1. Introduction

In recent years, the planar metasurfaces with the capability of robust control over the phase, amplitude, and polarization of reflected/transmitted light have attracted extensive attention due to the compactness, robust design paradigm, and fabrication simplicity compared to the bulky metamaterial counterparts. The graded-pattern metasurfaces as arrays of dielectric/plasmonic subwavelength nano/micro elements with spatially varying physical characteristics can provide various abrupt amplitude/phase discontinuities enabling wave-front manipulation and beam-forming [1–3]. One possible concern regarding these passive flat optical metasurfaces is the lack of real-time control over the functionality after fabrication. Recently, various kinds of actively controllable mechanisms have been introduced [4–19] in order to bring real-time wave-front manipulation into the conventional static metasurfaces such as mechanical reconfiguration [4,5], nonlinear and superconducting optical effects [6], and hybridization with functional materials. The latter one can be divided in several categories with intriguing principles including control over the surface conductivity in graphene [7,8], modulation of charge carrier concentration in doped semiconductors (GaAs and InSb) [9,10] and transparent conducting oxides e.g., indium tin oxide (ITO) [11–13], phase transition of insulator-to-metal in vanadium dioxide (VO₂) [14–16], internal nematic-to-isotropic transition in liquid crystals [17], and structural amorphous-to-crystalline transition in chalcogenides so-called phase-change materials (PCMs) [18,19]. Among the aforementioned functional materials, there has been remarkable progress and immense research interest on ITO, VO₂, and germanium-antimony-tellurium (GST) alloys due to the short response time (Table 1 in [14]), wide tuning range, compactness, and feasibility of fabrication in the near-infrared (NIR) regime – specifically two telecommunication wavelengths of 1.31 μm and 1.55 μm – as a reliable and practical optical communication spectrum.

Indium tin oxide (ITO) as one of the most well-known electro-optical materials yields power-efficient tunablility with potential ultrafast modulation speed (~ps [20] and fs [21]) in NIR regime. The recently proposed ITO-based designs exploit the unique epsilon-near-zero property and excitation of highly confined electromagnetic fields at the place of ITO active layer to attain wide phase modulation [11–13]. Despite these advantages, the intrinsic high level of dissipative loss in ITO, ultra-thin inhomogeneous active layer [12], and short interaction length with impinging beam lead to low reflection efficiency. In order to overcome the short interaction length with the impinging wave, alternative tunable materials like VO₂ and GST alloys can be utilized with drastic refractive index change within entire volumetric tunable active regime which leads to strong light-matter interaction, long spectral shift of geometrical resonances, and less sensitivity to the fabrication tolerance. VO₂ which is a non-chalcogenide volatile phase-switching material has the capability of transition between insulator and metal states [15]. The main drawbacks of VO₂ are optical loss in metallic state (e.g., refractive indices of 3.1309-j0.3612 and 2.1313-j2.8440 at room temperature and 363 K at 1.55 μm, respectively [15,16]) and necessity of continuous stimulus control to maintain the switching state. In contrast, GST alloys are known to have advantages of relatively lower dissipative loss in NIR regime and nonvolatility (i.e. preserving the amorphous/crystalline state even in the absence of the input power). Although the refractive index of GSTs is wavelength-dependent, it can experience fairly significant change by amorphous-to-crystalline transition within IR to visible spectra.

The concept of utilizing GST as a functional material has been extensively studied in order to surmount challenges in memory and data storage applications and enable sophisticated photonics and plasmonic functionalities [22–51]. In general, small modification in the refractive index of incorporated GST layer leads to a considerable change in the optical response (transmission, reflection, and absorption) of a hybrid structure. In [24], a non-volatile and reversible low-loss resonance switching is shown by varying the refractive index of a Ge₃Sb₂Te₆ layer next to the plasmonic nanorods. A broadband perfect absorber is theoretically studied in [25] and the first experimental demonstration of a band- and temperature-selective switchable perfect absorber by using a PCM is reported in [26]. Several two-state functionalities are also proposed such as an absorption-reflection switch [27] and a transmission-reflection modulator [28] by integration of an ultra-thin layer of GST-225 into a plasmonic subwavelength structure and tuning the already excited geometrical resonance. In addition, a beam switching metasurface and a bifocal metalens are experimentally demonstrated by integrating GST underneath of a geometric phase metasurface in [29]. Although previous studies on GST-based active devices mainly focus on switching between two well-known amorphous and crystalline states, the possibility of multi-level switching (intermediate crystallization states) is revealed by time-controlled external heating [30] or focused ultrashort laser pulses [31–37]. Based on this assumption, a GST-integrated metallic slit array is theoretically investigated in [38] where the Fabry–Pérot resonance in each slit could be spectrally shifted depending on the level of crystallization thus the phase of the transmitted light has been modulated in the range of 0.56π at the operating wavelength of 1.55 μm. In previously presented GST-based designs, continuous phase modulation has been realized through leveraging a single on-resonance operation where the presence of relatively large extinction coefficient for the crystallized GST leads to non-constant level of transmission/reflection (e.g., [38]). Recently, the potentials of all-chalcogenide metasurfaces instead of hybridization in plasmonic nanoantennas are studied in [39–41]. These active all-dielectric metasurfaces offer the possibility of excitation of both magnetic and electric dipolar (MD and ED) modes, lower dissipative losses, and greater ease of fabrication opposed to the plasmonic hybrid counterparts [40].

