Absorption modulation of quasi-BIC in Si–VO2 composite metasurface at near-infrared wavelength

Bound states in the continuum (BIC) have attracted great attention in nanophotonics in the past few years. The metasurface with inverted symmetry breaking exhibits high Q resonance through quasi-BIC (Q-BIC), which realizes light modulation, sensing and nonlinear generation. In this work, a symmetry-broken Si–VO2 composite metasurface is studied and modulate near-infrared light absorption in Q-BIC mode. First, a L-shaped Si metasurface with broken C4v symmetry is designed, which realizes the transition from BIC to Q-BIC and shows strong circular dichroism. Later, phase-change material VO2 is integrated into the L-shaped Si metasurface. By changing the ambient temperature, the Si–VO2 composite metasurface shows distinct light absorption characteristics, including insensitivity to incident angle and a maximum absorption modulation of up to 210%. The results show that VO2 can effectively modified Q-BIC resonator to realize the modulation absorption of near-infrared light.


Introduction
A metasurface is a type of artificial electromagnetic interface that is composed of planar structures with sub-wavelength thickness.These surfaces possess unique physical properties that cannot be found in natural materials [1].Indeed, metasurface have attracted significant attention from scientists due to their remarkable capability of flexibly and effectively modulate various characteristics of electromagnetic waves, such as polarization, amplitude, phase, propagation mode, and more.This makes them highly desirable for a range of applications, including telecommunications, sensing, imaging, and more [2].Achieving a compact high-quality factor (Q factor) is crucial in the design of metasurfaces.The use of quasi-bound states in continuum (Q-BIC) has been found to be one of the most effective approaches to achieve high Q factors in a compact structure.This is because the Q-BIC mode effectively confines the electromagnetic energy in a small volume, which leads to a significant enhancement of the Q factor.The use of Q-BIC modes has therefore been a major focus of research in the field of metasurfaces [3].BIC is a phenomenon related to scattering in a continuum.The BIC phenomenon occurs when the material can create a kind of bound state in the continuum by modulating the amplitude and phase of the scattered field [4,5].In recent years, BIC has been extensively studied for a variety of photon applications, including low-threshold lasers [6,7], nonlinear optical processes [8], and sensing [9].
BIC is essentially a completely dark state with an infinitely high Q factor, which can effectively trap the energy of electromagnetic waves with wavelengths greater than the diffraction limit on the metasurface without any significant radiation leakage [10][11][12].The ideal BIC with infinite lifetime and zero leakage characteristics can only exist in an ideal lossless infinite structure or at an extreme value of the parameter, making it difficult to identify in electromagnetic wave propagation [13].Therefore, structural symmetry breaking is typically introduced into a metasurface in order to achieve a Q-BIC mode through periodic interference effects.This mode allows electromagnetic wave energy to reside in the continuum for a long period of time [14].The Q-BIC mode is easily recognized in the electromagnetic spectrum due to its Fano resonance characteristic with finite linewidth [15][16][17].As for the methods for generating Q-BIC modes, there are two main approaches: periodic structure design and asymmetric structure design.The Q-BIC mode generated by the asymmetric structure means that destroy the metasurface consisting of C 4V symmetric atomic arrays.This symmetry breaking leads to the leakage of previously protected bound states, resulting in the formation of Q-BIC accompanied by radiation losses [18][19][20][21][22]. Yang et al leveraged the asymmetric field distribution in the Q-BIC by purposefully truncating the tips of the constituent elliptical nano-silicon bars to improve the resonance performance of the symmetry-breaking Q-BIC system and enhance the trapping of subwavelength particles [23].Meng et al studied the stimulation and properties of multiple BICs in silicon hexamer metasurfaces.They generated the Q-BIC by breaking the in-plane symmetry of the structures through moving the position of nanodisks and led the resonant wavelength relatively stable [24].
Recently, vanadium dioxide (VO 2 ) has received considerable attention due to its unique phase variability from an insulating to a metallic phase at around 68 • C.This property has made VO 2 an attractive candidate for use in developing photonic elements [25][26][27][28].Aiming at the phase transition characteristics of VO 2 , Ren et al has designed a metasurface composed of VO 2 nanoparticle matrix and patterned VO 2 film.Numerical modeling and electromagnetic simulation were carried out to characterize the performance of the metasurface in terms of solar modulation and luminous transmittance.The proposed metamaterial can obtain 23% solar modulation and 57% luminous transmittance [29].Ko et al designed and produced a near-infrared absorber with aesthetic reflection coloring based on the phase transition characteristics of vanadium dioxide.The remarkable phase transition properties of VO 2 are utilized to enable the absorber to switch between lower and higher absorption states depending on the external temperature [30].A dynamically tunable optical resonance is achieved by integrating a VO 2 thin film to this Q-BIC Si nanostructure.With the increase of temperature, VO 2 gradually changes from the dielectric state to metal state, and the optical response exhibits a significant change, realizing the regulation of the optical properties [31].
In this study, we investigated the properties of the Q-BIC resonator of a L-shaped Si metasurface.The in-plane inversion and mirror symmetry of the metasurface are broken, resulting in a Q-BIC resonator with a high Q factor and strong circular dichroism.The optical properties of the L-shaped Si metasurface were analyzed under various asymmetric parameters, and we identified the Q-BIC resonator as the result of different multipole resonances by analyzing the electromagnetic field.We integrated a thin film of VO 2 into the structure and investigated its light absorption effects at different ambient temperatures.We conducted multipole decomposition calculations and analyzed the near-field distribution of the composite metasurface to better understand the underlying radiation principles.Additionally, we explored the relationship between the absorption of the composite metasurface, its structural parameters, and the incident angle.Our results showed that the composite metasurface was insensitive to the incident angle, but the absorption peak wavelength exhibited a linear dependence on changes in structural parameters.Finally, we compared the absorption of the composite metasurface at different temperatures and various positions of VO 2 .The results demonstrated that the L-shaped Si-VO 2 composite metasurface achieved a remarkable maximum absorption modulation of 210%.This finding showed that VO 2 could effectively modified Q-BIC resonator to realize the modulation absorption of near-infrared light.

