Arash Nemati, Qian Wang, Norman Soo Seng Ang, Weide Wang,Minghui Hong and Jinghua Teng*

Keywords: metasurface; electrically tunable; indium tin oxide (ITO); epsilon-near-zero (ENZ); barium strontium titanate(BST); polarization-insensitive

Introduction

Metasurfaces are the two-dimensional equivalent of metamaterials, composing discrete subwavelength structures, possessing the capability of full control of light properties, such as amplitude, phase, dispersion, momentum, and polarization1-7.Metasurfaces are used in various applications covering electromagnetic spectra ranging from microwave, terahertz (THz), infrared, visible, to ultra-violet (UV)8.Active control of light propagation in visible and near-infrared (near-IR) spectra has practical and fundamental significance in autonomous vehicles, robots, display, augmented and virtual reality, consumer electronics, telecommunications, and sensing devices9-14.To tune a metasurface, we can change either the property of the unit cells or its ambient.This could be done by employing active materials in the metasurface, which can have their properties changed by an external stimulus.Each type of these materials has different properties and tuning mechanisms.

Transparent conductive oxides are optically transparent and electrically conductive.They have been widely used in photovoltaics, organic light-emitting diodes,displays, and electro-optics devices15,16.Recently, the tunable property of transparent conductive oxides, such as indium tin oxide (ITO), has attracted great attention for its applications in metasurfaces and flat optics17.Moreover, the tunability in ITO is a field-effect modulation mechanism that is based on the formation of charge depletion or accumulation regions.This gives them advantages of low power and high speed compared to the other common tuning mechanisms, such as MEMS,mechanical strain, liquid crystals, and phase change materials9,18-20.

So far most of the focus in using tunable ITO film has been on designing beamsteering metasurfaces21-23.To tune the electron density and optical constants in the ITO film, different structures have been proposed.A 300° phase change was shown in a reflective dual-gate metasurface structure using a single ITO film with the measured reflectance below 30%22.Recently, over 360°phase change and a scan angle of 8° with a deflection efficiency of 34% were achieved24.Although the strong resonance and electric and magnetic confinement in the ITO film has been very beneficial to achieving high phase change, it has limited the achievable efficiency.

Hence, ITO could be a better candidate for modulation of light intensity by playing with its plasmonic resonance.An electrically tunable metasurface working as a modulator could not only benefit from the fast tunability of ITO but also the compactness of metasurface design.Different structures have been proposed so far to answer such demand.Placing an ITO film inside a metal-insulator-metal (MIM) plasmonic cavity, a tunable reflective absorber with up to 15% change in amplitude of reflected light was achieved25.A broadband electro-optical modulator based on a multilayer structure was able to attain 37% modulation depth for the reflected light when the incoming light has a 78° incidence angle26.A high-efficiency transmittance modulator using ITO-based metasurfaces and hybrid plasmonic waveguide mode has shown a 33% gate-tunable transmittance change by applying a 6 V gate bias27.An all-dielectric Huygens metasurface was proposed to control the transmission of light with an on-state transmittance of 70% and a modulation depth of 31%28.Moreover, a circular MIM resonator with an ITO film that is polarization insensitive could realize the modulation of transmitted light with a large modulation depth up to 29 dB or 96%29.However, all of these metasurfaces comprise a single ITO film with limited modulation depth and their operational wavelength was also restricted toλ≥ ～1500 nm in the near-IR spectrum due to the low electron concentration of the deposited ITO film.

Here, a new circular resonator comprising two ITO discs is proposed.We use the coupling of magnetic dipole resonance in the circular resonator with the ENZ wavelength inside the accumulation layer of ITO film to achieve total absorption of reflected light.This is mainly due to the coexistence of magnetic dipole resonance and ENZ wavelength inside the ITO discs.A perovskite high dielectric constant barium strontium titanate (BST) film is sandwiched between two ITO films to increase the electric field and decrease the required voltage.An unprecedented ～84 dB or ～99.99% modulation depth in the reflection mode, insensitive to the polarization of light,was achieved atλ= 820 nm with a single bias voltage ofV=-2.5V.The results show a promising way for realizing electrically tunable metasurface for potential highspeed light modulation.

