Dynamic phase-change metafilm absorber for strong designer modulation of visible light

2.1 Design of near-unity absorptions in a dynamic phase-change metafilm absorber

We start from investigating tunable complex refractive index of a baer 40 nm-thick VO₂ film via the reconfigurable gradual IMT phenomenon. Figure 1A describes measured thermally-driven reconfigurable evolutions of (n, k) at the four representative wavelengths (blue: 473 nm, green: 532 nm, red: 633 nm, and deep red: 700 nm). n and k denote real and imaginary parts of complex refractive index of VO₂, respectively. Interestingly, increase of temperature leads to continuously decreasing tendencies of both n and k values regardless of wavelength while they show simultaneously large values [45]. The gradual IMT between the saturated insulating and metallic phases depends on the intermediate temperatures during heating and cooling processes. It implies that heating and cooling would induce gradual blue and red shifts of resonances in a VO₂-included nanophotonic resonator.

Figure 1:

Concept of dynamically tunable phase-change VO₂ metafilm absorber.

(A) Measured thermally driven cyclic evolutions of (n, k) coordinates of VO₂ at the representative blue (473 nm), green (532 nm), red (633 nm), and deep red (700 nm) colors. (B) Schematic illustration, cross-sectional scanning electron microscopy (SEM) image of the sapphire substrate-VO₂-Ag Gires-Tournois absorber (t = 40 nm), and calculated results of tunable near-unity absorption spectra of the absorber during heating. (C) Complex refractive index map for various materials and VO₂ at the representative four visible wavelengths (B: blue (473 nm), DR: deep red (700 nm)). (D) Schematic description of phase-change metafilm based dynamic Gires-Tournois absorber. SEM image shows cross-sectional image of the fabricated dynamic Gires-Tournois metafilm absorber with Ag filling factor about 0.2. The scale bars in SEM images of (B) and (D) denote 100 nm.

A baer VO₂ film shows low modulation performance owing to theoretically limited maximal absorption of 0.5 [46], [47]. On the other hand, it is well known that a Gires-Tournois VO₂ absorber configuration (Figure 1B and Figure S2 of Supplementary Materials) shows large modulation depth (η_m) of light intensity by excitation and modulation of near-unity absorption. Here, η_m is defined as η_m = |I_i−I_m|/max(I_i, I_m) and I_i and I_m correspond to reflection intensities at the insulating and metallic phases, respectively. The two distinct near-unity absorptions in the insulating and metallic phases at the wavelengths of 655 and 550 nm are verified through the theoretical calculation and measurement (Inset reflectance spectra of Figure 1B and Figure S2 of Supplementary Materials). It means the gradual blue and red shifts of absorption dip with change of the resonance wavelength about 100 nm, respectively. Yet, it is still hard to design tunable near-unity absorption with high reflection tunability by only adjusting thickness of VO₂ film to meet complex interference conditions of reflection phasors in highly dispersive and absorptive PCM such as VO₂ (the Section 3 of the Supplementary Materials).