Materials and methods
Finite element method is used to simulate the metasurface.Periodic boundary conditions are implemented in the x-and y-directions, while perfectly matched layers are applied in the z direction.The light transmission, Q factor and electromagnetic field of metasurface were simulated.In the simulation, the ambient environment is characterized by a dielectric constant of 1, while the substrate material utilized is conventional SiO 2 (the optical constants of Si and SiO 2 can be obtained from Palik's manual).
The analytical expression of light transmission can be simply derived from the Fano formula, and the parameters in the Fano formula can be obtained through the geometric parameters of the metasurface material and dimensionless frequency Ω = 2(ω − ω 0 )/γ, where ω 0 is the resonant frequencies and γ is the radiation loss [32]: here, q is the Fano asymmetry parameter, and T bg and T 0 describe the background contribution of nonresonant modes to the resonant peak amplitude and the offset, respectively.Importantly, the frequency dependence of q, T bg and T 0 can be neglected [32].Additionally, the length of the rectangular ∆L is fixed and the value is 160 nm.A chiral metasurface is formed and its original bound state leaks [33].The ideal BIC transforms from a stable symmetric structure to an unstable (x, y)/ → (−x, −y) for the perturbation of breaking in-plane inversion symmetry, and becomes a Q-BIC with a finite Q factor [34].
We analyzed the variation of the metasurface transmittance from BIC mode to Q-BIC mode.Figures 1(c) and (d) illustrate the transmission spectrum curve and mapping spectrum of the metasurface with different ∆S.It can be found that the asymmetry of the discrete spectrum is changed as the asymmetry parameter ∆S changing.When ∆S = 0, this structure is in the no-radiation loss BIC mode.The bound states and the continuous states are assigned to different symmetries and its symmetry incompatibility leading to the Fano coupling is prohibited [32].When ∆S ̸ = 0, the BIC mode of the symmetric structure transforms into Q-BIC mode, and the Fano resonance bandwidth gradually increases with the increase of |∆S |.
The variation of the peak wavelength λ 0 and the Q factor are also studied when the asymmetry parameter |∆S | increasing from 1920 nm 2 to 7680 nm 2 .Figure 2(a) shows that the resonance peak wavelength λ 0 gradually increases with the increase of ∆S.Conversely, the resonance peak wavelength λ 0 decreases when the −∆S decreases.Remarkably, these changes exhibit a symmetric pattern centered around the wavelength of 1010 nm.
For the Q-BIC mode, the formulation of radiative quality factor at Q-BIC mode Q rad = ω 0 /2γ rad (γ rad can be calculated as a sum of radiation losses) depending on the ∆S can be shown as, where α = ∆S/S and Q 0 is a constant determined by the metasurface [32].Figure 2(b) depicts the scatter plot illustrating the relationship between the Q factor value and the ∆S/S factor.The results reveal that, the Q factor value decreases from 5.9 × 10 3 to 0.26 × 10 3 with the degree of reverse and mirror asymmetry ∆S/S increases gradually.
Then, we investigate the optical characteristics of the Q-BIC of the L-shaped Si metasurface.Figures 3(a   L-shaped Si metasurface exhibit circular dichroism [35].In this work, the incident wave incident the metasurface perpendicularly.The electric field distribution depicts in the x-y plane, the white arrows on the plane represent the magnetic vector flow.At peak wavelength of 1001.6 nm, the electric field exhibits a strong concentration near the center of the metasurface, resulting in the gathering of magnetic vectors in all directions.The reason for the distribution of the magnetic vector in the plane is that the electric field excites the sub-oscillation of toroidal dipole (TD) and the magnetic vector threads clockwise in the central region [36].
In figures 4(a) and (b), we present the electric field distributions in the x-z plane under the resonance excitation of two circularly polarized incident waves at the peak wavelength of 1001.6 nm.The presence of mirror asymmetry with |∆S| > 0 leads to varying coupling strengths for RCP and LCP lights, resulting in distinct electric field distributions.Notably, the electric field intensity of RCP light is significantly different from that of LCP light, which confirms the dichroism of the asymmetric metasurface [33].
Figures 5(a)-(d) depict the transmission and reflection spectra for RCP and LCP incidence, while figures 5(e) and (f) illustrate the circular dichroism of the transmitted wave CD T and reflected wave CD R as the function of the asymmetry parameter ∆S.It can be observed there is no coupling between the eigenmodes and the external far field when ∆S = 0 nm 2 , resulting in the absence of circular dichroism.As depicted in the figures, the resonant spectral width expands with the increase of |∆S|.Based on these observations, we hypothesize that the excited polarization-dependent modes are associated with the symmetry-breaking-induced Q-BIC.

