## 5 Conclusions  
Using the TMM method, the beam wave propagation along 1D quasi-periodic GeSe/ plasma crystal is theoretically studied. The quasi-periodicity is built according to the classic Fibonacci sequence. In the first step of this study, the behavior of the wave beam appearing in the reflectance spectra is analyzed for different orders of the Fibonacci sequence. Afterward, we apply a deformation mathematical law \(y=x^{h+1}\) to the layer thicknesses of the strucutre, where \(x\) and \(y\) represent the main and the deformed z-coordinates of the layers, respectively, and \(h\) denotes the deformation degree. By increasing the deformation degree \(h\), the intensity of the output beam 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. In addition, the majority of the resonance peak intensities are attenuated. In the third step, the effect of parameter \(m\) on the refractive index formula of the plasma material is studied. When \(m=10\), the intensity of the output beams is maximal; afterward, and when parameter \(m\) increases to 20, the intensity of these beams attenuates, and again, they reappear with high intensity when \(m\) reaches 50. In the fourth step, the effect of parameter \(a\) on the refractive index formula of the plasma material is studied. The variation in \(a\) enables hiding the PBGs and controlling the intensity of the resonance peaks, and for different values of \(a\), we notice that these peaks are still in the same positions (\(f_{1}=193\) THZ, \(f_{2}=200\) THZ and \(f_{3}=207\) THZ). These results show that the proposed photonic system can be driven by the states of the parameters of the involved plasma material, as well as the iteration and the thickness of the whole layers. These electromagnetic behaviors of the theoretically studied photonic systems open the  
Figure 5: Reflectance spectra of quasi-periodic Fibonacci multilayered stacks as function of frequency and for different values of parameter \(a\) of the plasma refractive index (\(a\) set to be 2, 4, 6, 8 and 10; \(l=10\); and \(dp=10\)).  
way to experimentally validating these simulated results in the future. These structures have the potential to withstand high-power microwaves and pave the way for their use in filtering applications for communication and as micro-cavities to localize waves and to develop intense LASER equipment [34].  
Conceptualization, N.B.A. and Y.T.; methodology, H.A. and N.B.A.; software, N.B.A. H.A., O.K. and Z.E.; validation, N.B.A., Y.T. and H.A.; formal analysis, N.B.A. H.A., O.K. and Z.E.; investigation, Y.T. and H.A.; resources, Y.T., N.B.A. and H.A.; writing--original draft preparation, all authors.; writing--review and editing, Y.T.; visualization, N.B.A., O.K. and Z.E.; supervision, N.B.A.; project administration, funding acquisition, all authors. All authors have read and agreed to the published version of the manuscript.  
This research has been funded by Scientific Research Deanship at University of Ha'il--Saudi Arabia through project number <<RG-23 031>>.  
Not applicable.  
The data will be made available upon reasonable request from the corresponding author.  
The authors declare no conflict of interest.