Here, we introduce a metamaterial-based solution into the Gires-Tournois VO₂ absorber scheme to expand range of possible effective refractive index of VO₂ film by geometric implanting of subwavelength-spaced periodic nanostructures in an intrinsic PCM VO₂, which is called metafilm strategy [48], [49], [50], [51]. We would regard an anisotropic Ag-VO₂ film as a tunable effective metafilm with designed effective refractive index and the designed IMT (DIMT). The first step of designing phase-change VO₂ metafilm is to choose a proper material to embed geometrically in a VO₂ film. Figure 1C describes (n, k) coordinates of the several metals and the two distinct VO₂ phases in the visible range. Once a phase-change metafilm is designed as an effective mixture of VO₂ and another photonic nanostructure, effective refractive index coordinate of a metafilm would be located at somewhere between the coordinates of the photonic material and that of VO₂. Therefore, tunable effective refractive indices at the insulating and metallic phases and thermal transition between those phases could be designed by judicious embedding of certain photonic nanostructures. As shown in Figure 1C, the noble plasmonic metals with less lossy characteristics in the visible range, Al and Ag are the best options to be implanted in VO₂ so that the widest range of artificial (n, k) coordinates can be designed and thermally tuned since their (n, k) coordinates are located the most far from the (n, k) coordinates of VO₂. We select and embed Ag into the 40 nm-thick VO₂ film in the Gires-Tournois VO₂ absorber considering both (n, k) design degree of freedom and stable nanofabrication feasibility rather than Al. As a result, PCMA is constructed as depicted in Figure 1D. We demonstrate nanobeam type metafilm in the PCMA configuration with various Ag filling factors, f_Ag. PCMA depicted in Figure 1D can be approximately modeled as anisotropic effective Gires-Tournois VO₂ absorber where dynamic homogeneous permittivity tensor of VO₂ layer is artificially designated based on effective medium approximation. This simple concept enlarges the fundamental dynamic dielectric function properties in terms of possible range of spatial encoding as well as polarization-controlled characteristics of it in a single certain device while large dynamic tunability is guaranteed.

For systematic design of VO₂ metafilm layer in PCMA configuration, we propose the design rule based on anisotropic counter-intuitive properties of the Wiener’s bounds of effective medium approximation visualized in a complex (n, k) plane [52], [53], [54]. The two bound curves correspond to the normal and parallel effective dielectric functions, ε_TM and ε_TE, depending on f_Ag, respectively. If deep subwavelength resonances around Ag nanobeams are neglected, the ideal analytic first-order approximations of ε_TM and ε_TE are harmonic and arithmetic means of constitutive dielectric functions, respectively [52], [53], [54]. In Figure 2A, B, transverse magnetic (TM) and transverse electric (TE) polarization cases are numerically calculated for f_Ag varying from 0.05 to 0.95 based on complex reflection and transmission coefficients [55], [56].

Figure 2:

Design principles of anisotropic effective complex refractive indices of VO₂ metafilm and designed reflection tunability.

The numerically retrieved Wiener bounds of effective refractive indices with corresponding reflectance maps at the (A) green (532 nm) and (B) red (633 nm) colors. The points marked as Ag, i-VO₂, and m-VO₂ correspond to (n, k) coordinates of Ag, high index VO₂ at the insulating phase, and low index VO₂ at the metallic phase at the certain wavelengths, respectively. The white and black dotted lines denote effective refractive index coordinates with VO₂ at the insulating and metallic phases, respectively. ND in (A) and (B) implies nanodisk. The ND curves in (A) and (B) imply the VO₂ metafilm cases where isotropic circular Ag nanodisks are embedded in the VO₂ layer with same f_Ag (=πr²/p² where r and p are radius and period of Ag nanodisks) values compared to the Ag nanobeam embedded metafilm absorbers. f_Ag values of nanobeam and nanodisk type metafilms are varied from 0.05 to 0.95, and from 0.05 to 0.45, respectively. (C) Schematic illustration of intended mechanism and working principle of dynamic Gires-Tornois metafilm absorbers according to periodic photonic doping level of Ag nanobeams. (D) Schematic unitcell description with sidewall tapering effect and top view SEM images of the phase-change metafilm absorbers (PCMAs). Scale bars denote 500 nm.

The effective refractive index retrieval results regarding subwavelength resonant behaviors show similar trend of the zeroth order effective medium approximation (Figure S4 of Supplementary Materials). As f_Ag increases, effective refractive indices for TM and TE polarizations, εTM=(fAgεAg−1+(1−f)εVO2−1)−1 and εTE=fAgεAg+(1−fAg)εVO2, start to deviate from coordinates of metallic (m-VO₂) and insulting phases (i-VO₂) along the highly curved and nearly linear two-dimensional paths, respectively (Figure 2A, B). The real parts of ε_TM and ε_TE, increase and decrease, respectively, according to the increase of f_Ag for values under 0.5. As shown in Figure 2A, B a designed anisotropic (n, k) clearly yields the large anisotropic changes near the near-unity absorptions from the IMT (the gray arrow in Figure 2A, B) to the two DIMTs (the orange arrow in Figure 2A, B when f_Ag is 0.2). On the other hand, embedding isotropically-shaped Ag nanodisks (marked as ND in Figure 2A, B) do not make significant phase-change tunability when compared to intrinsic one and Ag nanobeam embedded cases (See the Section 4 of Supplementary Materials for the details).

