Color transparent monitor using nanoparticles with electrically tunable viewing angle

In this paper, a transparent display with an electrically tunable viewing angle is proposed and numerically simulated. In this work, Si-SiO2 nanoparticles as core–shell geometry in a periodic array are used. The nanoparticles used in this simulation can be designed in such a way that to absorb less at the blue, green, and red wavelengths. These nanoparticles are stacked horizontally. In this article, by applying a certain amount of voltage at different angles to the transparent screen, the user is given the ability to provide the transparent screen so that, by adjusting the viewing angle of the transparent screen, the content on the transparent screen will be hidden from the view of the people next to the user.


Introduction
There are several ways to make transparent displays, but almost none have reached mass production because each technology has its unique problems. For example, a transparent display based on OLED technology is expensive and requires more equipment (Park et al. 2019;Meyer et al. 2013;Yin et al. 2020;Song et al. 2017). Removing the background screen is a challenge to create a transparent display based on the LCD method (Li et al. 2017;Lin et al. 2012;Yamamoto et al. 2011;Heo et al. 2015). One of the new ways to make a transparent display is using nanoparticles. Hsu et al. (2014), coated nanoparticles with silica cores and silver shells were used to create a blue wavelength-sensitive transparent display that could scatter blue wavelength incoming light and show it on the screen. With this method, a display with a wider viewing angle than other methods was made with a larger size and lower manufacturing cost by SiO 2 -Ag coated nanoparticles. Dolatyari and her colleagues in Dolatyari et al. (2019) were able to increase the transparency of the transparent display by increasing the dispersion cross-section and decreasing the absorption 494 Page 2 of 11 cross-section by using spherical silica-silicon coated nanoparticles in a periodic structure. Eventually, they were able to create a transparent display for blue wavelength with more clarity and a higher figure of merit than the previous works. Seyyedi et al. (2020a), Seyyedi et al. were able to significantly increase the scattering cross-section relative to the periodic array by changing the array and position of the nanoparticles and using spherical silicasilicon nanoparticles. Also, by re-examining the size of the nanoparticles, they were able to reach a sharper and narrower peak of scattering cross-section peak at the blue wavelength than in the previous articles. As shown in Seyyedi et al. (2020b), by changing the morphology of nanoparticles, Prolate Ellipse nanoparticles show higher scattering and lower adsorption cross-section than other nanoparticle morphologies. Chen et al. (2020), Chen et al., by changing the polarization of gold-silver coated elliptical nanoparticles, were able to achieve a greater scattering cross-section and create a red wavelength-sensitive transparent display. Seyyedi et al. (2021a), different combinations of nanoparticles were simulated, and a suitable combination was obtained to have high scattering amplitude at three wavelengths of blue, green, and red and lower absorption amplitude for other wavelengths. Seyyedi et al. (2021b), more practical arrays such as Gaussian structure were compared with other arrays such as the Fibonacci, the periodic, the Thue-morse, etc. Therefore, using a combination of nanoparticles in the form of a Gaussian array makes it possible to create a transparent display with a greater scattering Cross-section at RGB wavelengths. Therefore, many works in the transparent color display have been studied to achieve an optimal structure with the highest scattering and the lowest absorption cross-section with a wide viewing angle. Imagine you are sitting on the subway and you want to watch a movie or read an article on the transparent screen of your mobile phone or you need to check an essential subject on your transparent display in a public place, but you do not want people sitting next to you to see the contents of your screen. Therefore, in this article, we try to limit the viewing angle of the transparent screen by applying different voltages so that people can communicate with their transparent screen in a personal and individual situation in a public place without being disturbed by anyone else.

