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Abstract
Active optical metasurfaces promise compact, lightweight, and energy-efficient optical systems with unprecedented performance. Chalcogenide phase-change material Ge2Sb2Se4Te1 (GSST) has shown tremendous advantages in the design of mid-infrared active metasurfaces. However, most of the GSST-based active metasurfaces can only work efficiently within a narrow frequency range. Furthermore, their design flexibility and reversible switching capability are severely restricted by the melting of GSST during re-amorphization. Here, we propose broadband, reversibly tunable, GSST-based transmissive metasurfaces operating in the long-wave infrared spectrum, where the GSST micro-rods are cladded by refractory materials. To accurately evaluate the performance of the proposed metasurfaces, two figures of merits are defined: FOMΦ for the evaluation of wavefront matching, and FOMop for the assessment of the overall performance incorporating both wavefront modulation efficiency and switching contrast ratio. For the proof of concept, two meta-devices are numerically presented: a multifunctional deflector that offers continuous beam steering and long-wave pass filtering simultaneously, and a large-area (1 cm × 1 cm) broadband (11-14 µm) varifocal metalens with the ability of achromatic imaging (12.5-13.5 µm). In particular, the metalens features high FOMop values over 16 dB in the achromatic band, with the average focusing efficiency approximating 70% (60%) in amorphous (crystalline) state and a spectral switching contrast ratio surpassing 25 dB. Our design scheme provides an additional degree of freedom for dynamic modulation and offers a novel approach for achieving high-efficiency mid-infrared compact optical devices.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces composed of customized subwavelength resonators have attracted much attention due to their potential in the design of ultra-compact optical devices [1–3]. Active metasurfaces have emerged as an intensively explored field as they enable dynamic tuning of optical functions and hence offer unprecedented performance and functions [4]. In contrast to mechanical tuning [5–11], the non-mechanical methods relying on tunable optical properties of meta-atoms have the potential to offer significant advantages in speed, power, reliability, and design flexibility. Out of the plethora of non-mechanical tuning mechanisms including free carrier [12], thermo-optic [13], electro-refractive [14], the nonlinear effect [15], and phase transition [16–18], phase transformation in nonvolatile optical phase change materials (OPCM) presents itself as a promising contender for midinfrared (MIR) applications owing to the extremely large refractive index contrast between the amorphous state (a-state) and crystalline state (c-state) [18–20]. The transition from a-state to c-state (crystallization) is driven by heating the a-state OPCM up to its glass transition temperature (Tg), and the inverse transition (re-amorphization) is enabled at the condition over the melting temperature (Tm) [18].
As a representative OPCM, Ge2Sb2Se4Te1 (GSST) provides wideband MIR transparency in both optical states [20] and allows fully reversible switching with film thickness over 1 µm [18,19], promising diverse MIR transmissive devices. Shalaginov et al. [21] demonstrated a bifocal Huygens metalens employing optical resonances in GSST meta-atoms. The focal length is electrically switched from 1.5 mm (a-state) to 2 mm (c-state) at the operating wavelength of 5.2 µm. For the same wavelength and with similar Huygens elements, Yang et al. [22] achieved a parfocal doublet zoom metalens whose field of view changes from 40° under a-state to 4° under c-state. Yue et al. [23] reported a nonlinear GSST metasurface offering a tenfold change of the third-order susceptibility for the pump wavelength of 4.5 µm. Multifunctional metalenses with a high degree of freedom are also numerically investigated by combining wavelength-dependent excitation [24]/polarization-division multiplexing response [25–27] and the GSST phase transition. For instance, switchable multidimensional spin decoupling is realized by synergizing the propagation phase and specific Pancharatnam-Berry (PB) phase in a considerable bandwidth of around 4.2 µm [27]. Based on PB phase in symmetry-broken unit cells, beam steering accompanied by circular dichroism (a-state) and spin decoupling (c-state) are switched [28]. Numerical proposals for reconfigurable holography have also been put forth, inspired by the potential manipulation of addressable crystallization [29]. These GSST-based active metasurfaces, however, can only offer efficient narrow-band responses in the mid-wave mid-infrared (3–5 µm) region while the broadband manipulation of the long-wave infrared (LWIR, 8-14 µm) waves facilitates numerous applications such as thermal imaging [30], thermal camouflage [31,32], molecules detection [33], and free-space wireless communication. Furthermore, the utilization of bare GSST structures sitting on a transmissive substrate hinders reversible switching as such configuration can be damaged upon reaching the melting temperature during re-amorphization.