Therefore, it is intuitively expected that the opposite trends of red (for TM) and blue (for TE) shifts of intrinsic absorption dips occur at the both VO₂ phases in the same PCMA with certain f_Ag of Ag nanobeams as described in Figure 2C. In other words, by designed increase and decrease of effective refractive indices of a metafilm layer, both the blue and red shifts of active near-unity absorption can be demonstrated via polarization-controlled operations in a PCMA with certain geometric parameters. The top subfigure of Figure 2D describes the periodic (period of 250 nm) unit cell of PCMA with Ag nanobeams considering tapering effect of ion beam milling fabrication. The four images below the subfigure are top view scanning electron microscopy (SEM) images of the fabricated nanobeam type PCMAs with the four different f_Ag values (Figure S5 of Supplementary Materials). The fabricated samples would be called as the NB1 (f_Ag = 0.17), NB2 (f_Ag = 0.23), NB3 (f_Ag = 0.34), and NB4 (f_Ag = 0.40). The corresponding parameter sets of (w₁, w₂) of the NB1, NB2, NB3, and NB4 are (18 nm, 51 nm), (20 nm, 70 nm), (40 nm, 94 nm), (40 nm, 120 nm), respectively. Here, NB stands for nanobeam. The difference between w₁ and w₂ accounts for modeling of abovementioned realistic tapering effect in ion beam milling fabrication.

2.2 Underlying physics of tunable phase-change effects using Ag nanobeams

In this section, the physical mechanisms of tunable effective refractive indices and their thermal DIMTs are theoretically studied with respect to effective medium approximation and Fano-like resonance interpretation of the near-unity absorptions. The theoretical concern starts by re-considering validity and assumption of effective medium theory discussed in the previous section. Based on the literature [54], [55], [56] and our numerical data of effective refractive index retrieval (Figure 2A, B and Figure S4 of Supplementary Materials), it is clear that the zeroth order approximation of effective medium approximation is only useful for prediction of anisotropic trend rather than calculation of exact effective refractive index values as the period of nanobeams (250 nm) is not small enough to guarantee the validity of the approximation.

The nanoscale physical origins of such difference between numerically retrieved effective refractive index and the zeroth order analytic effective medium approximation can be explained in terms of plasmonic and Mie-like resonances around Ag nanobeams. In case of TM polarized illumination, Ag nanobeams excite surface plasmons at the both VO₂-Ag and Al₂O₃–Ag interfaces (Figure 3A, B). If f_Ag is low and widths of nanobeams (w₁ and w₂) are narrow, near-unity absorption occurs mainly at the Ag-VO₂ interface between Ag nanobeams as shown in Figure 3A. However, if f_Ag, w₁, and w₂ increases, incident field funneling into the VO₂ region between Ag nanobeams gets harder while surface plasmon oscillation at the Al₂O₃–Ag interface gets easier with the increased interface length and SP excitation efficiency at the boundary of Al₂O₃–Ag. As refractive index of Al₂O₃ and effective SP mode index at the Al₂O₃–Ag interface is smaller than that of VO₂ and that at the VO₂-Ag interface, resultantly, overall effective resonance area increases by increase of f_Ag. On the other hand, as TE illumination cannot excite SPs, the dominant region of light trapping and absorbing is the inside of the dielectric VO₂ nanobeams capped between the Ag nanobeams via leaky Mie-like TE resonance (Figure 3C, D). As a result, the decreased size of VO₂ nanobeams owing to increased f_Ag induces decrease of effective resonator size and blue shift of resonance. In Figure 4A–H, anisotropic designer shifts and thermal tunings of near-unity absorption dips in the devices are verified numerically (Figure 4A–D) and experimentally (Figure 4E–H). When we compare Figure 4A–D, the red (TM) and blue (TE) shifts of the near-unity absorption dips owing to the opposite changes of the effective refractive indices are numerically verified according to the increase of f_Ag.