Mathematical modeling
To calculate far-field angular, scattering, and absorption cross-section, we assume that a plane wave propagates in the z-direction while the wave vector is zero in the x and y directions and k is only in the z-direction(k = 0,0,k). The amplitude of a complex electric and magnetic field is written based on the incident wave in the form of S and P polarizations according to the coordinates of the (x, y) planes and k = ωn/c (Bekshaev et al. 2013).
where ε, µ, n = √ represents permittivity, permeability, and refractive index respectively. The incident light hits the x-y planes and is emitted in the z-direction. In this work, we apply an electrical field to x-y planes with different angles to change the viewing angle. For this purpose, we used the E = (V a /L) V/m equation to estimate the amount of applied voltage. In this relation, V a and L are externally applied electric potential and length of media in applied voltage direction respectively. The applied field has DC and ac values. The goal is to limit the viewing angle to a specific and slightly limited range. We simulated angle tenability between − 30 to 30° and then generalize it to 360°. For this purpose, we considered the screen so that voltage can be applied to the screen separately from both sides, and the screen can be viewed at limited viewing angles. By changing the value of theta, the angle of the applied field can be changed. Note that increasing the applied field does not affect the rate of absorption and scattering cross-section. Therefore, it is easy to change the viewing angle by using voltage or field to the optimal structure obtained from Seyyedi et al. (2020a), Seyyedi et al. (2020b), Chen et al. (2020), Seyyedi et al. (2021a) and Seyyedi et al. (2021b) without affecting the other acquired optimal factors. For the convenience of making a transparent display, we assumed that the nanoparticles were placed next to each other periodically. As mentioned in previously published articles from this group, the optimal composition of nanoparticles was placed horizontally in a blue-redgreen combination. In this regard, according to the results obtained in previous articles, the radius of coated nanoparticles for the core and shell is 50-90, 60-90, and 75-105 nm to have the correct scattering rate for blue, green, and red wavelengths, respectively. Seyyedi et al. (2020a), we compared Si/SiO 2 and SiO 2 /Ag coated nanoparticles and found that the scattering cross-section for Si/SiO 2 coated nanoparticles is much higher than the other one. Both coated nanoparticles have relatively equal and low absorption cross-sections. Therefore, we considered the coated nanoparticles to be Si-SiO 2 . As we discussed in previous articles and can be seen in Fig. 1, using the structure of the combination of the three nanoparticles for the periodic structure, we were able to observe the scattering cross-section with sharp peaks in all three wavelengths of blue, red, and green and less absorption crosssection in the rest of the wavelengths. Also, the absorption rate is lower in the whole wavelength range. In the next step, we change the angle of view by applying the field at different angles.
The schematic of this work is shown in Fig. 2. By applying the field at angles of − 30 to 30°, the light scattered on the XY plate is reflected around − 30 to 30°, and only in the specified angles can the desired image be seen, and no image can be seen in other angles of view. Depending on the angle of incident light into the structure, we can change the angle of view on the screen and control it. From both sides of the transparent display, the electric field can be applied to the transparent display from different angles and the change of angle can be observed in the scattered light.***

