# A Self-Color-Changing Film with Periodic Nanostructure for Anti-Counterfeit Application
## 3 Results and Discussion
### The Parametric Studies  
In the study process, the initial W, L and H values are 110 nm. The parametric study starts out by adjusting the parameter W. When the optimal size of W is obtained, we can use it for the next parametric study. Finally, when we obtain the most satisfactory size of L, we use the best size of W and L to initiate the adjustment of the final parameter, H. The final result is the combined effect of all three parameters. Figure 2 demonstrates that at a wavelength of more than 500 nm, varying W does not affect the transmittance too significantly. The transmittance curves appear to overlap and do not differ much. At a wavelength of less than 500 nm, it is found that the transmittance decreases substantially.  
Figure 5 demonstrates that when W is more than 110 nm, the transmittance decreases substantially. The transmittance in the 400 to 550 nm regime is close to that in the 550 to 700 nm regime, which does not have an intersection point. Therefore, W = 110 nm is chosen as the value of choice for the subsequent studies. In the study cases of L and H, the transmittance changes from a low-pass filter to a convex curve when L and H are more than 140 nm and 130 nm, as shown in Figures 6 and 7, respectively. Therefore, we conclude that the best size of a nanocube to exhibit a low-pass filter is W = 110 nm, L = 140 nm, and H = 130 nm. The low-pass filter behavior leads to an intersection of reflectance and transmittance curves, as shown in Figure 8 for the 1.4-microns film thickness. As the transmittance decreases, the reflectance increases. This causes both sides of the film to show two different colors and change color automatically when the film is flipped.  
From the parametric studies, the transmittance can be controlled by varying the width (W), length (L), and height (H) of the nanocube. Adjusting the width (W) of the nanocube can induce the plasmonic effect, as observed by the emergence of a convex on the transmittance curve, consistent with the research by [PERSON] et al. [41] and [PERSON] et al. [38]. However, varying the width (W) alone to cause the convex is not sufficient to create a color-changing security film. Such behavior occurs when the transmittance curve exhibits a low-pass characteristic that divides the transmittance diagram into two regimes: high transmittance and high reflectance. Therefore, we need to vary the length (L) to adjust the nanocube size, in order to induce a frequency-selective surface behavior. The frequency-selective surface behavior rejects some wavelengths to allow the proposed film to show a low-pass filter behavior. The color of the light passing through or reflected from the film can be obtained [30].  
The incident light may not always strike the film's surface at a normal incidence in actual use; therefore, we simulate how the light incidence at an oblique angle with respect to the film's x-axis affects the transmittance and the reflectance, as in Figure 9. From the simulation, the film still works well. The transmittance does not vary much when the incident angle is between 0 and 30 degrees. In the range of 60-70 degrees, the color of the proposed film changes from blue to yellow without the need to reverse the film, because it falls in the critical angle regime. This phenomenon is a characteristic that is specific to our film and is not available in other security techniques.  
Figure 8: Transmittance and reflectance of the nanocube at optimal dimension.  
Figure 7: Transmittance when H is varied from 130 to 200 nm.