The discussion of the Si-VO 2 composite metasurface
VO 2 is a phase-change material, and exhibits temperature-dependent changes in its dielectric constant ε.It undergoes a reversible first-order metal-insulator transition at approximately 68 • C, where below this temperature it demonstrates insulating phase, while above 68 • C it exhibits metallic phase [26].The Lorentz-Drude model can be used to determine the complex dielectric constant ε of VO 2 thin films in the visible light and certain near-infrared light (more details are in section 1 of the supplemental material [37]).
The VO 2 thin film is integrated into the Si metasurface in order to modulate the absorption.Figure 6(a) shows the structure of the Si-VO 2 composite metasurface.The asymmetric parameter ∆S is 3200 nm 2 and the symmetry is broken, thereby establishing the Q-BIC mode.The 5 nm VO 2 film is placed in the middle of the silicon block.The experimental preparation of the VO 2 film can be executed as follows: initially, a gas mixture containing the vanadium precursor is mixed with the diluent gas, facilitating a chemical reaction on the surface of the silicon substrate, which leads to the formation of a VO 2 film.Subsequently, VO 2 film is fabricated by photolithography technology, enabling the creation of a patterned VO 2 array [38].Finally, a layer of silicon is deposited onto the prepared VO 2 film.
The dielectric constant of VO 2 is modulated by changing the ambient temperature (32 • C-82 • C), so that the conductivity of VO 2 changes from insulating phase to metallic phase.The change in the dielectric constant of VO 2 consequently induces a variation in the refractive index, leading to alterations in the optical properties of the composite metasurface.Figure 6(b) depicts the absorption spectrum of Si-VO 2 composite metasurface at different temperatures.It is evident the absorption of the metasurface increases as the temperature increasing, and the absorption peak continues the blue shift when VO 2 is in an insulating phase.When VO 2 transforms into the metallic phase, the absorption peak of the metasurface becomes further blue shift.The result shows that the temperature variation has little effect on the absorption peak.Figure 6(c) illustrates the transmission spectrum of the VO 2 embedded into the middle of Si metasurface at varying temperatures.In comparison to the smooth curve observed within the range of 945.6-950.8nm, characteristic of the BIC mode, a distinctive Fano resonance pattern emerges with an elevation in ambient temperature.Evidently, manipulation of the ambient temperature enables the transition from the BIC mode to the Q-BIC mode (The transmission of the VO 2 thin film placed above and below the Si block is in section 2 of the supplemental material [37]).Figure 6(d) further offers a comparison of the absorption spectra between the VO 2 structure without Q-BIC mode and the Si-VO 2 composite metasurface with Q-BIC mode.The results demonstrate that the Q-BIC mode can modulate the absorption rate and bandwidth of the Si-VO 2 composite metasurface by means of changing temperatures, while maintaining the structure in a bound state in the continuum [22].
In order to discuss the radiation mechanism of composite metasurface in different phases of VO 2 , the multipole decomposition is performed to analyze at temperatures of 32 • C and 82 • C. Firstly, we can obtain the current density ⃗ J according to the formula ⃗ J = −iωε 0 (n 2 − 1) ⃗ E, all multipole moments can be defined as [39,40]: where⃗ r is the displacement vector from the origin to the specific point (x, y, z), c and ω are the speed and angular frequency of light, respectively, and α, β = x, y, z.
, ⃗ T are the electric dipole moment, electric quadrupole moment, magnetic dipole (MD) moment, magnetic quadrupole (MQ) moment and TD moment, respectively.The distributed powers of these multipole moments are calculated as follow: Figures 7(a) and (c) present the log plot of multipole moments in Si-VO 2 composite metasurface at 32 • C and 82 • C. It is evident from the that MQ dominates in both the insulating phase and the metallic phase.However, in the metallic phase, the TD and MQ exhibit more active compared to the insulating phase.Typically, since both are induced by two opposite MDs, the response of TD is characterized by a significant MQ contribution [36].
The electric field distribution in x-z plane of the metasurface are investigated at the insulating phase (32 • C) and metallic phase (82 • C) in figures 7(b) and (d).The arrows are the current vectors.Figures 7(e) and (f) illustrate the magnetic field distribution in the x-z plane of the metasurface at the insulating phase (32 • C) and metallic phase (82 • C), respectively.It can be observed that, owing to the characteristics of Q-BIC, the electric and magnetic fields in both phases are concentrated at the center of the metasurface and exhibit the bound states.However, the local capabilities of the electric and magnetic fields at 82 • C are weaker than those at 32 • C. Consequently, it can be inferred that the insulating phase exhibits stronger light-harvesting properties.As depicted in figures 7(b), a clockwise electric field vortex appears in the metasurface under the insulating phase, indicating the induction of MD by the electric field in the z-direction.Conversely, under the metallic phase at 82 • C, two electric field vortices with opposite rotation directions form above and below the metasurface.This phenomenon is attributed to the increased influence of the TD, which alters the charge distribution [36].These observations are consistent with