Tunable dual-band and high-quality-factor perfect absorption based on VO 2 -assisted metasurfaces

: Perfect absorbers with high quality factors ( Q -factors) are of great practical significance for optical filtering and sensing. Moreover, tunable multiwavelength absorbers provide a multitude of possibilities for realizing multispectral light intensity manipulation and optical switches. In this study, we demonstrate the use of vanadium dioxide (VO 2 )-assisted metasurfaces for tunable dual-band and high-quality-factor perfect absorption in the mid-infrared region. In addition, we discuss the potential applications of these metasurfaces in reflective intensity manipulation and optical switching. The Q -factors of the dual-band perfect absorption in the proposed metasurfaces are greater than 1000, which can be attributed to the low radiative loss induced by the guided-mode resonances and low intrinsic loss from the constituent materials. By utilizing the insulator–metal transition in VO 2 , we further proved that a continuous tuning of the reflectance with a large modulation depth (31.8 dB) can be realized in the designed metasurface accompanied by a dual-channel switching effect. The proposed VO 2 -assisted metasurfaces have potential applications in dynamic and multifunctional optical devices, such as tunable multiband filters, mid-infrared biochemical sensors, optical switches


Introduction
Metasurfaces are planar arrays composed of artificial nanostructures on a subwavelength scale, which have shown unprecedented capabilities to manipulate the amplitude, phase, and polarization of optical waves [1][2][3].Owing to the extensive and rapid development of metasurfaces, they have emerged as a versatile platform for the implementation of integrated, miniaturized, and intelligentized optical devices [4].Latest developments on metasurfaces show their importance in a series of key applications in nanophotonics, such as full-Stokes polarization cameras, high-performance structural color, and aberration-corrected three-dimensional positioning [5][6][7].Although metasurfaces have achieved great success, the metasurfaces in most previous studies were static in nature, resulting in fixed optical functionalities.Compared to passive metasurfaces, tunable metasurfaces whose optical functionalities can be dynamically manipulated in both the space and time domains have attracted increasing attention from researchers in both nanophotonics and other disciplines [8].Owing to the rapid development and application of artificial intelligence in nanophotonics, the design and investigation of tunable metasurfaces will open new horizons for the development of self-adaptive and intelligent optical devices [9,10].
Using active materials as the constituent materials of metasurfaces is a common and effective approach to realize tunable metasurfaces.For example, biased diodes are widely used in the gigahertz region; semiconductors and perovskites are mainly used in the terahertz region; and two-dimensional (2D) materials, liquid crystals, germanium antimony telluride (GST), and vanadium oxide (VO 2 ) are widely used in the visible and infrared regions [11].By applying different external stimuli, such as heating/cooling, mechanical actuation, and optical pulses, a large contrast in the optical constants of the active materials can be produced, which results in a significant modulation of the optical responses of metasurfaces.As a strongly correlated electron phase-transition material, VO 2 plays an important role in the evolution of tunable metasurfaces.In VO 2 , the insulator-metal phase transition at approximately 68 °C causes a significant change in its dielectric permittivity.Because the phase transition in VO 2 can be driven by different external stimuli such as heating/cooling, light pulses, and intense electromagnetic fields, the VO 2 -assisted metasurfaces have emerged as an appealing alternative to realize the dynamic manipulation of optical waves [11,12].In recent advances, VO 2 -assisted metasurfaces have been widely used to realize optical modulators, dynamic light focusing, switchable chirality, and tunable perfect absorption [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].In particular, continuous reflectance tuning and switchable perfect absorption based on VO 2 -assisted metasurfaces have attracted great interest owing to their flexible and reconfigurable performances [21][22][23][24][25].For example, by integrating VO 2 into a metasurface plasmonic absorber structure, Liu et al. experimentally demonstrated an electrically active metasurface in the mid-infrared region, which can be used for continuous reflectance spectrum tuning and switchable absorption [28].However, owing to the high intrinsic loss of plasmonic absorbers, the absorption spectra in several previous studies are typically broadband [21][22][23][24][25][26][27].Tunable perfect absorption with high Q-factors based on VO 2 -assisted metasurfaces, which is important for high-performance biosensors, narrowband filters, and infrared spectroscopy [29-32], has not yet been explored.