Methods and results

ITO is a conducting material with free electrons which is optically modeled using the Drude model in the visible and near-IR spectra30:

whereτis scattering time, e is the electron charge,μis the electron mobility,ε0is the vacuum permittivity,m*is the effective electron mass, andNis the electron concentration.By changing the carrier concentration, the plasma frequency changes, thereby changing the dielectric constant.From Eq.(1), the real and imaginary parts of the permittivity are given by:

The epsilon-near-zero (ENZ) wavelength (λENZ) is the wavelength at which the real part of the dielectric constant becomes zero31,32.If the imaginary part of the permittivity is zero or near-zero at the same wavelength, the refractive index would become close to zero, much smaller than the refractive index of vacuum.Although common materials, i.e., metals, have ˜εr=0 at plasma frequency, the imaginary part of the permittivity is quite large.However, in transparent conductive oxides, the ENZ wavelength can be tuned in the visible and near-IR spectra while having a small value of the imaginary part of the permittivity33-35.From Eq.(4), the epsilon-nearzero wavelength (λENZ) is given by:

where c is the speed of light in the vacuum.It could be seen that changing plasma frequency changes the epsilon-near-zero wavelength.According to Eq.(3), by increasing the electron concentration (N), the plasma frequency (ωp) increases which according to Eq.(6) the epsilon-near-zero wavelength (λENZ) decreases.

As a result, to push the tunability of the ITO films to the shorter wavelength and possibly visible spectrum,one needs to increase the electron concentration of the film to aboveN=8×1020cm-3.This is validated through the ITO films we deposited using RF magnetron sputtering at room temperature with a deposition rate of 1.1 nm/min.In order to increase the electron concentration, the films were post-annealed at 350 °C using rapid thermal annealing for 3 minutes in a nitrogen atmosphere.Hall measurement and spectroscopic ellipsometry were used to model the electrical and optical properties of the ITO films deposited on quartz and Si substrates, respectively23.The electron concentration of the ITO film was increased fromN=3.383×1019cm-3in as-deposited film toN=8.22×1020cm-3in the post-annealed film.The electrical and optical properties of asdeposited and post-annealed ITO films, from the Drude model, are listed in Table 1.Our films are deposited at room temperature without introducing oxygen to the chamber to increase the oxygen deficiency.Post deposition annealing is performed in a nitrogen atmosphere to further increase the oxygen deficiency and improve crystal quality36,37.

A dielectric material with a high permittivity would be of great importance to achieve higher capacitance,charge accumulation, and tunability.Unlike the dualgate structure22where an ultrathin 5 nm thick ITO film was sandwiched between two oxide films and two metal electrodes on the sides of the oxide films, we employ a capacitive structure with two 5 nm thick ITO films sandwiching a 50 nm thick perovskite BST film, as shown in Fig.1.The BST is chosen as the oxide film due to its high dielectric constant (εDC＞500 at room temperature)which would increase the total capacitance and charge accumulation in the ITO films38.Considering an electric field ofE=500 kV/cm, the applied voltage would be equal toV=2.5 V.We keep the thickness of the ITO films as low as possible (5 nm) which would increase the amount of achievable modulation22.

Fig.1 | Schematic of the tunable double lTO capacitive structure.

The parameters for the ITO films are taken from the post-annealed 5 nm film shown in Table 1 asN=8.22×1020cm-3,μ=21 cm2/(V·s),m*=0.26me,andε∞=4.0212.This film has a plasma frequency ofωp=3.177×1015rad/s and damping constant ofΓ=3.232×1014rad/s, as calculated using Eqs.(2) and(3), respectively.These data are used to do electrical charge simulations using Lumerical Device software.The capacitive structure is simulated in a 2D setup and the applied DC voltage between the two ITO films is decreased fromV=0 V toV=-2.5 V.In simulations,the unstructured tetrahedral finite-element mesh with a minimum edge length of 0.1 nm is used for ITO films.