In this paper, an optically controllable metasurface consisted of geometrically fixed chalcogenide nanobars is theoretically investigated in which the optical characteristics of each nanobar can be tailored under assumption of multi-level partial crystallization (i.e. continuous variation of the refractive index of phase-change material from amorphous to crystalline). We leverage the recently emerged phase-change material Ge₂Sb₂Se₄Te₁ (GSST) [42,43] with simultaneous large index contrast between the amorphous and crystalline states (∆n≈1.8) and low optical loss compared to the classical GST alloy (Fig. 1 in [43]). In addition, a novel design paradigm is utilized to achieve significantly large phase modulation of 270° while the reflection efficiency is not only high but also exhibits minimal changes between 0.6 and 0.8 for all the intermediate crystallization states. This can be realized by taking into account the contribution of both electric and magnetic resonances (Mie-type dipolar modes) and operating at the middle of these geometrical resonances. In other words, we prevent from the concurrence of high confinement of electromagnetic fields and presence of large dissipative loss at this optical system which is known as the origin of an inevitable efficiency degradation in all the previously presented relevant works. The proposed methodology is leveraged to design an array of GSST nanobars with capability of steering the reflected light toward a desired direction only by varying the crystallization level of nanobars. The reflection efficiency of such active reflective array is numerically calculated greater than 45%. This is relatively higher than the recently reported reflection efficiencies for planar tunable metasurfaces with single on-resonance operation principle at NIR regime [12,15]. The possible challenges in fabrication and laser-induced crystallization of GSST nanobars are also discussed.

 

Fig. 1 The measured (a) refractive indices and (b) extinction coefficients of GST-225 in [19,39] and GSST in [43] for amorphous and crystalline states at 1.55 μm. (c) The ratio of refractive index and extinction coefficient changes between amorphous and crystalline states (∆n/∆k) for three studied PCMs. (d) The optical properties of GSST as a function of wavelength from visible to infrared spectra [43]. (e) Schematic overview of the proposed optically tunable reflective metasurface for beam manipulation of x-polarized incident beam. The control pulse is utilized to realize the laser-induced crystallization of GSST nanobars. The inset represents a unit-cell of GSST nanobar placed on a stack of MgF₂-Au backmirror. (f) The optical properties of several partially-crystallized GSST nanobars ranging from 0 (amorphous) to 1 (crystalline) calculated via Eq. (1).

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2. Concept and results

2.1 Selection of structural materials and topology

Considering the desired optical application, a specific PCM compound should be selected based on its stoichiometry-based physical properties and the related dielectric function. As described in [50], a strong resonant bonding in the crystalline state leads to a large change in the real part of the permittivity of PCM. In addition, relatively large band gap and low carrier concentration help to attain broad spectral range of low absorptive losses. Figures 1(a) and 1(b) demonstrate the refractive indices (n) and extinction coefficients (k) of three PCMs for amorphous and crystalline states, which are measured in [19, 39, 43] at the operating wavelength of 1.55 μm. It can be observed that the GST-225 in [19] can provide the highest contrast of refractive index (∆n≈3.1) and optical loss (∆k≈1.8) among the reported cases at the wavelength of 1.55 μm. These characteristics are usually desirable for design of two-state functional metasurfaces (e.g., absorption-reflection switch and transmission-reflection modulator). GST-225 and GSST which are recently fabricated and measured in [39] and [43] have almost the same extinction coefficient contrast between the amorphous and crystalline states (∆k≈0.4) but GSST can experience larger refractive index contrast (∆n≈1.8) compared to GST-225 in [39]. In order to examine the rate of refractive index change with respect to the increment of loss in these tunable materials, the ratio of refractive index and extinction coefficient changes (∆n/∆k) is plotted in Fig. 1(c). Based on the aim of this manuscript which is continuous wide reflection phase modulation and high uniform reflection level, GSST can provide more promising trade-off between the refractive index change (governing the spectral resonance shift) and the level of extinction coefficient (mainly governing the reflection magnitude) compared to two other GST materials as implied by Fig. 1(c). Further information regarding comparison of GSST and classical GST can be found in [43]. The optical properties of GSST as a function of wavelength are plotted in Fig. 1(d) from visible to infrared regime.