In this study, we theoretically and numerically demonstrated tunable perfect absorption with high Q-factors in a designed VO 2 -assisted metasurface.The absorption peaks with near-unity absorptance at 3049.9 and 3604.2 nm are validated by both simulated and theoretical results, and the Q-factors of these two peaks are 1112.8and 1381.1, respectively.The high-quality-factor perfect absorption in the proposed design is mainly attributed to the low radiative loss induced by the guided-mode resonances and low intrinsic loss from the constituent materials.A continuous tuning of the reflectance can be realized in the designed metasurface by utilizing the thermally induced insulator-metal transition in VO 2 .Therefore, the proposed VO 2 -assisted metasurface can be used as a dual-channel ultra-narrow-band optical switch, in which the reflectance modulation depths are 16.1 and 31.8 dB at 3049.9 and 3604.2 nm, respectively.We further demonstrate a dual-band optical switch with opposite switching characteristics ("on" or "off") at two working wavelengths by adjusting one of the structural parameters.Numerical analysis also shows that multiband and high-quality-factor absorption can be implemented in the designed metasurface for oblique transverse magnetic (TM) polarized illumination.Our study reveals the underlying physics of the realization of VO 2 -assisted-metasurface-based tunable high-quality-factor perfect absorption, which provides useful guidance for researches on tunable optical devices with high Q-factors.

Results and discussion
Figure 1(a) illustrates the active manipulation of the optical responses of the designed VO 2 -assisted metasurface.The metasurface can be treated as a perfect absorber at 60°C, partial reflector at 70°C, and highly efficient reflector at 88°C.Moreover, the continuous tuning of the reflectance can be implemented in the designed metasurface by utilizing the thermally induced insulator-metal transition in VO 2 .Figure 1(b) schematically illustrates the unit cell of the proposed metasurface.The designed VO 2 -assisted metasurface consists of VO 2 nanodisks, an amorphous silicon (a-Si) layer, aluminum oxide (Al 2 O 3 ) dielectric layer, and aluminum layer.The structural parameters of the designed metasurface were: p = 1300 nm, S = d/p = 0.3, t 1 = 400 nm, t 2 = 500 nm, and t 3 = 250 nm.Furthermore, the thickness of the aluminum layer was set to 300 nm to ensure zero transmittance.The finite-difference time-domain (FDTD) method was used to simulate, analyze, and explore the characteristics of the designed metasurface.In the simulation, the refractive index of Al 2 O 3 was taken as 1.70, and the optical constants of aluminum in the mid-infrared region obtained by linear interpolation of the experimental data were used [33].VO 2 was simulated using thermally tunable relative permittivity [34].The dielectric constants of a-Si were obtained from Palik ′ s Handbook [35].To illustrate the high-quality-factor perfect absorption in the designed VO 2 -assisted metasurfaces, we first simulated the absorption spectrum under TM-polarized normal illumination at 60 °C, as shown in Fig. 2(a).The absorption peaks with near-unity absorptance (over 97.70%) were observed at λ 1 = 3049.9nm and λ 2 = 3604.2nm, and the Q-factors of these two peaks were 1112.8 and 1381.1, respectively.The perfect absorption in the proposed metasurface is polarization-independent for normal incidence because the VO 2 nanodisk in the unit cell is isotropic in both the x and y directions.Meanwhile, we utilized the coupled mode theory (CMT) to further describe the input-output properties of the designed metasurface.Owing to the existence of the aluminum layer, the designed metasurface can be viewed as a single-port system, in which the transmittance is equal to zero.Accordingly, the absorption of the designed system can be characterized by the CMT [36,37]: Here, δ and γ describe the intrinsic loss rate and external leakage rate of the designed system, respectively, and ω 0 is the resonance frequency.According to Eq. ( 1), perfect absorption can be achieved at the resonance frequency (ω = ω 0 ) when the external leakage rate and intrinsic loss rate are equal (δ = γ), which is known as the critical coupling.As shown in Fig. 2(b), the fitted absorption spectra using the CMT and the simulated absorption spectra are consistent, which suggests that the CMT can provide a reasonable elucidation of the designed metasurface.Meanwhile, for this single-port system, the effective impedance of the absorber can be expressed as [38,39] Here, S 11 is the complex reflection coefficient of a single port.To achieve total absorption, the reflection must be completely suppressed (that is, |S 11 | = 0).This corresponds to perfect impedance matching, that is, Z = Z 0 = 1, where Z 0 is the effective impedance of the free space.Therefore, the calculated effective impedances of the designed metasurface at the resonance wavelengths λ 1 and λ 2 are Z 1 = 0.9899 + 0.2944i and Z 2 = 0.9701 + 0.0417i, respectively.These impedances are approximately equal to the effective impedance of the free space, thereby validating the perfect absorption at the two resonance wavelengths.