In this work, refractory Ge-clad GSST metasurfaces are numerically proposed for broadband reversible tuning of transmissive deflection beam and focusing in the LWIR spectrum. The concept is depicted in Fig. 1. When the optical state of GSST is tuned by external heating stimuli (from a-state to c-state under temperature over Tg, and from c-state to a-state under temperature over Tm), the broadband deflecting angle of the multifunctional deflector and the focal length of the broadband achromatic metalens is dynamically changed. Compared with the previous works, the distinctive features of the proposed metasurfaces are: (i) Broadband tuning in the LWIR spectrum is promised by waveguide-type meta-atoms, while narrowband responses in the MWIR band are previously reported via resonant-type metasurfaces. (ii) Reversibly dynamical tunning is achieved by GSST metasurfaces under the protection of refractory cladding material. (iii) Figures of merits are proposed for design methodology and performance evaluation, respectively. (iv) The proposed deflector offers long-wave pass filtering simultaneously, and the broadband deflecting angle is continuously tuned by the crystalline fraction of GSST. (v) The designed broadband metalens offers a double change in focal length for the 11-14 µm band, and achromatic varifocal imaging is achieved for wavelengths ranging from 12.5 µm to 13.5 µm. Our designs feature quantitative advantages compared with the aforementioned works offering similar functions [21,22,27,28] (Table S2 in Supplement 1). Owing to the weak adjacent coupling, high-efficiency numerical demonstration for large-area aperiodic metasurfaces is enabled by utilizing the angular spectrum theory [34], and the computation resources can be balanced by adjusting the calculation parameters (Section S3 in Supplement 1). Complex wavefront manipulation such as vortex generation can also be achieved in the case of the corresponding precise design. We believe the design of such reconfigurable metasurfaces provides an excellent approach for more efficient MIR compact optical systems.
Fig. 1. Schematic of the proposed reconfigurable GSST metasurface for broadband reversibly tunable applications in the long-wave mid-infrared (8-14 µm) band: a long-wave pass deflector with continuous beam steering (left) and an achromatic varifocal metalens (right).
2. Design and methods
2.1 Design methodology
GSST exhibits flat dispersion under both optical states and offers a large refractive index contrast (Δn≈1.42) in the 8-14 µm band, changing from about 3.18 under a-state (aGSST) to near 4.6 under c-state (cGSST) [20]. Meanwhile, the extinction indices in both states are near zero (Fig. S3 in Supplement 1). Hence, the abrupt phase imparted by the GSST-based subwavelength structure is dynamically tunable with extreme transparency. The designed meta-atom is comprised of an isolated GSST micro-rod sitting on a germanium (Ge) substrate and being covered by an ultrathin refractory film (Fig. 2(a)). Here, Ge is used as the refractory cladding, not only for its high melting point [31] but also due to its high transparency in the midinfrared. Therefore, it can keep the shape of the molten GSST during re-amorphization while maintaining high transmittance. The meta-atom could be in any shape with a top-view in C4 symmetry for a polarization-insensitive response. Square blocks are preferred here for the relatively small simulation and layout sizes (especially for the large-area case).
Fig. 2. Optical response of the eight selected meta-atoms. (a) Schematic of the designed GSST unit. The material in purple represents GSST, while Ge is presented with the color gray. (b) Abrupt phase modulation of the selected GSST blocks at the wavelength of 13 µm. The corresponding widths are 0.54 µm, 0.78 µm, 0.94 µm, 1.06 µm, 1.18 µm, 1.26 µm, 1.42 µm, and 1.54 µm, respectively. The blue circles and red asterisks represent the phase modulation by the selected meta-atoms under a-state (aGSST) and c-state (cGSST), respectively. The dashed blue and red lines represent the target discrete phases. (c) Transmission of each GSST block. (d) Normalized magnetic intensity field profiles of each meta-atom at the y = 0 plane. The structures are contoured with black lines.
