## 1 Introduction  
The photonic quasi-crystals built according to the deterministic aperiodic sequences have received particular attention in solid-state photonics [1; 2; 3; 4]. These types of structures are made of building blocks, following the simple substitution rules of quasi-periodic mathematic sequences. They still show sharp diffraction patterns with a lack of translational symmetry and rotational symmetry, where the Fourier transformation of their geometrical structures in real space is defined by \(F(k)=\underset{N\rightarrow\infty}{\lim}\sum R_{N}\text{exp}(\text{ik}\,R_{N})\), with \(R_{N}\) as the atomic positions [5].  
In the past decade, the use of plasma materials in photonic crystals (PCs), instead of the usual dielectric or metal materials, has attracted much attention due to their interesting properties compared to conventional photonic crystals [6; 7; 8]. The photonic crystalsinvolving plasma are made of alternating thin non-magnetized or magnetized plasmas and dielectric layers or metals and are characterized by a dispersive complex refractive index [9].  
In recent decades, quasi-photonic multilayer structures built using incorporated superconductors [10; 11; 12] or liquid crystals [13; 14] or semiconductors [15] have received special attention and have been proposed for various applications, such as temperature sensing, pressure sensing [16], optical signal filtering [11; 17] and light transport and localization [18]. Photonic quasi-crystals are non-periodic modulations of two or more refractive indices generated by recursive sequences, such as the Rudin-Shapiro [19], Thue-Morse [20] and Fibonacci [21] sequences. Quasi-periodic crystals (sometimes called aperiodic crystals) lie between the periodic and chaotic structures and still exhibit attraction, according to more recent studies [17; 18]. The most common quasi-periodic sequence is the Fibonacci [21] one due to its incommensurable periods in the spatial spectrum of the structure--the so-called pure point spectrum. It shows Bragg-like peaks in its spatial spectrum [22]. The well-known symmetry of the Fibonacci sequence is generated by the inflation rule, \(F_{k+1}=\{F_{k},\,F_{k-1}\}\). The tuning of photonic band gaps (PBGs) through Fibonacci quasi-periodic structures containing a variety of materials, including semiconductor materials, has been investigated [23; 24; 25]. The localized modes in photonic quasi-crystals are generated by lattice vacancies breaking off the quasi-periodic symmetry. The Eigen frequencies of such localized modes are investigated using a super cell approximation in the plane wave method [26]. The Eigen frequencies and electromagnetic field profiles of multi-resonator photonic circuits are related to micro-cavity designs. These characteristics of quasi-photonic systems render these structures suitable for various applications with tunable logical elements, such as switches, modulators and filters [11; 20], and they can be useful in optics and optoelectronic circuits.  
In this work, 1D Fibonacci quasi-crystals filled with sinusoidal modulated plasma material are designed and theoretically studied. Here, using the transfer matrix method, we aim to study the effect of the plasma material, as well as the geometric thickness of layers and the quasi-periodicity of the structure on wave transmission, localization and filtering. The multi-output beam intensity and the PBGs position and behaviors are investigated for different plasma refractive index states and for the applied systematic deformations on layer thicknesses. This deformation follows the function \(y=x^{h+1}\), where x and y represent, respectively, the initial non-deformed and the final deformed position (coordinates along the \(z\)-axis) of the layers, and \(h\) denotes the coefficient of deformation. It is shown that the PGB spectra exhibit high transmission states, which are very sensitive to the plasma parameters.