To reveal the physical mechanism of the high-quality-factor perfect absorption in the designed VO 2 -assisted metasurfaces, we simulated the electromagnetic field distributions at the two resonance wavelengths, as shown in Fig. 3(a) and 3(b).The field distributions indicate that typical TM 0 and TE 0 modes of the waveguide are formed at λ 1 = 3049.9nm and λ 2 = 3604.2nm respectively, which represent the existence of the guided-mode resonances.At 60 °C, VO 2 is in the insulator phase, thus the VO 2 nanodisk array can be viewed as a 2D dielectric grating.Therefore, the VO 2 nanodisks and the a-Si waveguide layer as a whole can be regarded as a typical resonant waveguide grating.It causes coupling between the incident light and the a-Si layer where most of the fields are localized [40,41].Thereafter, most of the localized field energy is absorbed by the bottom aluminum layer, and the rest is consumed by the upper VO 2 disks and a-Si layer.The high-quality-factor perfect absorption in the designed VO 2 -assisted metasurfaces can be attributed to the low radiative loss and low intrinsic loss [42].The guided-mode resonances with low radiative loss are excited, and the extremely small extinction coefficient of the VO 2 and a-Si induces a low intrinsic loss.Meanwhile, the electromagnetic fields near the aluminum layer are relatively small, which also results in a low intrinsic loss.In addition, utilizing a multilayer dielectric Bragg reflector instead of a lossy metal film may produce a higher Q-factor owing to its reduced intrinsic loss, which will also cause the structure to become thicker [37,38].
The high-quality-factor near-perfect absorption in the designed metasurfaces is directly related to the critical coupling induced by the guided-mode resonances.Hence, the variations in the structural parameters d, p, t 1 , t 2 and t 3 have a significant effect on the excitation of the guided-mode resonances, which will significantly change the absorption characteristic of the designed metasurface.We further analyzed the influence of the structural parameters on the absorption spectrum of the designed metasurface to determine the physical mechanism.The simulated results are presented in Fig. 4. With the increase of the ratio S (representing the increase in d), the external leakage rate γ significantly increased, while the intrinsic loss rate δ is slightly affected (owing to the extremely small extinction coefficient of VO 2 at 60 °C).Consequently, a transition from undercoupling (S = 0.20) through critical coupling (S = 0.30) to overcoupling (S = 0.40, 0.50) can be observed in Fig. 4(a), where the near-unity absorptances are achieved at the critical coupling condition and the larger or smaller S parameters will cause the absorptances to go down [37,43].The variation trends of the absorption spectra with the changes in p and t 2 are analogous, as shown in Fig. 4(b) and 4(d).The linewidths of the absorption peaks remain unchanged owing to the relative stability of both external leakage rate γ and intrinsic loss rate δ with variations in p and t 2 .Meanwhile, the two resonant peaks undergo a redshift with the increase of the period p and α-Si waveguide thickness t 2 .The increase of period p is equivalent to the amplification of the structure perpendicular to the propagation direction (the diameter of VO 2 nanodisks d = S * p, here, S is constant), which causes the resonant wavelengths to increase.The phase matching condition between the incident light and a lateral waveguide mode will be satisfied at a longer wavelength when the α-Si waveguide thickness t 2 is increased, leading to the redshift of the resonant wavelengths for guided-mode resonances [41].