The proposed dynamically controllable metasurface is schematically demonstrated in Fig. 1(e). The building block is a GSST nanobar with the square shaped cross-section which behaves as a multipole nanoantenna and has long interaction length with the impinging wave. The GSST nanobars with the width of w_GSST, height of h_GSST, and periodicity of P are periodically arranged along the x-direction (infinite along the y-axis) as shown in the inset of Fig. 1(e). Magnesium Fluoride (MgF₂) is a promising candidate as a substrate for ultra-thin dielectric metasurfaces due to non-dispersive low refractive index and negligibly small extinction in visible and NIR regime [52]. The thickness of stand-off layer ($h_{{\text{MgF}}_{\text{2}}}$) can control the coupling effects between the gold (Au) backmirror and the GSST nanobars. The relative permittivity of MgF₂ is ${\epsilon }_{{\text{MgF}}_{\text{2}}}$ = 1.9044. The presence of an electrically thick Au reflecting mirror (h_Au = 200 nm) increases the interaction of the incident beam and the GSST nanobars. The possibility of using higher index stand-off layer like ZnS-SiO₂ and a SiO₂ cover layer surrounding GSST nanobars to prevent heating-induced oxidation is examined in Appendix I. As shown in Fig. 1(e), a transverse electric (TE)-polarized plane wave is normally incident to the meta-array (i.e., the polarization of incident light is perpendicular to the GSST nanobars). Toward realization of PCMs based metasurfaces, various fabrication procedures are implemented [40, 41, 45]. In [41], two-dimensional GST nanopillars are fabricated by patterning the sputtered GST film via electron-beam lithography and dry etching to create separate GST nanoposts. In addition, a GST periodic grating has been fabricated by focus ion beam milling in an amorphous GST film as described in [40]. Due to the physical similarity between these two PCMs (i.e., GST and GSST), it is likely that the same fabrication techniques can be utilized.

The transition between the amorphous to crystalline states can be triggered thermally by applying electrical [48] or optical [49] pulses or thermal annealing. To enrich the functionalities of phase-change-type reconfigurable devices, the realization of multi-level partially crystallized states has been implemented by time-controlled external heating [30] or focused ultrashort laser pulses [31–37]. The latter approach has been utilized for multi-level memory [31], grayscale image [32], hologram [33], and color display [34]. The possibility of attaining stable multi-level states can be considered as a unique optical characteristic of PCMs and in particular GSST alloy. In other words, wide range of refractive index from n≈3.3 to 5.1 corresponding to amorphous and crystalline states can be discretized to n-level and realized through applying trains of optical pulses with different intensities and durations [31–37]. In the partially crystallized states, the nanoparticle includes a combination of amorphous and crystalline molecules and the crystalline-to-amorphous ratio can be tailored by the externally applied energy. The effective dielectric constant for the different crystallization ratios can be approximated through the effective medium theory and Lorentz-Lorenz relation as [38,39],

2.2 Optical modes in a GSST nanobar

Figure 2(a) represents the results for the optical reflection spectra of a periodic amorphous GSST nanobar unit-cell with width of w_GSST = 300 nm, P = 600 nm, h_GSST = 300 nm, and $h_{{\text{MgF}}_{\text{2}}}$ = 150 nm (infinite along y-axis and periodic in x-direction). The numerical simulation is carried out based on an in-house developed rigorous coupled-wave analysis (RCWA) method [53,54]. RCWA is a well-known technique which has been widely utilized for design and analysis of one-dimensional (1D) and 2D metasurfaces [55,56]. The model is based on eigenmodes expansion of electromagnetic fields in periodic structures utilizing Bragg diffraction condition. The amplitudes of reflected diffraction orders from the periodic GSST nanobar building block is computed by enforcing the boundary conditions at all interfaces. In contrast to the plasmonic nanostructures with the capability of excitation of single magnetic or electric resonance, the proposed high-index all-dielectric nanoparticle can excite Mie-type dipolar resonances along with other multipolar resonances. Figure 2(b) schematically shows the characteristics of the MD and ED modes (known also as TE₀₁ and TE₁₁) inside a 1D dielectric nanobar. A normally incident plane wave with TE-polarization is assumed where the magnetic field is along the nanobar axis (y-axis). In order to reveal the nature of these resonances, the near-field distributions are plotted at different resonant modes (i.e. λ₁ = 1.416 μm and λ₂ = 0.986 μm) in Figs. 2(c) and 2(d). In Fig. 2(c), the magnetic field distribution (|H_y|) and the corresponding electric displacement currents in the GSST nanobar demonstrate the characteristics of a magnetic dipolar mode at λ₁ = 1.416 μm where the electric displacement currents circulate around the strongly confined normal component of magnetic field (H_y, color bar) at the center of GSST nanobar. On the other hand, the geometrical resonance which occurs at the operating wavelength of λ₂ = 0.986 μm behaves as an electric dipolar mode (Fig. 2(d)). These results are consistent with the previously reported field profiles in [57] for a silicon nanowire.