the multipole decomposition results analyzed in figures 7(a) and (c).To investigate the modulation effect of the Si-VO 2 composite metasurface on the absorption spectrum under different modes, we conducted a simulation by varying the ambient temperature while keeping other parameters unchanged.The simulation aimed to quantify the modulation of light absorption in the Si-VO 2 composite metasurface [41].The quantitative modulation expression is defined as [42]: where A 0 is the absorption of Si-VO 2 metasurface at 32 • C, and A 1 is the modulated absorption.Figures 8(a) and (b) present the comparison of the absorption spectra and modulation results for the insulating phase (32 • C, 62 • C) and metallic phase (82 • C) of VO 2 .In the insulating phase, where the refractive index of VO 2 changes little, the temperature variation from 32 • C to 62 • C leads to a modest increase in the absorption peak of the composite metasurface from 47.9% to 53%, resulting in a maximum absorption modulation of approximately 33.5%.No significant enhancement is observed.However, as the temperature rises and VO 2 transits from the insulating phase to the metallic phase, the absorption peak of the composite metasurface undergoes the blue shift due to the increased absorption of VO 2 .In this case, the maximum absorption peak can reach 81%, showcasing a significant improvement.The modulation of absorption reaches up to 210%, indicating a pronounced influence of different modes on light absorption modulation of the composite metasurface.
In practical applications, it is important to study the correlation between the absorption of composite metasurfaces and structural parameters.Figure 9 illustrates the variation of the absorption of the composite metasurface at 82 • C concerning the structural parameters t d (figure 9(a)), W (figure 9(b)) and L (figure 9(c)).Additionally, figures 9(d)-(f) depict the absorption peak wavelength λ 0 as the function of the structural parameters.As observed in figures 9(a)-(c), the absorption peak of the composite metasurface gradually diminishes with increasing values of t d and W.However, when L = 410 nm, the composite metasurface achieves its maximum absorption, reaching the peak value of 88%.Figures 9(d)-(f) reveal that as t d , W, and L increase, the wavelength λ 0 corresponding to the peak point undergoes the continuous red shift, demonstrating a linear function.From this, it can be concluded that proper absorption at desired wavelength can be obtained through reasonable selection of structural parameters, which is of particular importance for practical applications.
Then we studied the effect of oblique incidence on the absorption of the Si-VO 2 composite metasurface.Figure 10 displays the absorption spectra at different incident angles θ at 82 • C. The absorption bandwidth hardly changes within the incident angle range of θ from −20 • to 20 • .These findings highlight the robust optical properties of the Si-VO 2 composite metasurface, indicating its insensitivity to incident angle.
To further analyze the effect of the VO 2 film on the composite metasurface, we integrated it at different positions of L-shaped Si metasurface to comprehensively analyze the optical modulation.Figures 11(a) and (d) are the structural diagrams of the VO 2 thin film placed above and below the Si block, respectively.Figures 11(b) and (c) present the comparison of absorption and modulation diagrams for the insulating phase (32 • C) and metallic phase (82 • C) when the VO 2 film is integrated above the Si block.Observing these figures, we note the slight blue shift of the absorption peak with phase transformation of VO 2 .However, the peak absorption exhibits little change, with a maximum transmission modulation of 78.8%.Meanwhile, the absorption phenomenon can be elucidated through the temporal coupled-mode theory (CMT), a tool apt for unveiling the underlying physical mechanisms governing the interaction among artificial atoms within metamaterials [43].The calculations of the absorption spectrum of VO 2 placed above the Si block is performed by using the CMT.The results are consistent with those obtained by the finite element method and show that the absorption peak experiences the blue shift and the peak value changes from 951.5 to 949.7 nm when the VO 2 transits into metallic phase with the increasing of temperature (more details are in section 3 of the supplemental material [37]).Similarly, figures 11(e) and (f) display the comparison of absorption and modulation diagrams for the insulating phase (32 • C) and metallic phase (82 • C) when the VO 2 film is below the Si block.In this case, we observe the blue shift of the absorption peak, which is slightly higher than that of VO 2 integrated above, resulting in a maximum transmission modulation of 91.96%.Therefore, it can be concluded that the composite metasurface demonstrates the optimal light absorption modulation ability when the VO 2 film is embedded in the middle of L-shaped Si metasurface.We proposed that this behavior arises due to the resonance frequency of the VO 2 multipole being almost identical to that of the Q-BIC.Moreover, by studying the field distribution, we can determine the optimal parameters of the VO 2 film to achieve the most effective light modulation.In summary, we have successfully demonstrated a method for achieving absorption modulation in composite metasurfaces by leveraging temperature changes.Furthermore, by adjusting the radiation of the Q-BIC multipole moments resonance and the dissipation loss of VO 2 , we can explore effective optical modulation strategies [41].

