In order to obtain tunable polarization modulation, the metasurface requires to support two plasmonic eigenstates. As a result, an array of anisotropic Al nanoantennas, rotated by θ = 45° with respect to the y-axis is designed and utilized as the building block.
Figure 4.2a schematically illustrates the metasurface unit cell. The length and width of the antennas are chosen to be L = 280 nm, w = 230 nm such that the metasurface supports resonances at wavelengths close to 1550 nm. The period of the metasurface is p = 400 nm.
To simulate the optical response of the metasurface, we use the FDTD method (Lumerical). In our simulations, we use PML boundary condition in the z-direction and periodic boundary conditions in both the x- and y-directions. Hence, the calculations of the reflection intensity and phase shift of the Al nanoantennas are performed in an array configuration. In our simulations, we assume that the incident beam is linearly polarized with an electric field Ein along the y-axis (with 1 V/m amplitude), and hence, making an angle of 45° with respect to the long axis of the nanoantennas (see Fig. 4.2b). This enables simultaneous excitation of two gap plasmon modes associated with the size of
the long and short axes of the Al nanoantenna at two distinct wavelengths in the telecommunication wavelength range, as shown in Fig. 4.2c.
For the first excited mode (blue curve in Fig. 4.2c), the electric field component along the long-axis of the nanoantenna is dominant, while for the second excited mode (magenta curve in Fig. 4.2c), the electric field component along the short-axis of the nanoantenna is influential. By projecting the reflected beam onto the x- and y-axes, one could see that the x- and y- polarized components of the reflected light can be modulated by controlling the interaction between the two induced plasmonic modes (see Fig. 4.2b).
Figure 4.2: Metasurface design principle for demonstration of tunable polarization conversion. (a) Schematic for the tunable metasurface unit structure. The metasurface consists of a 150 nm-thick Al back reflector, a 20 nm-thick HAOL, a 5 nm-thick ITO, and an array of Al nanostructures with a thickness of 80 nm. The unit element dimensions are defined as: L = 280 nm, w = 230 nm, θ = 45°, and p = 400 nm. (b) Design principle of tunable polarization converter. When a y-polarized light interacts with the patch antenna, two gap plasmon modes are excited. The amplitude and phase of the excited modes can be modulated by biasing the ITO with respect to the Al mirror. (c) The simulated reflectance spectrum of optimized metasurface design [177].
Then, we apply a DC bias between the Al back reflector and the ITO layer, leading to the modulation of the permittivity of ITO. Figure 4.3 shows the spatial distribution of
the real part of the ITO permittivity for positive (Fig. 4.3a) and negative (Fig. 4.3b) applied voltages. Here, the carrier concentration of ITO is assumed to be 2.8×1020 cm-
3. As can be seen in Fig. 4.3a, for some applied voltages, the real part of permittivity approaches zero, creating an ENZ condition in the ITO layer. By coupling this ENZ region to the resonances provided by the metasurface, one could alter the interaction between the induced plasmonic modes, leading to modulation of the polarization state of the reflected light. It is worth mentioning that the ENZ condition shows up only when the gate voltage is greater than ~3 V.
Figure 4.3: Modulation of ITO properties under an applied bias. Spatial distribution of the real part of permittivity of a 5 nm-thick ITO layer under (a) positive and (b) negative applied biases with respect to the back reflector. The operating wavelength is set to 1580 nm [177].
In order to investigate the dynamic behavior of the metasurface, we study the amplitude and phase of the x- and y-polarized reflected beams under applied bias, when the metasurface is illuminated by a y-polarized beam.
Figure 4.4 shows the reflectance spectra of the co- and cross-polarized reflected beams for different applied biases. As can be seen in Fig. 4.4, the intensities of both the x- and y-polarized reflected beams are modulated when applying bias, confirming the capability of the proposed metasurface to provide amplitude modulation. It should be noted that due to the absence of ENZ condition, the metasurface shows much weaker amplitude modulation under negative applied biases (see Figs. 4.4d, e).
Figure 4.4: Amplitude modulation provided by the tunable polarization conversion metasurface. (a) Simulated reflectance spectra of the co- (top panel) and cross-polarized (bottom panel) light for four different applied voltages. The inset of the bottom panel shows the orientation of Al nanoantenna. Simulated reflectance of the (b, c) co- and (d, e) cross- polarized light as a function of wavelength and applied bias for (b, d) positive and (c, e) negative voltages [177].
In order to obtain a polarization converter, the phase shift provided by the device plays a vital role. Figure 4.5 shows the phase difference between x- and y-polarized components of the reflected light as a function of wavelength and applied bias. Here, the phase difference is defined as ∆φ = φyy – φxy, where φij (i, j = x, y) presents the phase of the i-polarized reflected beam under a j-polarized illumination. As can be seen in Fig.
4.5, when changing the applied bias, the metasurface can provide a significant phase modulation. Similar to the amplitude modulation under positive applied biases (Figs.
4.4b, d), a more dominant phase modulation can be achieved at such bias voltages.
In order to further explore the operating principle of the metasurface, we investigate the near-field coupling conditions at different applied biases by studying the field distributions of the metasurface. Figure 4.6 shows the z component of the electric field (Fig. 4.6a) and the intensity of the magnetic field (Fig. 4.6b) at three different applied biases.
As can be seen, in the absence of applied bias, a strong near-field coupling between the Al nanoantenna and back reflector is observed, which results in a strong magnetic field confined within the HAOL gate dielectric layer.
Figure 4.5: Phase modulation provided by the tunable polarization conversion metasurface. The phase difference between x- and y-polarized reflected beams as a function of wavelength and applied bias. The white solid line marks the wavelength and voltage pairs at which equal reflectance values are observed for x- and y-polarized components of the reflected beam [177].
Figure 4.6: Spatial distribution of the electromagnetic fields in the tunable polarization conversion metasurface under an applied bias. Spatial distribution of (a) z-component of electric field and (b) intensity of the magnetic field for three different applied biases. Here, the incident beam is polarized along the y-axis and forms an angle of 45° with the long-axis of the nanoantennas. The incident plane-wave has an amplitude of 1 V/m and a wavelength of 1580 nm [177].
Under a linearly y-polarized illumination, the appearance of the z-component of the electric field in the x-z plane indicates a linear cross-polarization conversion. It can be observed that the z-component of the electric field has remarkably higher values in the y-z plane compared to that of the x-z plane. This will result in the reflected beam to be mostly aligned along the x-axis due to weaker field confinement.
When the applied bias increases to 4 V, the appearance of the ENZ condition breaks the field symmetry in the ITO layer. This weakens the magnetic field confinement in the HAOL layer, as shown in the middle panel of Fig. 4.6b. Moreover, as a result of the similar values of the z-component of the electric field in the x-z and y-z planes, one can anticipate observing closer x- and y-polarized reflectance values at an applied bias of 4 V.
Further increasing the applied bias to 14 V, the spatial position of the ENZ condition shifts towards central regions of the ITO layer (see the right panel of Fig. 4.6a). This results in a more significant interaction between the Al nanoantenna and the back reflector and makes the magnetic field to be less confined in the HAOL layer (see right panel of Fig. 4.6b). At this applied bias, we can expect to see similar reflectance values for the x- and y-polarized reflected beams because of the close values of the z- component of the electric field in the x-z and y-z planes.
The presented results show that by tailoring the ENZ condition of the ITO layer as a result of changing the applied bias, one can alter the interaction between the two excited gap plasmon modes, leading to the possibility of modulation of the amplitude, phase, and polarization state of the reflected light beam.
4.4. Dynamic Modulation of the Polarization State of the Reflected Beam by