 

Fig. 2 (a) Numerically calculated reflection amplitude and phase of a 300 nm-thick GSST nanobar with a 300 nm width backed by a stack of MgF₂-Au backmirror as a function of wavelength under illumination of a normally incident TE-polarized plane wave. (b) Sketch of the MD and ED modes inside a 1D dielectric nanobar. The dips in (a) correspond to the resonant modes which are characterized based on the magnetic field profiles. The near-field distribution of the normal component of magnetic field (|H_y|, color bar) and the electric displacement current loops (arrows) at (c) λ₁ = 1.416 μm (MD mode) and (d) λ₂ = 0.986 μm (ED mode) in the x-z plane.

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2.3 Design rules toward highly efficient tunable building block

The realization of a tunable PCM-based platform with simultaneous high level of reflection amplitude and wide phase agility faces with several challenges. First, although the loss of PCMs is low in the amorphous case, it is gradually increasing via the crystallization. Second, it has been previously observed that the wide phase modulation can be obtained at the place of resonances (called on-resonance operation). By the increment of crystallization ratio, the existing geometrical resonances will experience the decay of reflection level and significant spectral shift which may cross the operating wavelength. This phenomenon leads to concurrence of high field confinement originated from the geometrical resonance and large extinction coefficient inside the integrated PCM layer/nanoantenna which devastates the performance efficiency. This means that achieving solely wide phase modulation can be possible by on-resonance operation and utilizing single fundamental resonance (e.g., hybridization of PCM with plasmonic nanoantennas supporting single magnetic/electric resonance) but at expense of low and non-constant reflection level.

Here, the general steps and overall procedure of proposed design paradigm are presented which can overcome the aforementioned obstacles by considering the interplay of both supported electric and magnetic resonances. The design should be carried out in such a way that the pre-chosen wavelength (1.55 μm) has the maximum possible reflection amplitude and locates at the middle of well-separated MD and ED resonances when the GSST nanobar is close to half-crystalized state (we will call it reference crystallization level). The basic intent behind this step is preventing from the occurrence of the geometrical resonances at the operating wavelength when the crystallization level is increased (decreased) and both MD and ED modes shift to the higher (lower) wavelengths. Also, these geometrical resonances should have high quality factor (Q-factor) and rapid phase agility to guarantee a large phase modulation at the middle point.

In order to address fully foregoing criteria, a multi-objective parametric study is performed in order to maximize the phase coverage when the reflection level is not only as high as possible but also constant for all the crystallization ratios. Consequently, the structural parameters are chosen as w_GSST = 380 nm, P = 440 nm, h_GSST = 290 nm, and $h_{{\text{MgF}}_{\text{2}}}$ = 145 nm and the reference crystallization level should be selected as m = 0.65. Figure 3(a) shows the reflection amplitude of a periodic GSST nanobar when the crystallization level is 0.65. It can be observed that two well-separated resonances with high Q-factor are obtained at the wavelengths of ${\lambda }_{\text{MD}}^{(m=0.65)}$ = 1.808 μm and ${\lambda }_{\text{ED}}^{(m=0.65)}$ = 1.219 μm (${\lambda }_{\text{MD}}^{(m=0.65)}$-${\lambda }_{\text{ED}}^{(m=0.65)}$ = 0.589 μm) corresponding to MD and ED modes, respectively. The operating wavelength of 1.55 μm is nearly located at the middle of these geometrical resonances. The reflection spectra of the optimized phase-change GSST nanobar is also plotted for two limiting cases of amorphous and crystalline in Fig. 3(b). It can be seen that as m increases from 0 to 1, the low- and high-wavelength dips shifts up from ${\lambda }_{\text{ED}}^{(m=0)}$ = 1 μm and ${\lambda }_{\text{MD}}^{(m=0)}$ = 1.492 μm to ${\lambda }_{\text{ED}}^{(m=1)}$ = 1.398 μm and ${\lambda }_{\text{MD}}^{(m=1)}$ = 2.098 μm. This means that the increase in the refractive index of GSST related to the amorphous to crystalline transition red-shifts the MD and ED modes by around 0.606 μm and 0.398 μm, respectively. At the same time, an inevitable increment of the extinction coefficient occurs which broadens the bandwidth of geometrical resonances and decreases the overall reflection-level in entire studied wavelength regime from 0.8 μm to 2.5 μm. Comparing Figs. 3(a) and 3(b) reveals an important fact that the geometrical resonances for the case of m = 0.65 as the reference crystallization state are located at the middle of those for amorphous and crystalline.

 

Fig. 3 The reflection spectra of the proposed building block with structural parameters of w_GSST = 380 nm, P = 440 nm, h_GSST = 290 nm, and $h_{{\text{MgF}}_{\text{2}}}$ = 145 nm when the crystallization ratio is (a) m = 0.65 and (b) m = 0 (amorphous) and 1 (crystalline). The spectral positions of the electric resonances are 1 μm, 1.219 μm, and 1.398 μm and the dips corresponding to the magnetic resonances are located at 1.492 μm, 1.808, and 2.098 μm for m = 0, 0.65, and 1, respectively.