Differently, as shown in Fig. 4(c), owing to the fact that guided-mode resonances are weakly perturbed by the depth of upper VO 2 grating for the proposed structure, the resonance peak positions and efficiencies show good robustness to changes in thickness t 3 .The results in Fig. 4(e) indicate that the absorptance at the two resonance peaks reaches a maximum when t 1 = 400 nm, for which critical coupling is induced.Correspondingly, undercoupling and overcoupling are produced for t 1 = 300 nm and t 1 = 500 nm, respectively, resulting in a decrease in the absorptance.The intrinsic loss rate δ decreases with the increase of the Al 2 O 3 dielectric layer thickness t 1 , while the external leakage rate γ is relatively robust [44].As a result, the Q-factors of the absorption peaks become higher with the increase of t 1 .In fact, the dispersion of the extinction coefficient from the constituent materials in the wavelength region also affects the intrinsic loss rate δ.This effect can be ignored within a certain range of parameter changes, according to the simulation results.To verify the feasibility of the experiment, we further analyzed the effects of higher material loss of fabricated sample on the absorptances at the resonance wavelengths.As shown in Fig. 4(f), when the imaginary part of the relative permittivity of VO 2 increases from 0.05 to 0.25, the near-perfect absorption can still be achieved at λ 2 = 3604.2nm and over 89.5% absorptances can be maintained at λ 1 = 3049.9nm, which show the robustness of the proposed structure to material loss.As a matter of fact, the loss of VO 2 in the dielectric phase can be further reduced by cooling the structure.The results shown in Fig. 4 further validate the physical mechanism presented in this study.
Using the thermally induced insulator-metal transition in VO 2 , the critical coupling caused by the guided-mode resonances in the designed metasurface can be dynamically manipulated, thereby resulting in the active control of the absorption characteristic of the designed metasurface.To display the dynamic manipulation capability of the designed metasurface, we simulated the absorption spectra of the designed metasurface at different temperatures, as shown in Fig. 5(a).The results indicate that thermally induced continuous tuning of the absorptance is achieved at the resonant wavelengths λ 1 and λ 2 , which can be attributed to the disruption of the balance between the radiative loss and the intrinsic loss.With the increase in the temperature, VO 2 gradually transmits from the dielectric phase to the metallic phase, resulting in substantial changes in both real and imaginary parts of its permittivity.The phase transition induces a gradual reduction of the refractive indices of VO 2 , to some extent, resulting in less incident light is coupled into the α-Si waveguide layer.More importantly, a higher intrinsic loss is produced as the extinction coefficient of VO 2 increases significantly, leading to larger resonance widths (lower Q-factors).The thermally induced continuous tuning of the absorptance in the designed metasurfaces is equivalent to a continuous tuning of the reflectance because the sum of the absorptance and reflectance is equal to 1.It is worth mentioning that switching between broadband reflection and absorption beyond 80% absorption efficiency with raising the temperature from 60 °C to 88 °C, as shown by the gray shaded area in Fig. 5(a).At 88°C, VO 2 is in the metal phase, a vertical Fabry Perot-like mode is formed between the upper metal-phase VO 2 and bottom Al metallic layer due to the higher thickness of the spacer layer (α-Si and Al 2 O 3 ) [2,45].As a result, the field enhancement is mainly concentrated near upper VO 2 and the incident light is mainly absorbed by the VO 2 , resulting in the broadband high-efficiency absorption.In addition, as shown in Fig. 5(a) and 5(b), the designed metasurface can be considered as a dual-channel optical switch with the "off/off" state at 60°C and "on/on" state at 88 °C.Here, the "off" and "on" states correspond to high absorption and reflection rates, respectively.The reflectance increases from −16.5 dB (A = 97.74%) to −0.4 dB (R = 91.63%)at λ 1 = 3049.9nm and from −32.7 dB (A = 99.95%) to −0.9 dB (R = 80.84%) at λ 2 = 3604.2nm with the increase in the temperature from 60°C to 88°C.This result in the large modulation depths of 16.1 dB at λ 1 and 31.8 dB (approximately three orders of reflection modulation depth) at λ 2 .To the best of our knowledge, more than three orders of reflection modulation depth have not yet been reported for VO 2 -assisted metasurfaces.In the