Table 1 | Electrical and optical properties of the lTO films.

The simulated electron concentration for the top and bottom ITO film along the ITO film thickness versus the bias voltage is shown in Fig.2.The electron concentration is calculated using a charge monitor placed along theZaxis as shown in red color in Fig.1.The bottom of BST film is considered asZ=0, the top ITO film would be at 5 0nm＜Z＜55nm, and the bottom ITO film would be at-5nm＜Z＜0nm.UnderV=0 V biasvoltage, the electron concentration isN0=8.22×1020cm-3along the both ITO films thickness as shown in green color in Fig.2(a) and 2(b).By increasing the negative voltage on the top ITO film in Fig.1, the electrons accumulate on the interface of ITO with dielectric BST film, creating an accumulation layer of electrons inside the top ITO film.As shown with red color in Fig.2(a),the electron concentration is increased fromN0=8.22×1020cm-3to a maximum ofNa=1.62×1021cm-3inside the accumulation layer.On the other hand, as shown with blue color in Fig.2(b), the electron concentration is decreased inside the bottom ITO film at the ITO/BST interface as the voltage is increased, creating a depletion layer of electrons.The electron concentration inside this depletion layer is decreased fromN0=8.22×1020cm-3to a minimum ofNd=1.55×1020cm-3.According to the simulation results shown in Fig.2, the effective thickness of accumulation and depletion layers, which would affect the optical performance of the device, are approximately 0.5 nm and 1 nm under the bias voltages ofV=-2.5 V andV=2.5 V, respectively.As a result, the thicknesses of the accumulation and depletion layers, the tunable part of ITO films, are considered as 1 nm for the following optical simulation of the metasurface.After post-annealing, the ITO films are in the crystalline/polycrystalline phase, a particularly complex crystal structure with about 80 atoms per unit cell, with a lattice constant of ～1.01 nm39,40.In ITO film with such a high electron concentration, a degenerated gas of current-carrying electrons is created via chemical doping of tin for indium and increased by the presence of oxygen vacancy impurity states30.As a result, the 1 nm tunable layer of ITO film is divided into two 0.5 nm layers in which each layer has a different electron concentration estimated from simulation results shown in Fig.2.

Fig.2 | Electron concentrations in the (a) top and (b) bottom ITO films as functions of the applied voltage.The electron concentration along the Z axis, 50 nm ＜ Z ＜ 55 nm in the top ITO film and -5 nm ＜ Z ＜ 0 nm in the bottom ITO film.The initial electron concentration for both films equal to N0 = 8.22 × 1020 cm-3 is shown in green color.The increased electron concentration is shown with red color in the accumulation layer of the top ITO film and the decreased electron concentration is shown with blue color in the depletion layer of the bottom ITO film.

Plasma frequency (ωp) and damping rate (Γ) for ITO film, accumulation and depletion layers are calculated using theN0,Na, andNdfrom Eqs.(2) and (3).These values are used to calculate real and imaginary parts of the permittivity from Eqs.(4) and (5).Then, the refractive index (n) and extinction coefficient (κ) are calculated from complex refractive index asn˜2=(n+iκ)2=˜εr˜μr,where ˜μris the complex relative permeability.Since ITO is a non-magnetic material at optical frequencies, its relative permeability is equal to 1.The refractive index and extinction coefficients values could be deduced as:

ENZrwould be nearλENZ.The optical properties of the ITO in three states, un-biased (N0=8.22×1020), accumulation(Na=1.62×1021), and depletion (Nd=1.55×1020) layers are shown in Fig.3 with green, red, and blue color lines, respectively.Other parameters are taken from Table 1 asμ=21 cm2/(V·s),m*=0.26me, andε∞=4.0212, similar for all three states.