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In order to provide further clarification, the optical responses of a GSST nanobar building block as functions of wavelength and the crystallization ratio are plotted in Figs. 4(a) and 4(b). The dashed region with the spectral bandwidth of 0.18 μm ([1.475 μm, 1.654 μm]) in Figs. 4(a) and 4(b) has the potential to serve relatively wide phase change (>π) and high reflection amplitude (>0.4). Therefore, this design is not narrow-band (≈11.55% of the center wavelength of 1.55 μm). In particular, it is possible to achieve a high reflection with minimal variation between 0.6 and 0.8 and phase difference as large as 270° at the operating wavelength of 1.55 μm only by varying the crystallization fraction from 0 to 1 as shown in Fig. 4(c). Numerical simulations of the x-polarized reflected electric fields for seven individual GSST nanobars with various crystallization levels at the operating wavelength of 1.55 μm are shown in Fig. 4(d). It can be observed that the phase of the reflected field can be controlled via the selective modification of the crystallization level and these tunable building blocks create discrete phase shifts ranging from 0 to 270° indicated by the markers in Fig. 4(c). It is a well-known fact that there is always a trade-off between the level of reflection and phase coverage. In other words, full phase shift (2π) can be realizable via sacrificing the reflection efficiency. In the current design, by operating at the wavelength of 1.75 μm, the phase span increases to 330° but the reflection magnitude will be as low as 0.2 for most of this phase shift range. To satisfy both the high reflection level and 2π phase coverage, there are three potential ways such as utilizing larger periodicity with drawback of losing the compactness of building block, PCMs with negligibly small loss (larger bandgap and lower carrier concentration [50]) in amorphous-crystalline transition at 1.55 μm, and thicker GSST nanobar with possible difficulties in homogeneous and full phase transition.

 

Fig. 4 (a)-(b) Maps of reflection responses as functions of wavelength and crystallization level of a periodic GSST nanobar. The dashed regions indicate the possible operating bandwidth with promising efficiency. (c) Reflection amplitude and relative phase change (the reflection phase of the crystalline state is assumed zero) at the operating wavelength of 1.55 μm. (d) Color map demonstrates the discrete phase shift of the x-polarized light scattered from seven building blocks with selectively controlled crystallization level. The tilted dashed line represents the wave-front scattered from seven tunable unit-cells. The effects of varying (e)-(f) width (w_GSST) and (g)-(h) height (h_GSST) on the amplitude and phase of the reflection coefficient of the proposed GSST nanobar versus the crystallization level at the wavelength of 1.55 μm. (i) Real and imaginary parts of permittivities related to the amorphous, half-crystalized, and crystalline states [43]. (j) Near-field distributions of the normal component of magnetic field (|H_y|) at x-z plane for three cases of amorphous, half-crystallized, and crystalline states.

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In order to quantify the fabrication tolerance with respect to the structural parameters of GSST nanobar (w_GSST and h_GSST), the reflection amplitude and phase are calculated as functions of crystallization level at operating wavelength of 1.55 μm when the width of GSST nanobar varies between 0.34 μm to 0.42 μm as shown in Figs. 4(e) and 4(f). In similar fashion, the reflection responses are plotted in Figs. 4(g) and 4(h) when the height of GSST nanobar alters between 0.25 μm to 0.33 μm. From Figs. 4(e)-4(h), it can be concluded that the increment (decrement) of width/height causes the increment (decrement) of reflection level and the decrement (increment) of reflected phase coverage. The proposed building block can perform with promising efficiency within ± 20 nm modification in width and ± 10 nm change in height of GSST nanobars. Further modification will cause the degradation of performance efficiency (phase-coverage and level of reflection).

As earlier mentioned, the simultaneous high reflection level and wide phase agility could be realized in this unique design by avoiding from concurrence of high field confinement and presence of large dissipative loss inside the GSST nanobar at the operating wavelength. In order to clarify this claim, the real and imaginary parts of the permittivity of GSST (Re(ε_GSST) and Im(ε_GSST)) are calculated and indicated in Fig. 4(i) for three cases of amorphous, half-crystallization, and crystallization [43]. An important point which should be mentioned is that the amorphous (crystalline) case has the lowest (highest) imaginary part of permittivity, Im(ε_GSST), as depicted in Fig. 4(i). Therefore, the occurrence of a weak magnetic/electric resonance corresponding to the amorphous case at the vicinity of the chosen operating frequency will slightly influence the reflection efficiency but we should prevent from the occurrence of strong magnetic/electric resonance (i.e. the formation of highly confined electromagnetic fields) related to the higher crystallization level at the operating frequency due to the presence of remarkable loss. In Figs. 4(i) and 4(j), it can be clearly observed that there is an opposite trend between the GSST material loss and the field confinement. In other words, the field confinement is decreased in order to alleviate the effects of extinction coefficient of GSST on the reflection level.