Cross Section
Scattering Absorbtion

Numerical Simulation
In this paper, we apply electric fields at different angles to the periodic structure of nanoparticles and measure the angle of view for scattered light. We assumed the propagation direction along the Z-axis, the polarization along the X-axis, and the far-field on the XY plane. As shown in Figs. 3,4,5,6,7,8,9,10,11,12,13,14 and 15, by applying an electric field at − 30 to 30° from the − X side, the angle of view for scattered field changes to − 30 to 30° in the XY plane. The amplitude of the input field is 1 V per meter. As it is shown in Fig. 3, by applying an electric field at − 30° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too.
As it is shown in Fig. 4, by applying an electric field at − 25° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. Considering the radiated patterns distribution, it can be concluded that the considered transparent display has so narrow-band radiation pattern and only the observer in the desired direction can see the image and movie.
As it is shown in Fig. 5, by applying an electric field at − 20° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. The simulated result is similar to the reported case before. The radiated pattern is narrowband and it is very nice for some applications.
Considering Fig. 6, by applying an electric field at − 15° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. In this case, the radiation pattern in the X-Z plane is enhanced versus in previous cases.
Considering Fig. 7, by applying an electric field at − 10° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. In this case, the radiation pattern in the X-Z plane is enhanced versus in previous cases.
Considering Fig. 8, by applying an electric field at − 5° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. In this case, the radiation pattern in the X-Z plane is enhanced versus in previous cases and approximately is the same as the X-Y radiation pattern.
Considering Fig. 9, by applying an electric field at − 0° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. In this case, the radiation pattern in the X-Z plane is the same as the X-Y radiation pattern. The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) − 30° from the X side and b) − 30° from the − X side Considering Fig. 10, by applying an electric field at + 5° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. In this case, the radiation pattern in the X-Z plane is decreased versus in previous cases.
Considering Fig. 11, by applying an electric field at + 10° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. In this case, the radiation pattern in the X-Z plane is decreased versus in previous cases.
Considering Fig. 12, by applying an electric field at + 15° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. In this case, the radiation pattern in the X-Z plane is decreased versus in previous cases.
Considering Fig. 13, by applying an electric field at + 20° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. In this case, the radiation pattern in the X-Z plane is decreased versus in previous cases.
Considering Fig. 14, by applying an electric field at + 25° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. In this case, the radiation pattern in the X-Z plane is decreased versus in previous cases.
Considering Fig. 15, by applying an electric field at + 30° in + X and -X directions, the scattered fields appear in that direction in the X-Y plane. Also, radiation patterns in Y-Z and X-Z planes are considered too. In this case, the radiation pattern in the X-Z plane is decreased versus in previous cases.
Finally, for different angles in the whole 360°, the following result is obtained for field pattern rotation in the whole 360°.
As shown in Figs. 3,4,5,6,7,8,9,10,11,12,13,14,15 and 16, by applying an electric field with different angles, the angle of view for scattered light changes. On the other hand, by increasing the number of nanoparticles, the scattering and absorption cross-section can be changed, but the angle of view remains unchanged. Also, as mentioned, the amplitude of the applied electric field is 1 V/m, and changing the amplitude of the electric field does a b Fig. 4 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) − 25° from the − X side, and b) − 25° from the + X side a b Fig. 5 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) − 20° from the − X side, and b) − 20° from the + X side a b Fig. 6 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) − 15° from the − X side, and b) − 15°from the + X side a b Fig. 7 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) − 10° from the − X side, and b) − 10° from the + X side a b Fig. 8 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) − 5° from the − X side, and b) − 5° from the + X side a b Fig. 9 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) 0° from the − X side, and b) 0° from the + X side a b Fig. 10 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) 5° from the − X side, and b) 5° from the + X side a b Fig. 11 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) 10° from the − X side, b) 10° from the + X side a b Fig. 12 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) 15° from the − X side, and b) 15° from the + X side a b Fig. 13 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) 20° from the − X side, and b) 20° from the − X side a b Fig. 14 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) 25° from the − X side, and b) 25° from the − X side a b Fig. 15 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at a) 30° from the − X side, and b) 30° from the + X side not affect the amount of scattering, absorption, and angle of view. It is worth noting, that applying an electric field changes the polarization of light and therefore the reflection from the transparent display environment changes polarly.

Conclusion
In this paper, we numerically simulated a transparent display with Si-SiO 2 coated nanoparticles with a limited viewing angle by applying different fields. In this type of display, we used nanoparticles suitable for blue, green, and red wavelengths placed side by side horizontally in a periodic structure. By applying an electric DC field with amplitude value unity per meter and different angles, we were able to adjust the display field of view at a certain angle. We give the ability to users of the transparent screen to use it personally, and other people cannot see the content on the screen. Fig. 16 The amount of angle of view for the periodic structure of nanoparticles by applying an electric field at different angles in whole 360° with a 15° distance between them