Figure 3:

Nanoscopic mechanisms of the resonant near-unity absorptions: subwavelength light funneling into the metafilms.

Electromagnetic field profiles of (A, C) NB1 and (B, D) NB4 devices are numerically investigated at the resonances in the insulating phase for (A, B) TM and (C, D) TE illumination, respectively. Upper figures show the (A, B) E_z and (C, D) H_z, with the normalized black vector arrows of (a, b) displacement current and (c, d) magnetic field, respectively. Lower figures show normalized electromagnetic field profiles of (A, B) |H_y|² and (C, D) |E_y|². Black lines in the lower figures depict the flow of Poynting vectors coming from the free space of Al₂O₃ substrate to the PCMA structures. The scale bars correspond to 60 nm.

Figure 4:

Effects of Ag nanobeams on the dynamic modulation range.

Polarization and temperature dependent reflectance spectra of the PCMAs with varying f_Ag (0, 0.17, 0.23, 0.34, 0.4) obtained from (A–D) simulations and (E–H) experiments. (A, B, E, F) present polarization dependent spectra at the cold insulating phase of VO₂ while (C, D, G, H) present those at the hot metallic phase of VO₂. (A, C, E, G) and (B, D, F, H) show reflectance under TM and TE polarized normal illumination cases, respectively. The legend, TF, refers to the case of intrinsic thin film VO₂ without Ag embedding (the Gires-Tournois VO₂ abosrber case when f_Ag is zero). The direction of gradually colored arrows in (A-H) imply the increase of f_Ag.

Moreover, it is noteworthy that large near-unity absorption is achieved even though f_Ag increases so that large modulation depth is still achieved over the two wavelength bands for a certain PCMA device under the two polarizations (TM and TE). Figure 4E–H successfully verifies the numerical designs of extraordinary modulations via experimental results. We fabricated the micron scale PCMAs via four steps with pulsed laser deposition, e-beam evaporation, and focused ion beam milling. We measured the temperature-dependent backscattering spectra from the PCMA samples (See Experimental sections for the details.).

The f_Ag-controlled design of reflection spectra in Figure 4 involves the fascinating interference phenomena through the two distinct reflection mechanisms owing to both effective medium approximation and the subwavelength absorption resonances (Figure 3). Here, we introduce Fano-like resonance modeling based on temporal coupled mode theory for quantitative analysis on the two effects to understand the underlying mechanisms of the high-contrast reflection wave modulations. Over the decade, temporal coupled mode theory has been widely utilized to interpret Fano and Fano-like resonances stemming from interference between direct and in-direct scatterings of transmission and reflection waves [57], [58], [59], [60], [61]. In this case, the proposed PCMA can be modeled as a resonator with a single port and a single resonance at the each VO₂ phase (Figure 5A). Here, a direct reflection wave can be explained by the Fresnel-Airy reflection formula based on the first order analytic effective medium approximation (Section 6 of Supplementary Materials) and in-direct reflection wave can be modeled as scattering from TM (plasmonic) and TE (Mie-like) resonances discussed above [58], [61].

Figure 5:

Fano-like resonance modeling.

(A) Schematic illustration of the modeling of the dynamic dual resonances as Fano-like interferences between direct and in-direct reflection waves. (B, C) Indirect reflectance spectra of the NB1 metafilm when f_Ag is 0.17 neglecting tapering walls and their Lorentzian fitting results. The Indirect reflectance spectra and their fitting results for (B) TM and (C) TE polarizations, respectively. The legends account for polarization direction and phase of VO₂. The dashed lines in (B) and (C) are the results of Lorentzian fitting near resonances.