Conclusions
In summary, we investigate the light absorption of VO 2 metasurface in Q-BIC in near-infrared light region.The L-shaped Si metasurface supporting BIC is designed in the near-infrared light region, and the optical properties are analyzed.By breaking the in-plane inversion and mirror symmetry of the structure, we establish the Q-BIC mode in the L-shaped Si metasurface, which exhibits the high Q factor and demonstrates strong circular dichroic resonance.The circular dichroic resonance is further enhanced by increasing the asymmetry parameter, and the Q-BIC mode is found to be generated through different multipole resonances, as confirmed by the analysis of the electromagnetic field.Afterwards, under specific structural parameters, the Q-BIC mode is established and VO 2 thin film is integrated on different positions of the silicon metasurface.By varying the temperature, we observe different optical absorption.At ambient temperature 32 • C, 82 • C, the multipole decomposition analysis and the calculation of the near-field distribution and current-flow direction of the composite metasurface reveal the radiation behavior of the metasurface.Furthermore, we study the correlation between the absorption of the composite metasurface and the structural parameters, as well as the incident angle, and find that the composite metasurface exhibited insensitivity to the incident angle.Finally, we quantitatively evaluate the absorption modulation effects of the composite metasurface at different temperatures.The results show that the optimal absorption modulations of the Si-VO 2 composite metasurfaces can reach 210%.This study not only investigates the radiation mechanism of composite metasurface, but also show that VO 2 can effectively modified Q-BIC resonator to realize the modulation absorption of near-infrared light.