As a supplemental study, a multi-objective parametric investigation is performed in Appendix II to optimize the reflection response of the proposed building block when the constituent material of nanobars is modified from GSST to GSTs provided in [19] and [39]. The results for direct comparison are provided in Fig. 7.

In the current design, it is worth mentioning that the thickness of the GSST nanobars is considered 290 nm (λ/5.16, λ = 1.55 μm) which is fairly in the subwavelength effective regime. One of the possible challenges toward the practical implementation is the possibility of formation of inhomogeneous crystallization inside the GSST nanobars and unsuccessful full crystallization. The lack of full crystallization causes shorter spectral shift of geometrical resonances as reported in [40]. Therefore, it is expected that the occurrence of same phenomenon in our design will result in the decrement of range of possible effective refractive index change, lower spectral shift, and degradation of phase coverage (<270°). To reveal the limitations of a building block with ultra-thin GSST nanobar, a design with deeply subwavelength thickness of 90 nm (λ/17.22, λ = 1.55 μm) is presented in Appendix III.

3. Dynamically controllable beam steering metalens

So far, it is shown that although this tunable reflective metasurface is geometrically fixed, a considerable phase modulation can be realized under illumination of a 1.55 μm monochromatic wave as the crystallization level changes from m = 0 to 1. Among various kinds of optical applications which can be realized via the wave-front engineering such as focusing, holography, and flat-top generation, we will focus on the design and implementation of a highly efficient dynamically tunable beam steering lens in which partial-crystallization of each GSST nanobar will lead to feasibly steer an x-polarized incident beam. This approach is different from refs [29,45]. in which the presence of fixed graded pattern plasmonic metasurface on top of a GST film and consideration of only two operating states (amorphous and crystalline) lead to anomalous beam steering. In [45], the GST-integrated plasmonic metasurface could control the reflected beam toward designed angle in amorphous state and reflect back in an ordinary specular mirror-like fashion in crystalline state. Here, we leverage from phased-array concept and progressive phase-delay of nanoantennas in an array to attain continuous steering ability when each GSST nanobar is individually crystalized. This also offers more advantages compared to the case of digital beam scanning with binary holography and two angular states of 0 and π (applied in [12, 15]) by preventing from creation of diffracted beams in undesired directions [58]. A laser should be focused on the sample and scanned along each nanobar (y-direction) to ensure thorough crystallization of GSST. The accuracy and beam waist of the control pulse laser may be limited based on the available experimental facilities. Regarding the practically possible beam waist (equivalent to crystallized spot diameter), submicron spots with eight distinct data storage (i.e. multi-level crystallization of an ultra-thin GST-225 film) are experimentally realized on a 1.08 μm square grid by utilizing focused femtosecond pulse in [32]. The minimum width of 1 μm to perform crystallization is also experimentally implemented in [38] via continuous-wave laser. In [33], the reported resolution to locally crystalize the GST nanofilm is 0.59 μm. To ensure the generality of the idea, we have considered three widths of crystallization (w_Laser) equal to one, two, and three times of the period of proposed building block as schematically drawn in Figs. 5(a)-5(c), respectively.

 

Fig. 5 (a)-(c) Illustration of laser-induced crystallization of an array of GSST nanobars when one, two, and three neighbour nanobars should be crystallized to the same level depending on the waist of used laser pulse. (d) The required phase discontinuity to bend the impinging light towards θ_b = 20° at the operating wavelength of λ = 1.55 μm when the waist of control pulse is w_Laser = P, 2P, and 3P, respectively. (e)-(g) The simulated distribution of the real part of the x-polarized electric fields in x-z plane for a tunable array including 21 building blocks when (e) one, (f) two, and (g) three neighbour subwavelength elements are controlled similarly via laser-induced crystallization. (h) The far-field normalized intensity in dB (10log(|E_x/E_max|²)) for the cases studied in (e)-(g).