As shown in Fig.3(a), the epsilon-near-zero wavelength (λENZ) of the ITO film (N0), where the green line crosses zero, is aroundλ=1.2 μm.After applying bias voltage, the ENZ wavelength blue-shifts toλ=820nm inside the accumulation layer and red-shifts toλ ＞2μm inside the depletion layer.As theλENZmoves toward shorter wavelength, the loss (imaginary part of the permittivity) is increased in the visible spectrum, as shown in Fig.3(b).By increasing the electron concentration inside the accumulation layer, the plasma frequency is increased (Eq.(2)) and the imaginary part of the permittivity is also increased (Eq.(5)).On the other hand,the imaginary part of the permittivity and loss is decreased as the electron concentration is decreased.

Figure 3(c) and 3(d) show the refractive index and extinction coefficient of ITO in three different states.As explained before, the dip in the refractive index spectrum, which would be near the ENZ wavelength, blueshifts toward the visible spectrum in the accumulation layer of the film, and red-shifts in the depletion layer to wavelength longer thanλ=2 μm.It could be seen from the extinction coefficient that the ITO film becomes lossier in the accumulation layer and more transparent in the depletion layer.In other words, the accumulation layer is more metallic and lossy with more electron concentration and the depletion layer is more dielectric and transparent as it is less conductive.

One approach for designing the tunable metasurfaces could be taking advantage of significant change in the refractive index as shown in Fig.3(c).However, thischange only happens in very thin (～1 nm) accumulation and depletion layers.The better approach would be making use of the tunability of ENZ wavelength in the accumulation and depletion layers.The electric field would accumulate and intensify inside the ENZ layer and result in significant phase and intensity modulation34,35.However, these tunable metasurfaces suffer from low efficiency due to the inherent high loss of accumulation layer22,41, as shown in Fig.3(b) and 3(d).In other words,the total efficiency of the metasurface is limited by the ohmic loss of the ITO film.Here, this ohmic loss is going to be used as an advantage to design a reflective modulator using double ITO films.The modulator would have two states of ON and OFF.In the ON state, the reflection amplitude would be the maximum with ENZ wavelength far away from the operational wavelength.In the OFF state, the reflection amplitude would decrease dramatically due to the high loss with ENZ shifting to the operational wavelength.

Figure 4 shows the unit cell of such electrically controlled modulator metasurface comprising a 100 nm thick silver mirror, circular-shaped ITO-BST-ITO resonator, and silicon resonator withD=250 nm diameter,and fourW=20 nm wide bias connections on the sides of resonators.The ITO, BST, and Si films aretITO=5 nm,tBST=50nm, andtSi=50 nm thick, respectively.All the top ITO discs are connected through the top ITO film in bias connections.All the bottom ITO discs are electrically connected through the bottom Ag mirror and bottom ITO film in bias connections.A single voltage source is used to control the charge accumulation and depletion in the ITO discs, as shown in Fig.4(b), and tune the reflection amplitude of the light.Such a metasurface could be fabricated by using ebeam lithography(EBL) and conventional semiconductor processing.For example, a 100 nm thick Ag film could be deposited using ebeam evaporation on a highly doped Si substrate to allow the bottom ITO film to be addressed electrically through the substrate.Then the bottom ITO, BST, top ITO, and Si films would be deposited using RF sputtering.The nano-disc structure could be created by EBL patterning and plasma or deep reactive ion etching(DRIE) by using an appropriate masking layer.A postannealing would be performed to increase the electron concentration of ITO films.

Fig.4 | Schematic of the electrically controlled reflective modulator metasurface.(a) A square unit cell is constructed from a circular silicon resonator on the top of a circular ITO-BST-ITO resonator on the top of a silver mirror.Four symmetrical bias connections with the same layers are used to make bias connections between the ITO films.Parameter values are tAg =100 nm, tITO = 5 nm, tBST = 50 nm, tSi = 50 nm, W = 20 nm,D = 250 nm, and P = 520 nm.The initial polarization of light is shown along the X axis.(b) 3D schematic of the metasurface constructed from a 6×6 array of unit cells.The metasurface is controlled by applying the voltage between the bottom silver film (grey) and the top ITO electrode (orange).The electrical current passes to the resonators through a 2D array of bias connections.