Figure 1 .
Figure 1.(a) Geometry and surface parameters of symmetric L-shaped metasurface unit cell.(b) Top view of asymmetrically designed Si metasurface structure.(c) Specific transmission spectra curve wavelength λ and parameter ∆S.(d) Transmittance mapping of wavelength λ and parameter ∆S.

3. Results and discussion 3 . 1 .
Conversion of BIC to Q-BIC of L-shaped Si metamaterial Figure 1(a) shows the schematic diagram of L-shaped Si metasurface.The substrate is SiO 2 .A small rectangular is remove from or added to the large rectangular to destroy the in-plane inversion and mirror symmetry of the structure.Figure 1(b) depicts the top view of the L-shaped Si metasurface.The structural parameters are as follows: period Λ = 500 nm, thickness t d = 230 nm, length of the L-shaped Si L = 430 nm, and width W = 180 nm.
) and (b) depict the transmittance and reflectance spectra of left-handed and right-handed polarized light.Due to the broken in-plane inversion and mirror symmetry, the transmitted and reflected light of the

Figure 2 .
Figure 2. (a) The variation of |∆S| transmission peak corresponding to the wavelength λ0 for Q-BIC.(b) The magnitudes of Q factor as a function of |∆S/S| for Q-BIC.

Figure 3 .
Figure 3. (a) The corresponding spectra diagrams of the transmittance (T) under left-handed and right-handed polarized light at ∆S = −3840 nm 2 .(b) The spectra diagrams of the reflection (R) under left-handed and right-handed polarized light.(c) The circular dichroism of the transmitted wave CD T and reflected wave CDR.(d) The x-y plane diagram of the L-shaped Si metasurface, electric field intensity distribution in x-y plane and magnetic vectors at the peak of resonant wavelength.
Figure 3(c) shows the circular dichroism of the transmitted wave CD T and reflected wave CD R .The circular dichroism is determined by CD T = (T LCP − T RCP )/(T LCP + T RCP ) andCD R = (R LCP − R RCP )/(R LCP + R RCP ).Here, T and R represent the transmittance and reflectance, and the subscripts RCP and LCP indicate the right-handed and left-handed circular polarization of the incident light, respectively[33].The metasurface exhibits significant circular dichroism in a narrow spectral range centered at 1001.6 nm, where the peak values of circular dichroism for the transmitted and reflected waves are −0.27 and 0.47, respectively.