designed metasurface, the critical coupling induced by the guided-mode resonances can be realized under different working wavelengths at a fixed temperature and different resonant wavelengths at different temperatures by changing the structural parameter S. As shown in Fig. 6, a dual-band optical switch with opposite switching characteristics ("on" or "off") at two working wavelengths can be obtained for S = 0.75.The results in Fig. 6(a) indicate that the designed metasurface achieves critical coupling at the resonance wavelengths λ 1 = 2564.1 nm (Q = 102.6)and λ 2 = 3173.6nm (Q = 46.9)at 60°C and 70 °C, respectively.As a result, a switching effect between the "off/on" and "on/off" states are produced when the temperature increases from 60 °C to 70 °C for wavelengths λ 1 and λ 2 .The same switching effect also occurs at 60°C and 78°C for λ 1 = 2564.1 nm and λ 3 = 3260.3nm, respectively.Moreover, as shown in Fig. 6(b), for the working temperatures of 60°C and 70°C (or 78°C), the reflectance extinction ratios of 20.1 dB (21.3 dB) and 29.5 dB (34.5 dB) are achieved at λ 1 and λ 2 (λ 3 ) respectively, which represent significantly high modulation depth.It is worth mentioning that the phase transition in VO 2 can also be triggered by ultrafast laser pulses, and the time for switching between the two states of VO 2 can be in the sub-picosecond range.Thus, given this fact, it can be expected that the designed metasurface may provide useful guidance for achieving high-performance ultrafast active devices.Because the excitation of the guided-mode resonances is sensitive to the incident angle [46], the absorption characteristics of the designed metasurface were further investigated at different incident angles, as shown in Fig. 7.In contrast to previous perfect absorbers based on plasmonic metasurfaces, whose optical responses are robust to the incident angle, the absorption peaks of the designed metasurface exhibit a rapid variation with respect to the incident angle, which acts as a separation of resonances.This is because the resonances are degenerate at normal incidence, whereas a non-zero incident angle can remove this degeneration.The observed separation of the resonance peaks in Fig. 7(a) represents a type of typical inherent resonant characteristic that has also been reported in other nanostructures by previous studies [37,47,48].As shown in Fig. 7(b), multiple-wavelength and high-quality-factor absorption can be realized in the designed metasurface under TM-polarized illumination with larger incident angles.For example, five peaks with approximately 90% absorptance can be observed for the incident angle θ = 55°, and three of them achieve near-perfect absorption with the absorptance of over 99%.In particular, an absorption peak with a maximum Q-factor of 2797.7 appears at 3127.5 nm.Because of the existence of atmospheric transparency windows and molecular vibrational fingerprints in the mid-infrared spectral region, the multiple-wavelength and high-quality-factor absorption in the designed metasurface may facilitate mid-infrared biochemical sensing and thermal imaging.

Conclusions
We proposed VO 2 -assisted metasurfaces to realize tunable dual-band and high-quality-factor perfect absorption in the mid-infrared region.Both simulated and theoretical results validate the existence of two absorption peaks with near-unity absorptance at 3049.9 and 3604.2 nm, whose Q-factors were 1112.8 and 1381.1, respectively.The high-quality-factor perfect absorption in the proposed design was mainly attributed to the low radiative loss induced by the guided-mode resonances and the low intrinsic loss from the constituent materials.We demonstrated that the continuous tuning of the reflectance can be realized in the designed metasurface by utilizing the thermally induced insulator-metal transition in VO 2 .As a result, the proposed design can be used as a dual-channel ultra-narrow-band optical switch, in which the reflectance modulation depth is 16.1 and 31.8 dB at 3049.9 and 3604.2 nm, respectively.By varying the ratio S, we obtained a dual-band optical switch with opposite switching characteristics at two working wavelengths.The angle-sensitive multiband and high-quality-factor absorption in the designed metasurface under oblique TM-polarized illumination has also been discussed.This study reveals the potential use of the VO 2 -assisted metasurfaces in tunable narrow-band reflective intensity manipulation and optical switches, which provides useful guidance for researches on tunable multispectral optical devices with high Q-factors.Disclosures.The authors declare no conflicts of interest.