As is commonly understood, a metalens is conventionally implemented by matching the target phase map with those discrete meta-atoms offering local phase modulations. Thus, the target phase map covering 2π-change should be discretized into several phase levels. For example, the phase profile for a-state is discretized into eight phase levels, i.e., from -π to 0.75π with a step of 0.25π (dashed blue line in Fig. 2(b)). Then we only need to select eight meta-atoms and then construct the metasurface by spatial patterning with them. To enable switching between two phase profiles with the eight meta-atom design, we chose four phase levels of discretization for c-state, i.e., from -π to 2.5π with a step of 0.5π (two loops of 2π, dashed red line in Fig. 2(b)). Then the wave aberrations between discretized phases and the continuous counterparts are negligible for both states [3]. The optical responses of all meta-atoms are simulated with the finite-difference time-domain (FDTD) method, and a structure-phase library is constructed by sweeping the geometrical parameters (Section S2 in Supplement 1). Then the optimal eight meta-atoms are selected from the structure-phase library based on the following figure of merit:
2.2 Fabrication proposal
Such core-shell structures can be fabricated by depositing a Ge film on the GSST pattern after the lithography and etching steps. Figure 3 illustrates the detailed fabrication proposal: A 12 µm-thick GSST film could be first deposited onto a Ge substrate with the thermal co-evaporation technique (by controlling the ratio of evaporation rates of two isolated targets of Ge2Sb2Te5 and Ge2Sb2Se5) [21–23] or solution deposition method [35]. After the surface treatment with standard oxygen plasma cleaning (to improve resist adhesion) [36], the resist (such as ZEP520A [37,38]) could be spin-coated on top of the GSST film, and the electron beam writing [39] shall be subsequently carried out. Then the GSST would be possibly patterned by developing a particular Bosch process [40] combined with the RIE technique. Although achieving a high aspect ratio of nearly 24 for GSST remains a challenge, GSST metasurfaces with an aspect ratio of nearly 2 have been experimentally demonstrated with the RIE technique [21,22]. In addition, impressive results have been achieved by developing Deep-RIE (DRIE) techniques with the Bosch process, allowing Si slits with aspect ratios exceeding 100 [41] and Ge structures with an aspect ratio approaching 25 [42]. Given the escalating demand for GSST optical metasurfaces and advancements in nano-fabrication, we are confident in envisaging a feasible process of etching our designed GSST blocks. Subsequently, a Ge film with a thickness of 0.5 µm could be deposited using atomic layer deposition techniques [43–45] after removing the residual photoresist mask. Note that the optical performances of the selected units are robust against fabrication imperfections (Section S5 in Supplement 1). Regarding that the covering Ge will be oxidized into the lossy GeO2 under high temperatures [46], the meta-devices should be encapsulated after the fabrication.
2.3 Performance evaluation
To perform a quantitative assessment of the proposed tunable meta-devices, it is necessary to establish a figure of merit encompassing both the efficiency of wavefront manipulation for each state and the switching contrast ratio (CR) between the two states. The efficiency ${\eta _1}$(${\eta _2}$) of wavefront control for a-state (c-state) GSST is:
Low crosstalk between the two states is promised by a high contrast ratio. Consequently, the overall optical quality of the metasurfaces can be defined as:
A high FOMop value is obtained with high-quality meta-devices offering high efficiencies in both states and a high switching contrast ratio. The figure of merit is generic for applications including but not limited to binary deflectors and metalenses.
