Estrategias preventivas como medio de lucha contra el delito

The next step is the control of the LC by means of the electric field, i.e., by applying different voltages to the LC cell. This method is used in LC displays. In this case, the LC cell should be fabricated using substrates with a sputtered layer of the transparent conductor ITO to which electrodes will be connected. The thickness of such layers is usually about 10−50 nm, which is much smaller than the wavelength. Since the layers are transparent, they do not affect the numerical calculations of the propagation of the electromagnetic wave in this structure. In the case of electrical control, the LC layer should be considered not only as an anisotropic medium according to its nature but also as an inhomogeneous medium. In the applied electric field, the LC near the interface with the orienting coating tends to keep its orientation specified by this interface and, closer to the centre of the cell, is rearranged along the electric field.

The effective refractive index of the LC as a function of the orientation angle θ (see Fig. 3.1) is given by the formula

neff(θ) = no ne p n2 ocos2θ+n2esin2θ . (3.3)

Since the inclination of the LC in the cell is inhomogeneous, the angle θ =θ(x, y, z) depends on the coordinates. In theLumericalsimulation software, the LC can be simulated directly by specifying the inclination angle θ and ϕ, which can, in particular, depend on the coordinates. In order to find the dependence of the angle θ on the applied voltage, it is necessary to determine the minimum of the free energy of the LC in the electric field. I use several approximations: (i) only the azimuth angle θvaries, whereas the polar angle ϕ does not change; (ii) the free energy of the LC is simulated in the one-constant approximation; and (iii) rigid boundary conditions are imposed at the interface with the orienting coating, which corresponds to a high adhesion energy. Thus, it is necessary to

Figure 3.6: Distribution of the angle theta in the liquid crystal cell at various applied volt- ages [213].

solve the system of equations

( K∇2 x,zθ+ ε0∆ε1kHz|Ex(x,z)|2 2 sin(2θ) = 0 ∇ ·(ε0εE) = 0,whereE =−∇V . (3.4)

The main type of deformation in this orientation of the LC in the applied electric field is the transverse strain (S-strain). Thus, according to the technical specification for the LC E7,K=K11= 11.1 pN and ∆ε1kHz = 14.1 is the anisotropy of the dielectric constant of the LC at the frequency 1kHz of the applied electric field rather than in the optical range.

The system of coupled Equations (3.4) was solved using theCOMSOLnumerical sim- ulation packet. The solution is shown in Fig.3.6. As is seen in the figure, as the voltage increases, the LC approaches the surface, but the layer with the inhomogeneous distri- bution of the angle θ always remains owing to the orienting coating, which will certainly affect the optical response of the structure.

I found the two-dimensional distribution of the deflection angle of the LC, but my problem is three-dimensional. Since the disk is an axially symmetric figure, to find the volume distribution of the LC, I rotate my solution by 180° about the z axis. Knowing the distribution of the orientation of the LC in the bulk of the cell, I can calculate the transmission spectra and phase of light for any applied voltage. The results of these calculations are shown in Fig.3.7. According to this figure, resonances are shifted such that the transmittance changes at the wavelength at which the Huygens’ regime is observed. The Huygens’ regime is established at a voltage of 10 V. The phase of light changes byπ owing primarily to a change in the refractive index of the LC. Beginning with a voltage of 40 V, saturation occurs when a further increase in the voltage hardly changes the spectral and phase characteristics of light.

Figure 3.7: (a) Transmittance spectra of the liquid crystal cell with a metasurface at various voltages. (b) Voltage dependence of the transmittance. (c) Phase of light transmitted through the liquid crystal cell with a metasurface at various voltages.

3.4

Conclusion to the Chapter

To summarise, the effect of the refractive index of the environment on the fully dielectric metasurface which consists of an array of silicon disks and operates in the Huygens’ regime has been numerically simulated. It has been shown that the phase of light transmitted through the metasurface can be controlled with an amplitude efficiency close to 100% in the case of isotropic homogeneous variation of the refractive index of material around disks. Numerical calculations for the case of the use of the LC as the controlling medium demonstrate the possibility of modulation of only the amplitude of a light wave both by the temperature variation of the refractive index of the LC and by the application of a voltage to the LC cell. Thus, to produce tunable metasurfaces based on the LC to control the phase front of the light wave, the metasurface should be designed taking into account the anisotropy and inhomogeneity of the distribution of the refractive index in the LC cell.

Electrical tuning of metasurface

based on liquid crystal

The most valuable property of a liquid crystal is the possibility to control its orientation by an external electric field. When the thickness of an LC cell is small enough (tens of micrometres), it is sufficient to apply a low voltage to the cell, to get reorientation of the LC molecules inside. It means that we can control the optical response of an LC cell with electronics. This property made LC so widely applicable substance. Today LCD (liquid crystal display) industry is one of the biggest in the world, and this is entirely due to the electrical tunability of LC. We are going to use this feature for tuning all- dielectric metasurfaces. Using the temperature dependence of the refractive index of a nematic LC for tuning of silicon metasurfaces was implemented before [165]. I described this work in the Introduction. Another work proposed to use the electric-field induced reorientation of LC for tuning all-dielectric metasurfaces in the mid-infrared (mid-IR) wavelength region [215]. However, the effect in this work was only theoretically studied.

