Ultra-high extinction-ratio light modulation by electrically tunable metasurface using dual epsilon-near-zero resonances Opto-Electronic

The lossy nature of indium tin oxide (ITO) at epsilon-near-zero (ENZ) wavelength is used to design an electrically tunable metasurface absorber. The metasurface unit cell is constructed of a circular resonator comprising two ITO discs and a high dielectric constant perovskite barium strontium titanate (BST) film. The ENZ wavelength in the accumulation and depletion layers of ITO discs is controlled by applying a single bias voltage. The coupling of magnetic dipole resonance with the ENZ wavelength inside the accumulation layer of ITO film causes total absorption of reflected light. The reflection amplitude can achieve ~84 dB or ~99.99% modulation depth in the operation wavelength of 820 nm at a bias voltage of −2.5 V. Moreover, the metasurface is insensitive to the polarization of the incident light due to the circular design of resonators and the symmetrical design of bias connections. Ultra-high extinction-ratio light modulation by electrically tunable metasurface using dual epsilon-near-zero resonances. Opto-Electron , 200088 (2021).


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 polarization 1−7 . 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 devices 9−14 . 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, 1 Institute of Materials Research and Engineering, Agency for Science, Technology and Research (A*STAR), 2 Fusionopolis Way, Singapore displays, and electro-optics devices 15,16 . 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 optics 17 . 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 materials 9,18−20 .
So far most of the focus in using tunable ITO film has been on designing beamsteering metasurfaces 21−23 . 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°p hase change and a scan angle of 8° with a deflection efficiency of 34% were achieved 24 . 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 achieved 25 . 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 angle 26 . 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 bias 27 . 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 to λ ≥ ~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 at λ = 820 nm with a single bias voltage of V. 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 spectra 30 : where is the material permittivity, and are the real and imaginary parts of the permittivity respectively, is the high-frequency permittivity, is the angular frequency, is the plasma frequency, and is the damping rate. The plasma frequency and damping rate are defined as: where is scattering time, is the electron charge, is the electron mobility, is the vacuum permittivity, is the effective electron mass, and is 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 ( ) is the wavelength at which the real part of the dielectric constant becomes zero 31,32 . 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 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 permittivity 33−35 . From Eq. (4), the epsilon-nearzero wavelength ( ) is given by: c where 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. 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 above cm −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, respectively 23 . The electron concentration of the ITO film was increased from cm −3 in as-deposited film to cm −3 in 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 quality 36,37 .
A dielectric material with a high permittivity would be of great importance to achieve higher capacitance, charge accumulation, and tunability. Unlike the dualgate structure 22 where 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 ( at room temperature) which would increase the total capacitance and charge accumulation in the ITO films 38 . Considering an electric field of kV/cm, the applied voltage would be equal to V. We keep the thickness of the ITO films as low as possible (5 nm) which would increase the amount of achievable modulation 22 .
The parameters for the ITO films are taken from the post-annealed 5 nm film shown in Table 1 as cm −3 , cm 2 /(V·s), , and . This film has a plasma frequency of rad/s and damping constant of rad/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 from V to V. In simulations, the unstructured tetrahedral finite-element mesh with a minimum edge length of 0.1 nm is used for ITO 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 the Z axis as shown in red color in Fig. 1 voltage, the electron concentration is cm −3 along 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 from to a maximum of inside 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 from to a minimum of . 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 of V and V, respectively. As a result, the thicknesses of the accumulation and depletion layers, the tunable part of ITO films, are considered as 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 nm 39,40 . 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 states 30 . 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.
Plasma frequency ( ) and damping rate ( ) for ITO film, accumulation and depletion layers are calculated using the , , and from 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 ( ) and extinction coefficient ( ) are calculated from complex refractive index as , where is 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: Since for the ITO film the has small values near the , where the , the minimum value of would be near . The optical properties of the ITO in three states, un-biased ( ), accumulation ( ), and depletion ( ) layers are shown in Fig. 3 with green, red, and blue color lines, respectively. Other parameters are taken from Table 1 as cm 2 /(V·s), , and , similar for all three states.