Assuming eiωt time dependence of modes, total complex reflectivity (r_tot), a sum of direct (r_d) and in-direct (r_id) ones, can be derived as Eq. (1) (See Section 6 of Supplementary Materials for derivation.).

Here, D, γ, ω₀, and φ are real valued constants and D, γ, and ω₀ are positive real values. The fitting to extract proper D, γ_tot, ω₀, and φ is conducted as follows. At first, r_id is calculated by subtracting analytic r_d based n_eff from r_tot obtained from numerical full field simulation and Rid(=|rid|=D2/{(ω−ω0)2+γror2}) is fitted according to Lorentzian function to determine D, γ, and ω₀. Then, using the fitted parameters, φ=∠rid+tan−1((ω−ω0)/γtot) is calculated for TM and TE resonances at the both phases of VO₂ (See Figure 5B, C, and Section 7 of Supplementary Materials). But the validity of this modeling is based on the assumptions of low γ_tot and single in-direct resonance mode at ω₀ [54], [55], [57]. As shown in the plots in Figure 5B, C and Figure S6A of Supplementary Materials, it is revealed that the dynamic resonances of the NB1 metafilm absorber can be well interpreted as Fano-like resonances through good numerical fittings of r_id. On the other hand, the indirect TM and TE reosnances of the NB4 absorber are not clearly fitted at the both phases of VO₂ (Figure S6 B, C). It is basically due to enalarged loss and γ_tot of the NB4 absorber with larger f_Ag which induces severe violation of the two assumptions (Tables S1 and S2 of Supplemenatry Materials), modeling of a single, high quality factor resonance [58], [60].

2.3 Versatile optical applications and design extensibility

In this section, we prove excellent multiple functionalities of a single PCMA device as dynamic optical applications based on high-contrast gradual phase-change capabilities and polarization-controlled responses. As the NB1 sample with f_Ag about 0.17 shows the best (high-contrast and largely anisotropic) dynamic performances of near-unity absorptions among the demonstrated NB-type samples, it is considered to investigate gradual thermal modulation of both large anisotropy and near-unity absorptions. Figure 6A, B exhibit gradual blue shifts of resonance in the NB1 sample in cases of TM and TE-polarized illuminations via thermal heating in the different wavelength regions. It implies that the NB1 sample with a fixed geometry can continuously shift a near-unity absorption dip in a broad bandwidth of wavelength ranging from about 530 nm to about 670 nm by help of polarization control. Under TM and TE polarizations, blue shifts of absorption dips are verified from about 670 to 590 nm and from about 570 to 530 nm, respectively. The gradual measurement results of the NB1 sample show good agreement with numerical simulation results both in heating and cooling processes (Figure 3A, B and Section 8 of Supplementary Materials).

Figure 6:

Optical applications of an anisotropic PCMA: modulation of intensity, color, and polarization.

(A, B) Heating induced gradual tuning of near-unity absorption spectra of the NB1 sample under illumination of (A) TM- and (B) TE-polarized light, respectively. Anisotropic broadband modulation depth spectra of reflection intensity from the NB1 sample obtained from (C) full-field simulation and (D) experiment. (E) Polarization-dependent gradual multi-level coloring of the NB1 sample described in CIE space. (F) Polarization rotation controlled intermediate color generations with the NB1 sample between TE and TM curves during the heating processes. The inset figure depicts top view scheme when linearly polarized light normally illuminates the sample with rotation angle, θ. (G, H) Thermally switchable R_TE/R_TM of the NB1 device, at the wavelength of 590 nm derived from (G) simulation and (H) experiment, respectively.