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The required phase distribution at the interface of meta-array and the steering angle of θ_b can be related by using phased-array concept as $\psi (x)=\left(2\pi /\lambda \right)x\sin {\theta }_b$ [59]. In order to realize a reflection with the bending angle of θ_b = 20°, the necessary phase profile is calculated and plotted in Fig. 5(d) where one, two, and three neighbour nanobars have the same crystallization levels. An optically tunable meta-array including 21 unit-cells is designed where the required phase shift at the place of each GSST nanobar can be simply mapped to a specific crystallization level by Eq. (1) and Fig. 4(c). In Figs. 5(e)-5(g), the real part of the reflected electric field (Re{E_x}) is numerically calculated for the aforementioned cases. The far-field normalized intensities (10log(|E_x/E_max|²)) are also plotted in Fig. 5(h). It can be observed that the reflected beam could be successfully steered toward the desired angle of 20° even when the waist of utilized laser to perform crystallization is three times larger than the periodicity of the proposed building block. The half-power beam-widths of steered beams are nearly equal to 9° and the level of side-lobes are at least 8.5 dB lower than the main directed lobe in all cases as shown in Fig. 5(h). The reflection efficiency is defined as the ratio of the reflected power to the incident power for these arrays and it is numerically calculated more than 45% for all these cases. A careful study is also carried out in order to quantify the maximum possible beam steering angle. In case of w_Laser = P, the meta-array can be redesigned in order to realize bending angles as large as 60°. The tilting angle will be limited to 40° and 30° for the cases of w_Laser = 2P and 3P, respectively. The results are omitted here for the sake of brevity. To the best of our knowledge, this is the best reported reflection efficiency with promising broad scanning angles for a tunable platform at NIR regime [12, 15]. One of the possible challenges toward implementation of such laser-induced crystallization and switching scheme is the thermal cross talk between the building blocks of the array, which can be arisen, due to the comparability of thermal diffusion length with separation of GSST nanobars. Therefore, thermal cross-talk may occur between the adjacent unit-cells during the laser-induced crystallization. This can be addressed by the adjustment of the external stimulus throughout the practical realization in order to attain exact required crystallization level for each GSST nanobar. Due to the fact that GSST can experience significant change by amorphous-to-crystalline transition within IR to visible spectra, the proposed design paradigm and building block can also be utilized to realize highly efficient tunable platform at other optical spectra like visible regime.

4. Conclusion

While tunable optical metasurfaces suffer from low reflection/transmission responses and cannot lead to wide phase agility due to the high dissipative loss of tunable materials, small interaction length, and ineffective physical mechanism (e.g., hybridization in plasmonic nanoantennas), here we theoretically study an optically controllable reflective platform including an array of GSST nanobars where the low loss nature of tunable material with large interaction length coupled with a unique physical mechanism of utilizing both excited electric and magnetic dipolar modes and operating at the middle of these geometrical resonances lead to high reflection level varying between 0.6 and 0.8 over entire phase shift coverage of 270°. This design is realized by preventing from the concurrence of the high field confinement and large extinction coefficient which deteriorates the performance efficiency. Under assumption of realization of multi-level partially crystallized GSST from amorphous to crystalline state (equivalent to drastic change of refractive index), the opportunity of robust control over the phase-front of the reflected light is accomplished. An array of GSST nanobars with selective modification of crystallization level is designed in order to perform dynamically controllable wave-front modulation and steer the reflected light toward desired direction. The numerical simulation results reveals that the reflection efficiency of such active structure is greater than 45%.

Appendix I

Heating-induced oxidation of the GSST nanobar is known as one of the possible practical issues which may arise during the experimental implementation. To avoid this undesired phenomenon, the active material can be covered with a SiO₂ capping layer as schematically depicted in Fig. 6(a). In addition, the spacing layer is considered ZnS-SiO₂. The permittivities of ZnS-SiO₂ and SiO₂ are 4 and 2.1025 [60]. A parametric study is carried out to optimize the updated building block and attain wide phase agility and high reflection amplitude. As a result, the structural parameters are chosen as w_GSST=350 nm, P=500 nm, h_GSST=275 nm, $h_{{\text{ZnS-SiO}}_{\text{2}}}$=150 nm, and $h_{{\text{SiO}}_{\text{2}}}$=335 nm (moderate modifications compared to the basic design in Sec. 2.3). The reflection amplitude and phase as functions of wavelength and crystallization level are plotted in Figs. 6(b) and 6(c). As shown in Figs. 6(d) and 6(e), the reflection level varies between 0.6 and 0.8 and the reflected beam can experience 255° phase shift (similar to the reflection performance of the basic design in Sec. 2.3).

 

Fig. 6 (a) The schematic overview of the tunable GSST-based metasurface. The inset shows the proposed building block consisting of a GSST nanobar surrounded by SiO₂ and located on top of a ZnS-SiO₂ spacer and gold substrate. The reflection (b) amplitude and (c) phase of the unit-cell as functions of wavelength and crystallization level. (d)-(e) the results in (b)-(c) at the operating wavelength of 1.55 μm annotated by the black dashed lines.