3. Applications
3.1 Broadband transmissive deflector
To implement a transmissive deflector, the arrangement of the selected eight elements is designed to generate a constant phase gradient along the x-axis $\nabla \phi = d\phi /dx$. Bloch boundary condition is set for x and y directions, and the z boundaries are set as perfectly matched layers (PML). The phase profiles at the wavelength of 13 µm for normal incidence are depicted in Fig. 4(b). The constant phase gradients for the a-state and c-state are $\nabla {\phi _a} \approx \pi /16\; \mu {m^{ - 1}} $ and $\nabla {\phi _c} \approx \pi /8\; \mu {m^{ - 1}}$, respectively. The simulated spatial phases of the designed periodic array are consistent with the phase modulation of each meta-atom for both states, albeit with a few fluctuations resulting from the weak adjacent coupling. The transmitted light is deflected with an angle of θ1, as described by the generalized Snell’s law [47]:
where ${\theta _i}$ is the incident angle; ${\lambda _0}$ is the wavelength in a vacuum; ni is the refractive index of the incident medium; nb is the refractive index of the refracted medium. For the backward case (incidence from the bottom of the Ge substrate, which is the conventional case in previous works), ${\theta _1}$ is the deflecting angle. However, we would like to discuss the other case, with incidence from the top of the metasurface (Fig. 4(a)).Fig. 4. Broadband beam steering application. (a) Schematic of the design and the behavior of the propagating light. (b) The simulated phase profile of the designed array along the x direction for the wavelength of 13 µm. The results for a-state and c-state are depicted as blue and red dots, respectively. The corresponding results for every single unit are also shown for comparison. (c) Angular spectra of the deflected waves in Ge substrate. The dashed lines indicate the critical angle. (d) Transmission of the deflector for a-state (blue line) and c-state (red), which exhibits the capability of a long-wave pass filter. (e) Effect of the crystalline fraction on the deflecting angle.
According to the refraction principle, only when the propagation angle ${\theta _1}$ in the Ge medium is smaller than the critical angle ${\theta _c}$, the light is finally output with an angle: ${\theta _2} = \textrm{asin}({{n_b}\sin {\theta_1}} )$. By setting the near-field profile monitor in the Ge medium, the propagation angles are simulated via the far-field extraction method [48]. For both amorphous and crystalline states (Fig. 4(c)), the propagation angles of short wavelengths (8-11 µm) are larger than the critical angle while ${\theta _1} < {\theta _c}$ is satisfied for long wavelengths (12-15 µm). Hence, the deflector acts as a long wave pass filter simultaneously (Fig. 4(d)). The greatest change in the deflecting angle is presented at the design wavelength of 13 µm, changing from 24° to 54°(Fig. 4(e)). As discussed in Section 2.3, the overall performance of our proposed deflector can be quantitatively evaluated by defining ${P_{i,j}}$($i = 1,2;j = a,c$) as the power for the central angle θi (within angular full width at half maximum) with the GSST in j-state. As shown in Table 1, the proposed metasurface presents high deflecting efficiencies for both states, with average efficiencies of 45.45% and 84.47% in the 12-15 µm band for a-state and c-state, respectively. The lower efficiency in a-state mainly results from the larger deflecting angles that are easily blocked by the reflection at the Ge/air interface. At the wavelength of 13 µm, the switching contrast ratio reaches 4.09 dB, and the FOMop value is 2.22 dB.
Table 1. Quantitative performance of the proposed deflector
Phase modulations for the intermediate state are also performed, where the wavelength-dependent permittivity of GSST can be approximated by an effective-medium theory using the Lorentz-Lorenz relation [49] :
3.2 Broadband and achromatic varifocal metalens
(1) Simulation for small aperture metalens
The second application demonstration is broadband varifocal metalens. Owing to the aperiodic nature of metalenses, the simulation time and memory usage requirements for global simulations increase exponentially with aperture size. To avoid running over the computing resource limit, a small metalens with $59 \times 59$ units is performed with the commercial Ansys Lumerical FDTD software [50] first. The phase profile is designed as a hyperboloid function [3]:
Fig. 5. Simulation results for varifocal metalens at the wavelength of 13 µm. (a) Phase profiles under a-state, including the simulated result (blue dots) and the corresponding designed (orange line) and continuous (yellow line) counterparts. (b) Calculated electric intensity profile at the x-z plane with continuous phase (left) and discrete phase (middle) exhibited in panel (a), and FDTD-simulated far-field profile (right). (c) Phase profiles under c-state, including the simulated result (blue dots) and the corresponding discrete (orange line) and continuous (yellow line) counterparts. (d) Calculated electric intensity profile at the x-z plane with continuous phase (left) and discrete phase (middle) exhibited in panel (c), and FDTD-simulated far-field profile (right).