Here, I demonstrate an active control of the spectral response of Mie-resonant silicon metasurfaces using voltage induced reorientation of the anisotropic nematic LC in a mod- erate electric field. I achieve a broad tuning range of 50 nm and 75% absolute transmission change atλ≈1550 nm by application of an AC bias voltage of 70 V at 1 kHz. In addition, I directly retrieve the tuning of thetransmittance phase across the Mie-type resonance of a dielectric metasurface.

I use an all-dielectric metasurface composed of silicon nanodisks integrated into an LC cell, as shown in Figs. 4.1(a) and 4.1(b). Being composed of crystalline silicon, the nanodisks exhibit very low absorption losses at wavelengths above the silicon electronic bandgap around 1.1 µm and support the strong electric and magnetic dipolar Mie-type resonances in the telecommunication spectral range, which can be tailored by adjusting the disk height, diameter, or lattice constant of the metasurface [96,121], as is described in the Introduction. Furthermore, such metasurfaces can be designed to operate as highly transparent Huygens’ metasurfaces by bringing their electric and magnetic dipole reso- nances into spectral overlap [97,121]. In this work, I choose the parameters such that the electric and magnetic resonances are well separated to reveal and evaluate the resonance shifts induced by the voltage controlled LC realignment.

The fabrication of the metasurfaces is performed by my colleagues using electron-beam lithography on silicon-on-insulator wafers, followed by reactive ion etching and residual resist removal with an oxygen plasma, as described in detail in Chapter2. Figure4.1(b) shows a scanning electron microscopy (SEM) image of a typical nanodisk metasurface. In my experiments, the nanodisks have a height of h = 220 nm and a diameter of d =

Figure 4.1: (a) Sketch of a silicon nanodisk metasurface integrated into the LC cell. (b) SEM image of a fabricated silicon nanodisk metasurface. (c) Schematic of the LC alignment for no applied voltage (“off” case) and for the case when a moderate voltage is applied between the two electrodes of the LC cell (“on” case). The red arrow indicates the polarization of the incident light [216].

606 nm. They are arranged in a square array with a lattice constant of a= 909 nm. The dimensions of the disks are chosen such that the electric and magnetic dipolar resonances occur in the telecommunication wavelength range. The fabricated metasurface is then integrated into an LC cell in such a way that the silicon nanodisks are fully embedded into the LC. I employ the nematic LC Merck Licristal E7, which is widely used in display technologies and exhibits high birefringence (∼ 0.2), with ne = 1.7 and no = 1.51 at room temperature [214]. The LC cell preparation process is shown in Fig. 4.2. The cell is constructed by sandwiching the LC between the metasurface wafer and a glass substrate coated with indium-tin-oxide (ITO) and with a brushed layer of Nylon-6 in 2,2,2-trichloroethanol (alignment polymer). A suitable spacer material is employed to fix the (inside) thickness of the LC cell to 5µm. The brushed Nylon-6 layer induces a preferred alignment direction of the LC. The ITO layer renders the substrate conductive for use as an electrode. In this way, a bias voltage can be applied between the ITO electrode and the silicon handle wafer of the metasurface sample. Although I do not additionally control the alignment of the LC on the metasurface, without an applied voltage, the LC alignment induced by the brushed Nylon-6 layer is approximately sustained throughout the LC cell (see Fig. 4.1(c), voltage “off”). This was verified by the strong optical anisotropy of the metasurface embedded into the LC without applied voltage. The application of a bias voltage between the two electrodes reorientates the LC molecules perpendicular to the metasurface (see Fig. 4.1(c), voltage “on”). I choose an AC bias voltage (1 kHz), which is common in the modern LC industry standards and allows to avoid current flows, liquid crystal orientation instabilities, heating, and other detrimental effects associated with DC fields [217,218]. The small thickness of the LC cell allows for strong reorientation of the LC in the vicinity of silicon disks.

Figure 4.2: LC cell fabrication process.

4.1

Numerical simulation of spectral tuning

In order to investigate the effect of LC reorientation on the optical properties of the metasurface, I numerically calculate the transmittance spectra of the silicon nanodisk metasurface covered by an ideal uniformly distributed nematic LC. I use the software package COMSOL Multiphysics and represent the LC as a homogeneous anisotropic di- electric medium with ne = 1.7 and no = 1.51 [214]. The refractive index of silicon disks is 3.5, and silica substrate is 1.45. The angle between the metasurface plane and the LC anisotropy axis is denoted with ΘLC, with ΘLC= 0◦ being equivalent to the voltage “off” case and ΘLC = 90◦ to the voltage “on” case (see Fig. 4.3(a)). The polarisation of the incoming field is parallel to the anisotropy axis of the LC in the “off” case. Thereby, the extraordinary wave is excited during the “off” state and the ordinary wave during the “on” state. To model the reorientation of the LC in the externally applied electric field, I tune the angle ΘLC from 0◦ to 90◦ in steps of 10◦. These numerical results are shown in Fig. 4.3(a). The white lines highlight the spectral positions of the two resonances of interest. We observe a red-shift of the magnetic dipole resonance and a blue-shift of the electric dipole resonance with increasing angle ΘLC. Thus, the two resonances, having a clear spectral separation in the “off” case, move closer together for the LC realignment. Figure 4.3(b) shows the transmittance spectra for the ideal “on” and “off” cases for com- parison with experimental data. The spectral shift for electric dipole resonance is 69 nm and for magnetic dipole resonance is 61 nm.