Due to the circular shape of the resonator and symmetrical design of the bias connections on the four sides of the resonator, the modulator metasurface is insensitive to the polarization of incident light, explained in detail in another work29.The performance of the modulator metasurface is simulated using Lumerical FDTD software.A single unit cell with periodic boundary conditions is simulated to numerically calculate the reflection amplitude of the modulator metasurface.A local mesh cell with dimensions ofdx×dy×dz=5nm×5nm×0.5nmis chosen for ITO discs to accurately model the accumulation and depletion layers.The ITO film is modeled using the Drude model with the properties measured and explored previously.The first 1 nm thick layer of the ITO films at the interface with BST film is considered as the tunable accumulation/depletion layers.The electron concentration of the first 0.5 nm near BST film is changed fromN0toNaorNdaccording to the applied voltage, while the next 0.5 nm is changedaccording to the applied voltage and simulation results in Fig.2 to accurately model the accumulation (0.5 nm) and depletion (1 nm) layers.UnderV=0 V bias voltage(ON state), the electron concentration of both layers is consideredN0.UnderV=2.5 V bias voltage (OFF state 1), the electron concentration of the top 0.5 nm tunable layer is changed toNd(depletion layer) and the bottom 0.5 nm tunable layer toNa(accumulation layer), while underV=-2.5 V bias voltage (OFF state 2), the electron concentration in the top 0.5 nm tunable layer is changed toNaand the bottom 0.5 nm tunable layer toNd.

Simulated reflection spectra of the modulator under three different voltagesV=-2.5,0 and 2.5 V are shown in red, green, and blue colors, respectively, in Fig.5(a).As explained before, the operational wavelength is set at the ENZ wavelength of the accumulation layer,λ=820 nm, to get the strongest resonance and thus the highest loss and the largest modulation depth.The reflection amplitude atλ=820 nm underV=0 V is 5 6.3%.It is a dip in the reflection spectra mainly due to magnetic dipole resonance in the ITO-BST-ITO resonator.By decreasing the voltage toV=-2.5 V (OFF state 2), the accumulation layer is created at the bottom of the top ITO film which drops the reflection down to 3.58×10-3%.This is due to the coexistence of magnetic dipole resonance and ENZ wavelength inside the accumulation layer at this wavelength.If the voltage is reversed toV=2.5 V, the accumulation layer is created in the bottom ITO film and the reflection amplitude drops to 4.2% (OFF state 1).As the distance between the accumulation layer and the silver ground plane is changed, the resonance wavelength is slightly changed and the resonance strength is slightly weakened.The modulation depth(MD) is defined as:

whereRMin=3.58×10-3% andRMax=56.3% are the minimum and maximum reflection amplitudes before(ON state) and after (OFF state 2) applying the bias voltage, respectively, atλ=820 nm.Hence, underV=-2.5V the proposed modulator metasurface achieves 84 dB modulation depth, equal to ～99.99%, if defined asMD= (|ΔR|/RMax) × 100.UnderV=-2.5 V,where the accumulation layer is created in the top ITO film, the reflection amplitude remains below 1% (MD～40 dB) in the range of 8 05nm＜λ＜835 nm and remains below 5% (MD ～22 dB) in the range of 7 95 nm＜λ＜850nm.UnderV=2.5 V, where the accumulation layer is created in the bottom ITO film, the reflection amplitude remains below 1% in the range of 7 90 nm＜λ＜860nm and below 5% in the range of 7 8 5 nm＜λ＜870nm.