Interestingly, the demonstrated focal length in a-state is shifted to 670 µm, while the calculated and simulated results are both consistent with the designed focal length in c-state. Moreover, the accuracy of angular spectrum theory seems not sufficiently good: the calculated focal spots with the continuous phases (left figures in Fig. 5(b), d) are worse than the far-field simulation results (right figures in Fig. 5(b), (d)). The error in the focal length and the imperfection of calculated profiles both result from the small aperture of the metalens. In particular, the phase profile for a-state does not cover a full loop of 2π-change (Fig. 5(a)), leading to the shift of the focal length. By increasing the diameter to offer sufficient loops of 2π-change, the angular spectrum theory can restore the real profiles of focal spots as well as the accurate focal lengths (Section S3 in Supplement 1). Therefore, to obtain the far-field distribution of a metalens, one can choose the far-field FDTD simulation for metalenses with small apertures (e.g., that offers nearly one loop of 2π-change) and prefer the angular spectrum theory for large-area metalenses (fewer computation sources and sufficient accuracy).
(2) Numerical calculation for large-area metalens
Subsequently, a metalens with an aperture of $1\; \textrm{cm} \times 1\; \textrm{cm}$ is designed for better performance and fidelity (Fig. 6). Regarding the computation burden, angular spectrum theory applied for designed phases is preferred in this case instead of the expensive (or even unrealistic) full-wave 3D simulation. The two focal lengths are fa = 10 cm and fc = 5 cm for λ=13 µm. By tuning the crystalline fraction, intensities of the two focal spots are simultaneously tuned whilst retaining the constant spot locations (Fig. 6). Therefore, binary switching of focal length is achieved. The computational resources can be further released by performing the corresponding one-dimensional focusing array (Section S7 in Supplement 1).
Fig. 6. Effect of the crystalline fraction (m) on the focusing performances for λ=13 µm. The aperture of the metalens is $1\; \textrm{cm} \times 1\; \textrm{cm}$, and the two focal lengths are fa = 10 cm and fc = 5 cm, respectively. The intensity profiles are normalized to the corresponding peak intensities, respectively.
The binary switching of focal length is valid for a bandwidth of 3 µm ranging from 11 µm to 14 µm, while an inverse switching occurs at the wavelength of 10 µm (Fig. 7(a)). In particular, for wavelengths ranging from 12.5 µm to 13.5 µm, the relative variations of focal length $\mathrm{\Delta }f = |{{f_\lambda } - {f_i}} |/{f_i}\; $(where fi represents the designed focal length for the wavelength of 13 µm (i = 1, 2), and fλ is the spectral focal length) are all less than 4%. Thus, achromatic focusing is achieved within this band (Fig. 7(b)). The achromatic performance is mainly attributed to the flat dispersion of GSST under both states (Section S8 in Supplement 1). The generic performance evaluation can also be applied to our varifocal metalens. Here, ${P_{i,j}}$($i = 1,2;j = a,c$) is defined as the focused power (concentrated within a radius of the corresponding diffraction-limited spot) at the i-focal plane with the GSST in j-state. As shown in Fig. 7(e), the FOMop is higher than 16 dB in the achromatic band (12.5-13.5 µm) and reaches the peak value of 25.3 dB at the wavelength of 12.7 µm. The average focusing efficiencies are near 0.7 (${\eta _1})$ and 0.6 (${\eta _2})$ for a-state and c-state, respectively (Fig. 7(c)). In particular, the FWHMs (full widths at half maximum) of the focal spots are close to diffraction limitation for both states (Inset in Fig. 7(c)) as the hyperboloid phase profiles (which is free of spherical aberration) are perfectly matched by meta-atoms selected according to our FOMΦ. The corresponding spectral switching contrast ratios exceed 25 dB, with a peak value of 41.4 dB at 12.7 µm wavelength (Fig. 7(d)). The overall performance of our proposed metalens theoretically surpasses that of the authoritative counterpart reported in Ref. [21]., whose FOMop is calculated as 13.3 dB at 5.2 µm wavelength based on the simulation results (${\eta _1} = 0.395,\; {\eta _2} = 0.254$, CR =42.1 dB, as listed in Table S2 in Supplement 1).