As shown in Fig. 3(a), the epsilon-near-zero wavelength ( ) of the ITO film ( ), where the green line crosses zero, is around μm. After applying bias voltage, the ENZ wavelength blue-shifts to nm inside the accumulation layer and red-shifts to μm inside the depletion layer. As the moves 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 concentra-tion 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 than 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, this   change 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 modulation 34,35 . However, these tunable metasurfaces suffer from low efficiency due to the inherent high loss of accumulation layer 22,41 , 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 with nm diameter, and four nm wide bias connections on the sides of resonators. The ITO, BST, and Si films are nm, nm, and 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.
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 work 29 . 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 of is 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 from to or according to the applied voltage, while the next 0.5 nm is changed according to the applied voltage and simulation results in Fig. 2 to accurately model the accumulation (0.5 nm) and depletion (1 nm) layers. Under V bias voltage (ON state), the electron concentration of both layers is considered . Under V bias voltage (OFF state 1), the electron concentration of the top 0.5 nm tunable layer is changed to (depletion layer) and the bottom 0.5 nm tunable layer to (accumulation layer), while under V bias voltage (OFF state 2), the electron concentration in the top 0.5 nm tunable layer is changed to and the bottom 0.5 nm tunable layer to .
Simulated reflection spectra of the modulator under three different voltages and 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, nm, to get the strongest resonance and thus the highest loss and the largest modulation depth. The reflection amplitude at nm under V is %. It is a dip in the reflection spectra mainly due to magnetic dipole resonance in the ITO-BST-ITO resonator. By decreasing the voltage to V (OFF state 2), the accumulation layer is created at the bottom of the top ITO film which drops the reflection down to %. 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 to V, the accumulation layer is created in the bottom ITO film and the reflection amplitude drops to % (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: where % and % are the minimum and maximum reflection amplitudes before (ON state) and after (OFF state 2) applying the bias voltage, respectively, at nm. Hence, under V the proposed modulator metasurface achieves 84 dB modulation depth, equal to ~99.99%, if defined as MD = (|∆R|/R Max ) × 100. Under 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 nm and remains below 5% (MD ~22 dB) in the range of nm nm. Under V, where the accumulation layer is created in the bottom ITO film, the reflection amplitude remains below 1% in the range of nm nm and below 5% in the range of nm nm.
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 the XZ plane, according to Fig. 4, in the middle of the circular resonator. Under V bias voltage, it could be seen in Fig. 5 that there was a small dip in the reflection spectrum at λ = 820 nm indicating a slight resonance in the resonator. 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 concentration cm −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 as λ ENZ ~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 to 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 at λ = 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 wavelength 42 . 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 around λ = 820 nm resulting in two dips at λ = 795 nm and λ = 845 nm 25 .
As shown in Fig. 6(c), the same phenomenon happens at 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 cre-λ > 2 ated 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 to 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 the XY plane inside the accumulation layer in the top ITO film under a bias voltage of V. The electric and magnetic fields at λ = 820 nm are shown in Fig. 7.
The electric and magnetic field intensities in the XY plane inside the accumulation layer are shown in Fig.  7(a) and 7(b). The magnetic field looks like an ellipse stretched along the Y axis, 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 the X axis and the magnetic field along the Y axis, 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 positive Y direction 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 the Y axis is created inside the accumulation layer. V = −2.5 Figure 8 shows the impact of the Si disc thickness on the reflection spectra under the bias voltages of V = 0 V and V. As shown in Fig. 8(a), under the bias voltage of V = 0 V, the wavelength of the magnetic dipole resonance is increasing from 630 nm to 820 nm as  the thickness of Si disc is increased from 0 to 50 nm. Moreover, the FWHM of the resonance is increasing from ~15 nm at t Si = 0 nm to ~100 nm at t Si = 50 nm. As shown in Fig. 8(b), under the bias voltage of V, the reflection spectra are similar to Fig. 8(a) without bias voltage. However, as the thickness of the Si disc is in-creased 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 for t Si ≥ 40 nm. This could be explained by the coexistence of ENZ wavelength by two neighboring magnetic dipole resonances. Moreover, the effect of polarization of  incident 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.

× 10 20 cm −3
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 for 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. 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 of and 40 dB in the wavelength range of nm nm under 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.