To investigate the phenomena behind such ultra-high modulation depth, the electric field inside the resonator is studied at the resonance wavelength (λ= 820 nm).The electric field intensity under three different bias voltages is shown in Fig.6.A field monitor is placed along theXZplane, according to Fig.4, in the middle of the circular resonator.UnderV=0 V bias voltage, it could be seen in Fig.5 that there was a small dip in the reflection spectrum atλ= 820 nm indicating a slight resonance in theresonator.The cause of that resonance could be seen in Fig.6(a), as the electric field is confined inside the top and bottom ITO discs.As explained earlier, ITO films are modeled using the Drude model with electron concentrationN0=8.22×1020cm-3, implying semi-metallic properties of the ITO in visible and near-IR spectra.Moreover, the ENZ wavelength of un-biased ITO film was calculated in Table 1 asλENZ～1.2 μm, relatively close to the wavelength of geometrical resonance, implying a weak ENZ resonance inside the top and bottom circular ITO discs.This geometrical resonance is a magnetic dipole resonance which would be explored in Fig.7.By changing the voltage toV=2.5 V, the accumulation layer is created in the bottom ITO layer interfacing the BST, as shown in Fig.6(b).This accumulation layer has the ENZ wavelength atλ= 820 nm which was the resonance wavelength of the magnetic dipole resonator.A combination of the electric field enhancement in the ENZ layer and magnetic dipole resonance confines the light inside the 0.5 nm thick ITO accumulation layer.This could also be explained as a narrow channel with a deep subwavelength transverse cross-section made of ENZ material, in the resonance wavelength42.As shown in Fig.3(b) and 3(d), at the ENZ wavelength the accumulation layer becomes very lossy.This strong resonance and confinement of the light inside a very thin accumulation layer cause total loss of the light with almost no reflection, acting similar to a complete absorber.As shown in Fig.5(a), due to the short distance between the ENZ resonator and the ground plane, there are two identical magnetic dipole resonances aroundλ= 820 nm resulting in two dips atλ= 795 nm andλ= 845 nm25.

Fig.5 | Performance of the electrically tunable modulator metasurface.(a) Simulated reflection spectra of the modulator under three different voltages.Under V = 0 V bias voltage, both ITO films have an electron concentration of N0.Under V = -2.5 V, the top ITO film has a 0.5 nm thick accumulation layer with an electron concentration of Na and the bottom ITO film has a 1 nm thick depletion layer with an electron concentration of Nd.Under V = 2.5 V, the top ITO film has a depletion layer with an electron concentration of Nd and the bottom ITO film has an accumulation layer with an electron concentration of Na.(b) Modulation depth spectra of modulator under V = -2.5 V.The modulation depth peaks to ～84 dB at the wavelength of λ = 820 nm.

Fig.6 | Electric field intensity along XZ plane under the bias voltages of (a) V = 0 V at λ = 820 nm, (b) V = 2.5 V at λ = 800 nm, and (c) V = -2.5 V at λ = 820 nm.The edges of the Si disc and silver mirror are shown with green dashed lines.

As shown in Fig.6(c), the same phenomenon happens atV=-2.5 V but the accumulation layer is created inside the top ITO film interfacing with the BST disc.It is important to note that as the accumulation layer is created inside one ITO disc, the depletion layer is created in the other ITO disc.The depletion layer has a much lower electron concentration and its ENZ wavelength redshifts toλ＞2 μm.This results in lower electric field confinement compared to the un-biased ITO film and accumulation layer, which could be seen in Fig.6.

To further investigate the resonance inside the accumulation layer, a field monitor is placed along theXYplane inside the accumulation layer in the top ITO film under a bias voltage ofV=-2.5 V.The electric and magnetic fields atλ= 820 nm are shown in Fig.7.

The electric and magnetic field intensities in theXYplane inside the accumulation layer are shown in Fig.7(a) and 7(b).The magnetic field looks like an ellipse stretched along theYaxis, while the electric field is stronger on the left and right side of the ENZ region where the magnetic field is the weakest.This is in agreement with the polarization of light, where the electric field was along theXaxis and the magnetic field along theYaxis, as shown in Fig.4(a).The top and side views of the electric field vectors are shown in Fig.7(c) and 7(e), respectively.The electric field vectors represent an electric current in the shape of a stretched circular loop,antiparallel on two sides of the ENZ region.The top and side views of the magnetic field vectors are shown in Fig.7(d) and 7(f).The magnetic field vectors are stretched along the positiveYdirection in the center of the ENZ region, strongest in the center of the ENZ region where the electric field is the weakest.All of this implies a magnetic dipole stretched along theYaxis is created inside the accumulation layer.

