 1.5 μm and 1.58 μm also indicate that the CTL values within this band are less than 0.25. A half-waveplate (λ/2 waveplate) can introduce an additional π phase delay (an optical path difference of half a wavelength), which can alter the polarization direction of linearly polarized light or reverse the chirality (left-handed/right-handed) of circularly polarized light. Figure 3c,d present the cross-polarization and co-polarization efficiencies of the metasurface. Taking “Co-P(LCP)” and “Cross-P(LCP)” in the legend as examples, the LCP in parentheses indicates that the incident light on the metasurface is LCP. The value of Co-P(LCP) is the intensity of the LCP component in the reflected light that has the same polarization characteristics as the incident light (LCP) divided by the total intensity of the reflected light. The value of Cross-P(LCP) is the intensity of the RCP component in the reflected light that is orthogonal to the polarization of the incident light (LCP) divided by the total intensity of the reflected light. As shown in Figure 3c, for the linearly polarized incident light, the cross-polarization efficiency is greater than the co-polarization efficiency, and within the bandwidth represented by the red rectangle, the cross-polarization efficiency is greater than 90%. Figure 3d corresponds to the case of the circularly polarized incident light, presenting a similar situation as in Figure 3c, indicating that the metasurface possesses the characteristics of a half-waveplate. Additionally, the intersection of the light blue rectangle and the light red rectangle represents the actual bandwidth of the phase metasurface, which are the wavelengths of 1.485 μm to 1.505 μm and 1.57 μm to 1.59 μm, respectively.

3.1. Sb₂Se₃ in Low-Temperature (LT) (Amorphous) Phase

When the metasurface is in the amorphous state, the reflection spectra of the TM and TE modes present a typical asymmetry phenomenon. This asymmetric spectral line typically corresponds to Fano resonance, as depicted in Figure 4a. Fano resonance [34] is a quantum interference phenomenon induced by the interference between the discrete state (discrete energy level) and the continuous state (continuous energy level). Distinct from Lorentz (symmetric) resonance, Fano resonance exhibits a shape with one side being steep and the other side being gently sloped. The line shape of Fano resonance can be described by the Fano formula:

$${\sigma }_{\left(E\right)}={\sigma }_0{\displaystyle \frac{{\left(q+ϵ\right)}^2}{1+{ϵ}^2}}+{\sigma }_b$$

(1)

$$ϵ={\displaystyle \frac{E-E_r}{\mathsf{\Gamma }/2}}$$

(2)

Here, ${\sigma }_{\left(E\right)}$ represents the scattering or absorption cross-section, $E_r$ is the resonance energy, ${\sigma }_0$ is the intensity scale of the discrete state’s effect, Γ is the linewidth, q is the Fano parameter, ${\sigma }_b$ represents the contribution of the non-resonant background, and E is the energy of the incident free photon. Through formula fitting, it can be discovered that when (${\sigma }_0,$ ${\sigma }_b$, $E_r$, $\mathsf{\Gamma }$, $q$) = (0.4, 0.54, 1.45, 0.007, −0.3), the reflection spectrum of the TM mode can match Formulas (1) and (2). When (${\sigma }_0,$ ${\sigma }_b$, $E_r$, $\mathsf{\Gamma }$, $q$) = (0.23, 0.67, 1.5, 0.013, −0.51), the reflection spectrum of the TE mode directly exported by the COMSOL software can be reconstructed by the Fano formula. The phenomenon that the reflection curve directly exported from the port of COMSOL perfectly coincides with Formulas (1) and (2) indicates that the optical resonance characteristics of the amorphous metasurface might be manipulated by Fano resonance. Figure 4b shows the XZ cross-sectional view of the magnetic field intensity of the phase-change metasurface in TM mode. There exists a typical magnetic field localization phenomenon within the phase-change material Sb₂Se₃, which might correspond to a special dielectric waveguide mode. The dielectric waveguide is composed of an air–Sb₂Se₃–air ternary planar waveguide, and its energy is confined within the high-refractive-index material, which is highly similar to the waveguide mode of the typical FP laser. Furthermore, at the boundary between the metal backplate and the phase-change material Sb₂Se₃, there seemingly exists a typical characteristic of the Surface Plasmon Polariton (SPP) [35] mode. This evanescent wave electric field can penetrate the metal and decays exponentially in the direction perpendicular to the interface. Figure 4c shows the YZ cross-sectional view of the magnetic field intensity of the phase-change metasurface in TE mode, and its resonance characteristics are similar to those in Figure 4b. Based on the above results, we conjecture that the spectral lines of the reflection valleys are generated by Fano resonance, and Fano resonance is caused by the interference between the dielectric waveguide mode and SPP.