Fig. 7. Broadband binary focus switching of the designed varifocal metalens. (a) Broadband varifocal response for the 7-15 µm band. (b) Achromatic varifocal response in the 12.5-13.5 µm band. The error bars represent the full width at half maximum along the z-axis. The blue and orange marks represent the focal length at a-state and c-state, respectively. The designed focal lengths are indicated by the dashed black lines for comparison. (c) Spectral focusing efficiencies of the designed metalens. Inset shows the corresponding focal spot size. (d) Switching contrast ratio considering the two foci corresponding to the two optical states. (e) Overall performance of the designed metalens.
4. Conclusions
In summary, broadband reversibly reconfigurable metasurfaces operating in the LWIR spectrum are numerically presented utilizing the propagation phase of Ge-clad GSST micro-rods. The shape of the meta-atoms remains unchanged when the GSST is re-amorphized (molten) as the melting point of the cladding Ge film is higher than the re-amorphization temperature of GSST. Hence, it is worth noting that the wavefront manipulations are not only reconfigurable but also reversible. Two criteria are proposed to assess the performance of the device: one (FOMΦ) is tailored for designing reconfigurable wavefronts, and the other (FOMop) quantitatively evaluates the overall performance by considering both efficiency and switching contrast ratio. For the proof of the concept, a refractory and broadband tunable long-wave pass deflector and an achromatic varifocal metalens are numerically implemented. For the tunable deflector, the transmission of short wavelengths ranging from 8 µm to 11 µm is blocked, while the deflecting angle for the transmitted wavelengths (12-15 µm) is continuously tunable by changing the crystalline fraction of GSST. The second application demonstration involves a broadband metalens that offers a dual focal length variation in the 11-14 µm band and particular achromatic focusing for wavelengths ranging from 12.5 µm to 13.5 µm. The metalens features high FOMop values over 16 dB in the achromatic band, with the average focusing efficiency approximating 0.7 (0.6) for amorphous (crystalline) state, and achieves switching contrast ratios that exceed 25 dB. The peak FOMop value reaches 41.4 dB at the 12.7 µm wavelength, which is theoretically competitive with the previous works. Owing to the weak adjacent coupling, high-efficiency numerical verification of large-area aperiodic metasurfaces is enabled by far-field calculation with the designed discrete phase instead of the full-wave FDTD simulation. The switching is enabled by external optical, electric, and thermal stimuli. For instance, to achieve non-volatile integrated photonic switches, the phase transition of GSST has been actuated by modulating the laser output [20]. Regarding the 12 µm-thickness of GSST, a typical three-dimensional profile of the laser spot should be precisely designed to ensure the uniform distribution of the crystalline fraction. In contrast, a surface heat source applied to the other side of the substrate can homogeneously distribute the crystalline GSST (Section S9 in Supplement 1). Since the GSST is a nonvolatile phase-changing material, the meta-device can be used after the crystallization is manipulated by a heating plate. The meta-devices can also be dynamically tuned via external thermal sources when the back side is covered by a thin film processing a broadband mid-infrared transparency, an ultrahigh thermal conductivity, and a high melting temperature (such as graphene [52–54] and carbon nanotube films [55,56]). Regarding the electrical tuning, a refractory mid-infrared transparent electrode (such as graphene [52–54], carbon nanotube films [55,56], and In2O3 [57,58]) should be deposited on the other side of the substrate, and it could be the homogeneous surface heat source via electrical stimulus. The concept of utilizing the phase change material provides an extra degree of freedom for designing active metasurfaces, holding potential applications in microscopy, imaging, and spectroscopy systems.
Funding
National Natural Science Foundation of China (62105120, 12104182); Basic and Applied Basic Research Foundation of Guangdong Province (2022A1515140113, 2020A1515110971); Youth Innovation Funds of Ji Hua Laboratory (X220221XQ220).
Acknowledgments
The authors would like to thank Yining Zhu (Ph. D. candidate in Qiang Li’s group) for his assistance in the thermal analysis and thank Boqu Chen (Ph. D. candidate in Min Qiu’s group) for his suggestion on the fabrication proposal.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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