## 4 Results and Discussion
In addition, a multi-oscillation beam with a different resonance mode was found between the PBGs when the incidence wave angle was \(\theta\sim\frac{\pi}{2}\). In this part, we study the effect of the deformation of layer thicknesses on the position of the PBGs and the intensity of the resonance peaks. By modeling the deposition layer by layer on the silicon substrates of the main plasma quasi-periodic PCs (PQPCs), we assume that the deformation of layer thicknesses approximately follows the mathematic law \(y=x^{h+1}\), where \(x\) and \(y\) represent the main and the deformed z-coordinate of the layers, respectively, and \(h\) denotes the deformation degree. Figure 3 shows the reflectance spectra of PQPCs as a function of frequency (Hz) and the incidence angle (\(\theta\)) and for different values of the deformation degree \(h\). It is clear that the reflectance of waves is sensitive to the applied deformation strain. By increasing the deformation degree \(h\), the intensity of the output beam when \(h\) = 0 (see Figure 2) decreases progressively, and several pseudo-PBGs appear, where the propagation of waves is inhibited. The actual PBGs shift toward the low frequencies, and an enlargement of their width is noted. Physically, the increase in the deformation strain allows an increase in the geometric thicknesses of the layers, which corresponds to the adjustment of the refractive indices' contrast. This phenomenon influences the propagation of waves and the distribution of the electromagnetic field. Here, in Figure 2, we note that the maximum shift of PBGs is obtained when \(h\) = 0.02. In addition, the majority of the resonance peaks are attenuated. Figure 1: A schematic representation of the proposed multilayer PC structure according to the seventh generation of the classic Fibonacci sequence. The multilayers are made of GaSe (layers H) and sinusoidal plasma (layers L) materials. Figure 2: _Cont._  
Figure 3: _Cont_. Figure 2: Reflectance spectra of quasi-periodic Fibonacci multilayered stacks as function of frequency and the incidence angle (\(\theta\)) and for different sequence orders (\(l\) set to be from 10 to 13). In Equation (11), we see that the refractive index of the modulated sinusoidal plasma layer depends on two parameters, \(m\) and \(a\). In this part, we study the effect of the variation of the coefficient \(m\) of sinusoidal plasma layers on the reflectance spectra, and in the next part, we will study the effect of parameter \(a\). In Figure 4, we note that by changing the coefficient \(m\), the output beam intensity can be controlled. The oscillation beams in the reflectance spectrum appear in the blue zones between the PBGs. When \(m=10\), the intensity of these beams is maximal; afterward, and when parameter \(m\) is changed to 20, the intensity of these beams attenuates, and again, they reappear with high intensity when \(m=50\) (see the blue zones with red circles in Figure 4). The presence of these oscillation beams is due to the sinusoidal refractive index formula of the plasma layers. Therefore, the modulation of the plasma refractive index permits the modulation of the resonance peaks between PBGs. However, the tuning of parameter \(m\) has no effect on the position of the PBGs. These modulations are due to the Bragg resonance phenomena occurring in the building blocks, which show a weaker modulation and a narrower range of transmitted frequencies. Figure 3: Reflectance spectra of deformed quasi-periodic Fibonacci multilayered stacks as function of frequency and the incidence angle (\(\theta\)) and for different deformation degrees (\(h\) set to be from 0.005 to 0.02). Figure 5 shows the reflectance spectra properties when parameter \(a\) of the plasma layer refractive index varies from 2 to 10. By increasing parameter \(a\), the PBGs disappear. In addition, the intensity of the output beams decreases with \(a\). The resonance peak positions remain at the same frequencies \(f_{1}=193\) THz, \(f_{2}=200\) THz and \(f_{3}=207\) THz.