Figure 4 .
Figure 4.The x-z plane electric field distribution at 1001.6 nm for (a) RCP and (b) LCP incidents.

Figure 3 (
Figure 3(d)  shows the x-y plane electric field distributions of the L-shaped Si metasurface when ∆S = −3840 nm2 .The electric field distribution depicts in the x-y plane, the white arrows on the plane represent the magnetic vector flow.At peak wavelength of 1001.6 nm, the electric field exhibits a strong concentration near the center of the metasurface, resulting in the gathering of magnetic vectors in all directions.The reason for the distribution of the magnetic vector in the plane is that the electric field excites the sub-oscillation of toroidal dipole (TD) and the magnetic vector threads clockwise in the central region[36].In figures 4(a) and (b), we present the electric field distributions in the x-z plane under the resonance excitation of two circularly polarized incident waves at the peak wavelength of 1001.6 nm.The presence of mirror asymmetry with |∆S| > 0 leads to varying coupling strengths for RCP and LCP lights, resulting in distinct electric field distributions.Notably, the electric field intensity of RCP light is significantly different from that of LCP light, which confirms the dichroism of the asymmetric metasurface[33].Figures5(a)-(d) depict the transmission and reflection spectra for RCP and LCP incidence, while figures 5(e) and (f) illustrate the circular dichroism of the transmitted wave CD T and reflected wave CD R as the function of the asymmetry parameter ∆S.It can be observed there is no coupling between the eigenmodes and the external far field when ∆S = 0 nm 2 , resulting in the absence of circular dichroism.As depicted in the figures, the resonant spectral width expands with the increase of |∆S|.Based on these observations, we hypothesize that the excited polarization-dependent modes are associated with the symmetry-breaking-induced Q-BIC.

Figure 5 .
Figure 5. (a)-(d) Transmission T and reflection spectra R for RCP and LCP incidences as the functions of asymmetry parameter ∆S.The magnitudes of circular dichroism for both (e) transmission CD T and (f) reflection CDR as the functions of asymmetry parameter ∆S.

Figure 6 .
Figure 6.(a) Schematic diagram of the Si-VO2 composite metasurface.(b) Absorption of Si-VO2 composite metasurface under different temperatures.(c) Transmission of Si-VO2 composite metasurface under different temperatures.(d) Comparison of absorption spectra of the VO2 structure without the Q-BIC mode and Si-VO2 composite metasurface.

Figure 7 .
Figure 7. Log plot of multipole moments in Si-VO2 composite metasurface at (a) 32 • C and (c) 82 • C. Electric field distribution diagram and current vector in x-z plane of Si-VO2 composite metasurface at (b) 32 • C and (d) 82 • C. Magnetic field distribution in x-z plane of Si-VO2 composite metasurface at (e) 32 • C and (f) 82 • C.

Figure 8 .
Figure 8.(a) The comparison of the absorption spectra of Si-VO2 composite metasurface at 32 • C, 62 • C and 82 • C. (b) Corresponding absorption modulation of the composite metasurface.

Figure 9 .
Figure 9. Absorption spectra of Si-VO2 composite metasurface at 82 • C for different structural parameters t d (a), W(b), and L(c).The corresponding wavelength λ0 of the peak absorption for different structural parameters t d (d), W(e), and L(f).

Figure 11 .
Figure 11.(a), (d) Schematic diagram of the structure of VO2 placed at different locations.(b) The simulated absorption spectrum and the theory absorption spectrum of VO2 placed above the Si block at 32 • C and 82 • C. (e) Absorption spectrum of VO2 placed below the Si block at 32 • C and 82 • C. (c), (f) Corresponding absorption modulation.