Fig.7 | The electric and magnetic fields under a bias voltage of V = -2.5 V inside the accumulation layer at λ = 820 nm.(a) Electric and(b) magnetic field intensities in the XY plane inside the accumulation layer in the top ITO film.Top view of the vectors of the (c) electric and (d)magnetic fields from the same monitor.Side view of the vectors of the (e) electric and (f) magnetic fields from the same monitor.The vector figures (e) and (f) share the same scalar bar as vector figures (c) and (d), respectively.The edge of the ITO disc is shown by the red dashed lines.

Figure 8 shows the impact of the Si disc thickness on the reflection spectra under the bias voltages ofV= 0 V andV=-2.5 V.As shown in Fig.8(a), under the bias voltage ofV= 0 V, the wavelength of the magnetic dipole resonance is increasing from 630 nm to 820 nm asthe thickness of Si disc is increased from 0 to 50 nm.Moreover, the FWHM of the resonance is increasing from ～15 nm attSi= 0 nm to ～100 nm attSi= 50 nm.As shown in Fig.8(b), under the bias voltage ofV=-2.5 V,the reflection spectra are similar to Fig.8(a) without bias voltage.However, as the thickness of the Si disc is increased above 20 nm, a new resonance with a slightly longer wavelength appears in the reflection spectra.The minimum reflection at the dip of spectra becomes nearly zero fortSi≥ 40 nm.This could be explained by the coexistence of ENZ wavelength by two neighboring magnetic dipole resonances.Moreover, the effect of polarization ofincident light, angle of the incident light with the surface normal, the width of the bias connections, and ITO discs thickness are explored and the simulation results could be found in the Supplemental Material.

Fig.8 | lmpact of the Si disc thickness on the reflection spectra.Map of the reflection spectra of the modulator metasurface with a varying thickness of the Si disc (0 nm ≤ tSi ≤ 50 nm) under the bias voltages of (a) V = 0 V and (b) V = -2.5 V.

The operational wavelength of the modulator is the result of the coexistence of magnetic dipole resonance and ENZ wavelength.Hence, both of them should be shifted to change the operational wavelength of the modulator.The wavelength of magnetic dipole resonance could be tuned by changing the diameter of the resonator.For example, by increasing the diameter of the circular resonator, the wavelength of magnetic dipole resonance would increase.In such a case, the ENZ wavelength of the accumulation layer inside the ITO film also should be increased to this new longer wavelength.This could be achieved by either applying a smaller voltage between the ITO films or choosing an ITO film with a lower initial electron concentration (longer initial ENZ wavelength).However, decreasing the operational wavelength is not possible.The magnetic dipole resonance wavelength could be reduced by decreasing the diameter of the resonator.However, decreasing the ENZ wavelength of the accumulation layer is not possible since it requires an increase in the initial electron concertation of the deposited ITO films which according to our experiments is maxed out at 8.22×1020cm-3for 5 nm ITO film.Note that increasing the applied voltage to further blue-shift the ENZ wavelength is not an answer since it may cause the breakdown of BST film due to extremely high dielectric field.

Conclusion

An electrically tunable polarization-insensitive modulator metasurface operating in reflection mode was proposed.It has a tunable capacitive structure comprising a high dielectric constant perovskite BST film sandwiched between two ultra-thin 5 nm ITO films.These ITO films act as active tuning media through electron accumulation/depletion and also the electrodes for applying the bias voltage.The coupling of magnetic dipole resonance with the ENZ wavelength inside the accumulation layer was used to achieve the total absorption of reflected light.The metasurface achieved 84 dB or ～99.99% modulation depth at the operation wavelength ofλ=820nm and～40 dB in the wavelength range of 8 0 5 nm＜λ ＜835 nm underV=-2.5 V.By designing circular resonators and symmetrical 2D bias connections, the metasurface was insensitive to the polarization of the incident light.The proposed tunable metasurface could potentially be used for the active control of the light intensity with fast electrical signal modulation in the visible and near-IR spectra as a tunable flat optical interconnect, switch, and sensing device.