Fig. 1 .
Fig. 1.Schematic representation of the designed VO 2 -assisted metasurface.(a) Artistic rendering of the continuous reflectivity modulation in the designed metasurface using the thermally induced insulator-metal transition in VO 2 .(b) Schematic representation of the structure of a unit cell of the designed metasurfaces.

Fig. 3 .
Fig. 3. Guided-mode resonances in the designed VO 2 -assisted metasurface.(a) Simulated results of the distribution of the magnetic field intensity (|H|) and the real part of the magnetic field components H x in the y-z plane at the resonance wavelength λ 1 = 3049.9nm.(b) Simulated results of the distribution of the electric field intensity (|E|) and the real part of the electric field component E y in the x-z plane at the resonance wavelength λ 2 = 3604.2nm.

Fig. 4 .
Fig. 4. Effect of the structural parameters and material losses on the absorption spectrum of the designed VO 2 -assisted metasurface.Change in the absorption spectra under TMpolarized normal illumination with respect to (a) S (defined as the ratio between the diameter d of the VO 2 disks and the period p of a unit cell), (b) period p, (c) height t 3 of the VO 2 nanodisk (d) thickness t 2 of the a-Si layer, and (e) thickness t 1 of the Al 2 O 3 dielectric layer at 60°C.(f) Change in the absorption spectra under TM-polarized normal illumination at 60°C when varying the imaginary part of the relative permittivity (ε ′′ ) of VO 2 .The material parameters in the black box represent the ε ′′ values of VO 2 at resonance wavelengths λ 1 and λ 2 used in the above simulation.Except for the interested parameters, the other structural parameters remain unchanged.

Fig. 5 .
Fig. 5. Implementation of continuous reflectivity modulation based on the designed VO 2 -assisted metasurface by utilizing the thermally induced insulator-metal transition in VO 2 .(a) The absorption spectra of the designed metasurface under TM-polarized normal illuminations at different temperatures with S = 0.30.The gray dashed lines represent the positions of the two resonance wavelengths at 60°C at the wavelengths λ 1 = 3049.9nm and λ 2 = 3604.2nm.Moreover, the gray shaded area represents a tunable broadband absorption.(b) The reflection spectra of the designed metasurface under TM-polarized illuminations at 60°C (insulator phase) and 88°C (metallic phase), respectively.The inset shows the reflectance at λ 2 = 3604.2nm.

Fig. 6 .
Fig. 6.Dual-band optical switch based on the designed VO 2 -assisted metasurface.(a) Simulated results of the absorption spectra of the designed metasurface under TM-polarized normal illuminations at different temperatures with S = 0.75.The gray dashed lines represent the positions of the three working wavelengths: λ 1 = 2564.1 nm, λ 2 = 3173.6nm, and λ 3 = 3260.3nm.(b) Simulated results of the extinction ratio (ER) of the reflectance between 60°C and 70°C (or 78°C and 60°C) with S = 0.75.ER = −10log 10 (R 2 / R 1 ), where R 2 and R 1 are the reflectances at the corresponding temperatures.

Fig. 7 .
Fig. 7. Angle-sensitive multiband and high-quality-factor absorption in the designed VO 2 -assisted metasurface.(a) Change in the absorption spectra of the designed metasurface (S = 0.30) under different incident angles of TM-polarized illumination at 60°C.(b) Simulated results of the absorption spectra (at 60°C) of the designed metasurface (S = 0.30) under TM-polarized illumination with incident angles equal to 45°, 50°, and 55°.