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Appendix II

In Sec. 2.1, it has been discussed that GSST has promising advantages over two other classical GSTs which are experimentally measured in [19] and [39] in order to realize simultaneous continuous wide phase shift and high reflection magnitude. This will be more clarified by direct comparison of the reflection responses of the building block when the constituent material of the grating nanobars is modified from GSST to GSTs provided in [19] and [39]. A careful investigation is carried out to ensure that the multi-objective parametric study leads to the most possible efficient tunable design. For the classical GST in [19], the structural parameters are selected as w_GST=225 nm, P=355 nm, h_GST=215 nm, and $h_{{\text{MgF}}_{\text{2}}}$=495 nm (case I). The solid blue lines in Figs. 7(a) and 7(b) represent the reflection amplitude and phase versus crystallization level in which the amplitude varies between 0.55 and 0.75 and the phase coverage is ≈180° for the case I. In similar fashion, the proposed unit-cell is redesigned when the PCM nanobars are made from the GST in [39]. The optimized design can be realized when the geometrical parameters are modified to w_GST=375 nm, P=500 nm, h_GST=295 nm, and $h_{{\text{MgF}}_{\text{2}}}$=175 nm (case II). In Figs. 7(a) and 7(b), the red dashed lines are related to the reflection amplitude and phase as function of crystallization level for the case II. It can be clearly seen that the reflection magnitude changes between 0.55 and 0.8 and the reflected beam experiences up to ≈210° phase-shift. The results regarding the GSST-based design which is studied in-depth throughout the manuscript (case III) are also provided in Figs. 7(a) and 7(b) to be easily compared by cases I and II. It can be concluded that when the reflection magnitude is higher than 0.55 for all the three cases, case III can provide the widest phase modulation. It should be mentioned that the structural parameters of case II are only slightly different compared to those of case III studied in Sec. 2.3. The reason behind the fact that case II cannot realize same phase coverage as case III can be revealed by taking into consideration Figs. 1(a) and 1(b) where both of GSST [43] and GST [39] have almost the same extinction coefficient change between amorphous and crystalline but GSST can experience larger refractive index change. To provide complementary information regarding cases I and II, their reflection trends are plotted as functions of wavelength and crystallization level in Figs. 7(c) and 7(d) and Figs. 7(e) and 7(f), respectively. Case II is studied only for wavelengths from 0.8 μm to 1.58 μm due to the lack of experimental data for the optical characteristics of GST at wavelengths higher than 1.58 [39]. It should be emphasized that the utilized optimization techniques for cases I and II have considered all the possible physical mechanisms and they have not been limited to a specific paradigm (e.g., excitation of both ED and MD modes and operating at the middle of them).

 

Fig. 7 The reflection (a) amplitude and (b) phase of the PCMs nanobar for cases I, II, and III as a function of crystallization level at the operating wavelength of 1.55 μm. Reflection phase of the crystalline state (m = 1) is assumed zero. Maps of reflection responses as functions of wavelength and crystallization level for (c)-(d) case I and (e)-(f) case II. The black dashed lines correspond to the desired wavelength of 1.55 μm in (c)-(f).

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Appendix III

In the recent years, great efforts have been taken to realize amorphous-to-crystalline transition in the thicker PCMs films and nanoelements (greater than 100 nm), for example, GST-225 nanobars with thickness of 300 nm (λ/5.16, λ=1.55 μm) [40], 220 nm thick GST nanopillars [41], and multi-level partial crystallization of 170 nm GST-225 thin film [36]. However, the inhomogeneous realization of crystallization inside the optically thick nanoelement/film and unsuccessful full crystallization are still known as persistent challenges. Therefore, the possibility of redesigning the GSST nanobar building block with the thickness smaller than 100 nm (<λ/15.5, λ=1.55 μm) is studied and the reflection response of the optimized design is presented in Fig. 8. The structural parameters are chosen in such a way that there is a reasonable trade-off between the reflection level and phase coverage (w_GSST=680 nm, P=800 nm, h_GSST=90 nm, and $h_{{\text{MgF}}_{\text{2}}}$=10 nm). Figures 8(a) and 8(b) represent the reflection amplitude and phase of such building block as functions of wavelength and crystallization level. It can be observed in Figs. 8(c) and 8(d) that the reflection amplitude is higher than 0.6 and phase agility is 215° (55° smaller than the studied case in Sec. 2.3). It should be also noted that this range of phase modulation could be obtained at the expense of losing the compactness of building block i.e. the periodicity is increased from 440 nm in Sec. 2.3 to 800 nm.

 

Fig. 8 (a)-(b) Maps of reflection responses of an ultra-thin GSST nanobar building block as functions of wavelength and crystallization level when the thickness is only 90 nm (h_GSST). The other structural parameters are selected as w_GSST = 680 nm, P = 800 nm, and $h_{{\text{MgF}}_{\text{2}}}$ = 10 nm. (c)-(d) The reflection amplitude and relative phase shift (the reflection phase of crystalline state is assumed zero) versus crystallization level at the operating wavelength of 1.55 μm.

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Funding

U.S. Air Force Office of Scientific Research (AFOSR) (FA9550-14-1-0349, FA9550-18-1-0354).

Acknowledgments

The authors would like to thank Juejun Hu at Photonic Materials (PMAT) laboratory, Massachusetts Institute of Technology, for his great comments and discussions.

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