Area of reflection of longitudinal waves in multilayer Fibonacci arrangements

In this article, we study the total reflection in 1D phonic crystals in quasiperiodic Fibonacci type arrangements of solid/solid layers. It was found that the reflection occurs in an area centered at a normalized frequency of 2π, and an angle of incidence of 61.6° which has not been observed in periodic systems. For studies in arrangements n > 4, the geometric evolution and breakdown of the area of interest is presented, starting from n = 6 arrays, giving rise to the formation of resonances (lR falls), which give rise to transmission and reflection of transverse waves, as well as the widening and formation of relative reflection peaks towards the critical angle. The global matrix method was used to obtain transmission and reflection spectra in quasiperiodic arrangements, when acoustic waves of longitudinal polarization were made. It is concluded that the geometric shape of the reflection zone observed after the critical angle depends on the FS arrangement, and its filling factor [f = a/(a + b)]. The calculations were made in super networks with Pt/Zn, where the first and the last layer are the means: incident and transmitted respectively.