These largely anisotropic and gradually tunable phase-change characteristics of a single PCMA device can be applied to multiple high-contrast modulations of broadband intensity, reflected color, and polarization direction. Numerical and experimental results of Figure 6C, D shows that intensity of reflected wave is thermally modulated with large modulation depth over broad bandwidths both for TM and TE polarizations. In terms of the locations of modulation depth minimum and maximum, the results of the simulation and measurement show good agreement. However, the maximum value of measured modulation depth (∼0.6) is a bit lower than that of simulation (∼0.9). We guess that a bit larger reflectance of measurement rather than simulation is mainly due to offset baseline reflection from the air-substrate side (seen in measurement configuration in Figure S11) not considered in simulations, and sidewall imperfection of fabrication (seen in Figure S5). In particular, the baseline reflection from air-sapphire substrate for normal illumination is about 0.077 (7.7%) at the wavelength of 600 nm, which is a considerable value when calculating modulation depth.

Moreover, color spectrum and polarization direction of reflected light are also gradually modulated with high contrast in the certain device. Figure 6E shows thermally-driven gradual color generation along largely separated Commission internationale de l’éclairage (CIE) curves according to polarization direction. Blue to light violet and violet to orange thermal colorings are verified experimentally under illumination of TM and TE polarizations, respectively. Here, reflection Jones matrix of a PCMA, r(λ, T), can be written as the Eq. (2).

In this formalism, (1 0)^T and (0 1)^T correspond to TE and TM polarization Jones vectors while rTE and rTM are complex reflectivity values dependent on operation wavelength and temperature, respectively. The intermediate colors in a CIE space between the curves for two orthogonal polarizations can be formulated as Rθ(λ,T)=RTE(λ,T)cos2θ+RTM(λ,T)sin2 when RTE=|rTE|2 and RTM=|rTM|2. Such dynamic colorings are demonstrated with intermediate polarization direction rotated (rotation angle of θ) from TM or TE (illustrated in the sub-figure of Figure 6F). In Figure 6F, the red and blue dotted-curves correspond to the cases when polarization rotation angle, θ, is 15 ° and 45 °, respectively.

In case of polarization direction, tunable polarization filtering between nearly-TM and nearly-TE polarizations can be achieved at certain resonant wavelength. In Figure 6A, B, the near-unity absorption dip of the NB1 sample at the insulating phase for TE polarization and that at the metallic phase for TM polarization are closely met (The dip wavelengths are about 610 and 590 nm, respectively. Also see Section 9 of Supplementary Materials.). At the wavelengths near those dip positions, 590 and 610 nm, reflectance is highly anisotropic. Particularly at the wavelength of 590 nm, numerically calculated reflectance ratio defined as R_TE/R_TM = |r_TE/r_TM|² is modulated between about 0 and 14 via heating and cooling (Figure 6G and the Section 8 of Supplementary Materials). As described in Figure 6H, experimental results at the same wavelength exhibit similar trend that reflectance ratio is modulated between about 0.5 and 3.3 in the reconfigurable manner with hysteresis.

As discussed above, it has proved that multi-functional optical applications with the capability of high contrast active thermal modulation are achieved with the PCMAs. Lastly, we would address the design extensibility of the concept for more design degree of freedom in a simple method. Once effective refractive indices of a certain metafilm layer is numerically characterized, this layer can be coupled with other thin film resonators vertically as an example described in Figure 7A. Then, it is possible to calculate reflectance and its tunability only by transfer matrix method without numerical full-field simulations. In case of an example of PCMA heterostructure in Figure 7A, it can exhibit not only near-unity absorptions but also resonant reflection peaks mainly stemming from a Si₃N₄ etalon. As the transparent dielectric film can induce reflection peaks of Fabry-Pérot resonance (See field profiles in sub-figures of Figure 7B, C), a change of VO₂ phase can induce change of coupling between reflective Fabry-Pérot resonance and thermally shifted absorption dip of PCMA. Thus, as shown in Figure 7B, C, thermally-driven blue shifts of absorption dips induce weakened Fabry-Pérot resonance strengths with polarization-dependent manners. Variation of t_f would enable shift of a spectral location of a Fabry–Pérot peak and more diverse spectral tunability in the visible spectrum, potentially. In the perspective of dynamic color generation, this novel and simple strategy can dynamically enhance and tune purities of reflection color (Figure 7D) without significant fabrication problems compared to the original PCMA devices. Such PCMA heterostructures also hold a potential of vertical integration with other functional metasurfaces [62], [63], [64].