3.2. Sb₂Se₃ in High-Temperature (HT) (Crystalline) Phase

Figure 5a,b depict the XZ cross-sectional magnetic field distribution maps of the crystalline metasurface at reflection valleys c and d. Multiple highly localized magnetic field spheres are arranged in a vertical row within the Sb₂Se₃ cubic block, with nearly no energy leakage into the air on both sides. This optical resonance with energy tightly confined in the lateral direction conforms to the characteristics of Fabry–Pérot (FP) resonance. This resonance causes the internal photons to oscillate repeatedly at the interface between the air and the phase-change material, accumulating a specific phase difference that matches the optical coherent constructive interference. Figure 5c presents the two-dimensional reflection spectrum associated with the geometric parameter a1 under the TM incident mode. The circles in Figure 5c correspond to the reflection valleys c and d in Figure 2b. It is evident that there exist reflection peak curves strongly correlated with the geometric parameter a1 which traverse the reflection valleys c and d. The significant redshift of the reflection resonance peaks with the increase in a1 is highly in accordance with the FP resonance. Figure 5d,e illustrate the electric field intensity distribution and the equivalent current direction diagrams of the metasurface at reflection peaks a and b under the TE mode. In contrast to Figure 5a,b, under the two reflection peaks, the electric field can leak from the phase-change material into the lateral air, and the electric field intensity diagrams do not correspond to significant optical resonance modes. Nevertheless, through observation, it can be found that the rotational directions of the equivalent currents within the phase-change material exhibit highly significant regularities. For peak a, two counterclockwise current loops and half a clockwise current loop appear successively from top to bottom. For peak b, two clockwise current loops and one counterclockwise current loop appear successively. We hypothesize that these internal current loops can be approximated as a series of electromagnetic radiation oscillation elements [36], and the electric field generated at the reflection end interferes with the TE incident mode, resulting in a reflection enhancement effect.

3.3. The Influence of Potential Process Errors on Metasurfaces

In the preceding chapters, we have presented the polarization regulation capabilities of the phase-change metasurface in two states and have also conducted a focused analysis of the corresponding optical resonance modes. In this chapter, we primarily discuss the impact of potential errors that may occur during the actual fabrication process of the metasurface on its performance. Figure 6a–d, respectively, display the images of the fillet radius r0, etching inclination angle θ, under-etching error ∆h1, and over-etching error ∆h2. Figure 6e–h, respectively, correspond to the LTC capabilities of the amorphous metasurface under the aforementioned errors. As depicted in Figure 6e, when the fillet radius r0 is less than 40 nm, it scarcely exerts any influence on the metasurface. Figure 6f indicates that as the etching inclination angle θ decreases, the LTC at wavelengths λ1 and λ2 initially increases and subsequently decreases. When θ is less than 88 degrees, the metasurface will gradually lose its function as a quarter-waveplate. Figure 6g reveals that when the under-etching error ∆h1 does not exceed 40 nm, the metasurface can operate normally. Based on Figure 6h, it can be discerned that the performance loss of the metasurface under over-etching is more pronounced. When the over-etching error ∆h2 is greater than 30 nm, the efficiency of LTC is reduced. Figure 6i–l, respectively, showcase the performance degradation of the crystalline metasurface under different processing errors, which can be evaluated by the cross-polarization efficiency. Figure 6i indicates that when the fillet radius r0 is less than 40 nm, the cross-polarization efficiency of the micro-device is greater than 0.9. Figure 6j shows that if the etching inclination angle θ can be greater than 88 degrees, the cross-polarization efficiency can also exceed 0.9. As shown in Figure 6k, when the under-etching error ∆h1 is less than 40 nm, the performance of the metasurface is hardly compromised. Figure 6l indicates that the cross-polarization efficiency remains invariant initially and then declines as the over-etching error ∆h2 increases.

To validate the correctness of the COMSOL simulation model, we computed the impacts of several typical simulation variables on COMSOL. The discretization in the electromagnetic finite-element method transforms the continuous problem into a discrete algebraic system through polynomial shape functions, and the selection of the polynomial order and type directly influences the calculation accuracy. Figure 7a indicates that when the number of polynomial terms is greater than or equal to 2, the performance of the metasurface in both states scarcely changes. As depicted in Figure 7b, when the thickness of the PML layer ranges from 500 nm to 4000 nm, the calculation results of COMSOL remain consistent. To guarantee that no photons can penetrate the metal backplate, the thickness of the metal backplate is typically required to exceed its skin depth. Figure 7c shows that when the thickness of the metal backplate is greater than 120 nm, the effect of the metasurface becomes independent of the thickness of the metal backplate. Figure 7d indicates that when the mesh size of the phase-change material is less than 150 nm, the regulation effect of the metasurface has stabilized.

4. Discussion

We have designed a metasurface based on the phase-change material Sb₂Se₃, which can manifest the functionalities of a half-waveplate and a quarter-waveplate, respectively, under different conditions. A functional form has been achieved that is operable in multiple modes with only a single device. The phase-change metasurface consists of a TEC, a metal backplate, and a periodic Sb₂Se₃ graphic array from bottom to top. The temperature-controlled dual-function phase-change metasurface waveplate (HWP at high temperature/QWP at low temperature) we designed possesses revolutionary application potential, being capable of resolving multiple problems that traditional optical systems are unable to overcome, and is anticipated to pioneer new possibilities in dynamic optics, integrated photonics, and extreme environment optics.