6.2. S I - BASED D IELECTRIC A CTIVE M ETASURFACES
6.2.2. Optical Response of the Si-based Dielectric Active Metasurfaces
the Si permittivity in a region smaller than 20 nm-thick in the case of electron depletion, and less than 40% decrement in the real part of permittivity in a region narrower than 1.5 nm-thick in the case of hole accumulation at the wavelength of = 1.55 µm.
Moreover, the formation of the ENZ region in the ITO layer enhances the light-matter interactions substantially. As a result, the main contributing factor to the tunable optical response of the metasurface is the charge accumulation inside the ITO layer. It was also shown previously that the modification of Im{εITO} has an important role in achieving considerable wide phase modulation through satisfying the critical coupling condition (so-called impedance matching) [246]–[251].
In the current design, the refractive indices of undoped Si, Al2O3, and SiO2 are derived from the experimentally-measured data by Palik [252].
part of the electromagnetic field confined below the Si bias lines would be able to enhance the effect of a slight modification of carrier concentration within the ultrathin ITO accumulation layer due to the vicinity to the ITO layer. As a result, one could expect a notable modulation of the optical response of the metasurface contributed to this mentioned field confinement.
Figure 6.2: Dual-mode Si-based metasurface operating in the reflection mode. (a) amplitude and (b) phase of the reflection from the Si-based dielectric metasurface illuminated by x-polarized incident beam for the unbiased case in the presence (solid blue lines) and absence (dashed red lines) of the bias lines. Spatial distribution of the electromagnetic fields in the x-z plane at the resonant wavelengths of (c) 1696 nm in the presence of the bias lines (d) 1691 nm in the absence of bias lines. The color bar shows the magnitude of the y-component of the magnetic field and the white arrows present the normalized electric displacement currents. The spectrum of the (e) amplitude and (f) phase of the reflection from the metasurface under applied bias. The dashed lines denote the points for which the real-part of ITO permittivity, Re{εITO}, at the ITO-Al2O3 interface is equal to −1, 0, and 1, illustrating the ENZ region of the ITO accumulation layer. (g) Amplitude and (h) phase of the reflection from the metasurface as a function of applied voltage at the operating wavelength of λRefl ≈ 1696 nm. The shadowed regions present the dielectric breakdown of the gate dielectric [71].
In order to delve deeper into the effect of the bias lines, the amplitude and phase response of the metasurface without the bias lines are also plotted in Figs. 6.2a, b. As can be seen, in the absence of the bias lines, a low Q-factor resonance as well as a spectral phase variation of ~π would be obtained at the operating wavelength of λ = 1691 nm. Figure 6.2d presents the spatial distribution of the magnetic field within the metasurface with no bias line. As can be seen, no strong field enhancement is observed
near the ITO active region in this case. As a consequence, the Si nanobars, which serve as the electrodes that electrically connect the nanodisk antennas, could give rise to the required resonant reflection in a critical spectral regime for phase modulation by breaking the geometrical symmetry of the unit cells.
The spectra of the amplitude and phase of the reflection from the metasurface under an applied bias voltage are depicted in Figs. 6.2e, f, respectively. As can be seen, when increasing the applied bias, the resonance will first blueshift and then redshift. Figures 6.2g, h present the reflection amplitude and phase, respectively at the operating wavelength of λRefl ≈ 1696 nm. One can observe an amplitude modulation accompanied by large phase modulation of ~240˚ with an applied gate bias lower than the breakdown threshold of 10.5 V.
After confirming the tunable optical response of the metasurface in reflection mode, the metasurface is illuminated by a TM polarized incident with the magnetic field vector being normal to the plane of incidence as shown in Fig. 6.1a, to examine the optical response of the metasurface in transmission mode. Similar to the reflection mode, the geometrical resonance of the structure should overlap with the ITO accumulation layer to achieve relatively large electrical modulation of the optical response of the metasurface in transmission mode. The amplitude and phase of the transmission through the metasurface are plotted in Figs. 6.3a, b, respectively.
As can be seen, the transmission response features two resonances: i) a high-Q-factor resonance and a rapid transmission phase variation at the resonant wavelengths of λ1Tran
≈ 1563 nm, and ii) a low-Q-factor resonance and a slow transmission phase variation at the resonant wavelengths of λ2Tran ≈ 1641 nm. The spatial distributions of the electromagnetic fields in the y-z plane at these two resonance wavelengths are depicted in Figs. 6.3c, d.
As can be seen in Figs. 6.3c, d, at both wavelengths, there is a circulation of the electric displacement currents around the strengthened magnetic field at the center of the unit cell, confirming the magnetic nature of the corresponding resonances. It can also be observed that there is a confinement of the magnetic field between the Si nanodisk and the Si back slab in the vicinity of the ITO active layer. However, the strength of the confined magnetic field at λ1Tran is nearly 2.2 times larger than the one at λ2Tran. This large local field enhancement at λ1Tran could be coupled to the ENZ region of the ITO
layer which itself would lead to a significantly enhanced electric field to satisfy the continuity of the normal displacement field. As a consequence, one can expect a large phase modulation at the operating wavelength of λ1Tran. It should be noted that unlike the reflection mode, the presence or absence of the bias lines and choice of their dimensions had negligible impacts on the transmission response of the unit cell. That is due to the fact that the bias lines will be effectively transparent in the case of a y- polarized beam which is the illumination used in the transmission mode.
Figure 6.3: Dual-mode Si-based metasurface operating in the transmission mode. (a) Amplitude and (b) phase of the transmission through the Si-based dielectric metasurface.
Spatial distribution of the electromagnetic fields in the z-y plane at the resonant wavelengths of (c) λ1Tran ≈ 1563 nm and (d) λ2Tran ≈ 1641 nm. The color bar shows the normal component of the magnetic field and the white arrows present the normalized electric displacement currents.
Spectrum of the (e) amplitude and (f) phase of the transmission through the metasurface under applied bias. The dashed lines denote the points for which the real-part of ITO permittivity, Re{εITO}, at the ITO-Al2O3 interface is equal to −1, 0, and 1, illustrating the ENZ region of the ITO accumulation layer. (g) Amplitude and (h) phase of the transmission through the metasurface as a function of applied voltage at the operating wavelength of λ1Tran ≈ 1563 nm.
The shadowed regions present the dielectric breakdown of the gate dielectric [71].
Figures 6.3e, f show the spectra of the amplitude and phase of the transmission through the metasurface as functions of wavelength and applied bias voltage. As can be seen, when increasing the bias voltage, the resonance first faces a redshift followed by a blueshift. It should be noted that the spectral shift and the phase swing of the transmission resonance as a function of applied bias voltage exhibits an opposite trend compared to the reflection resonance. The amplitude and phase of the transmission at
the fixed operating wavelength of λ1Tran ≈ 1563 nm as functions of the applied bias are plotted in Figs. 6.3g, h, respectively.
It can be observed that when changing the applied bias, modulation of the transmission amplitude, accompanied by a phase modulation coverage of ~270° is realized at the operating wavelength of λ1Tran ≈ 1563 nm.
As seen in this section, using Si-based active metasurfaces, we can achieve dielectric metasurface elements operating both in transmission and reflection modes (dual-mode operation) at two distinct operating wavelengths. By altering the bias applied between Si nanoantennas and an ITO layer, one can tune the amplitude and phase of the reflected/transmitted light, and accordingly, engineer the wavefront of the scattered light at will.