Figure 7:

Dynamic metafilm heterostructure absorber: extensibility of the phase-change metafilm for extraordinary spectrum tunability.

(A) Schematic illustration of of Si₃N₄ film inserted PCMA heterostructure using the NB1 metafilm. Phase-change tunability of device described under (B) TM and (C) TE illuminations, respectively. Sub-figures of (B, C) present spatial intensity profiles of H_y and H_x fields at the reflection peaks at the insulating phase, respectively. The legends in (B, C) describe phase of VO₂ and value of t_f. (D) Reflected anisotropic color tunability of the device described in (A) is graphically shown in CIE space. The legends imply polarization and values of t_f (200 and 300 nm).

4.1 Sample fabrication

The device was fabricated through the four steps. Firstly, we use a pulsed laser deposition method (LAMBDA PHYSIK, COMPEX 205) with a KrF excimer laser at 248 nm for deposition of 40 nm-thick VO₂ on a sapphire substrate. Secondly, 150 nm-thick Ag was deposited for a hard mask on a VO₂ film by e-beam evaporation (Korea Vacuum Tech, KVE-3004). Then, 10 μm by 10 μm sized nanobeam-type patterns were defined by focused ion beam milling machine (FEI, Quanta 200 3D). Ag hard mask enables accurate high resolution focused ion beam patterning in large area and protects VO₂ film from direct stoichiometric Ga⁺ ion contamination which would deteriorate molecular bonding structure as defects [23]. At last, we deposited a 200 nm-thick Ag film by e-beam evaporation to form metallic inclusions and mirrors.

4.2 Material property measurement

Temperature-dependent cyclic evolution of dielectric functions of 40 nm-thick VO₂ film is measured by using a variable angle spectroscopic ellipsometer system (J. A. Woollam, V-VASE) and temperature-controlled Peltier stage (Linkam, PE120). The complex refractive indices and effective exact thickness of VO₂ film have been fitted by Kramers-Kroning relation and general oscillator model with combination of Tauc-Lorentz, Lorentz, and Drude oscillators (Section 10 of Supplementary Materials). We used the measured permittivity data of metals and Al₂O₃ measured by E. D. Palik [65] and I. H. Malitson [66]. Temperature-dependent resistivity of a VO₂ film is measured for the verification of IMT phenomena using a source meter, a hot plate, and a thermocouple (Figure S12 of Supplementary Materials). Atomic force micrograph (Park Systems, XE150) is scanned with non-contact type tip for surface roughness and grain measurement of VO₂ film (Figure S10 of Supplementary Materials).

4.3 Temperature-controlled bright field backscattering spectroscopy and imaging

Bright field backscattering spectra from microscopic metafilm samples are measured using our custom-built setup with an optical microscope and spectrometer (Princeton Instruments, SpectraPro 2300) (Figure S11 of Supplementary Materials). Temperature of the samples were controlled by Peltier stage (Linkam, PE120) in our thermostatic laboratory of about 20 °C. Spectral data is scanned over about 6 μm by 6 μm region of samples through an aperture of spectrometer. Broadband illumination of white light (Thorlabs, MNWHL4 LED) is focused on the sample through the iris, broadband polarizer, and 50X objective lens. The spectra are normalized by the reflection spectrum from a sapphire substrate coated by optically thick silver film (deposited with the thickness over 500 nm by e-beam evaporation). The 100X magnified charge coupled device images are captured under the incidence of our neutral white light emitting diode.

4.4 Numerical simulation

Electromagnetic full field simulations are conducted with commercial finite element method tool (COMSOL Multiphysics 5.3, RF module, Frequency domain solver).