## 1 Introduction
In addition to the multi-layer structures, few works have been devoted to quasi-periodic coaxial photonic crystals by some of us [60; 61; 62]. In Ref. [60] [PERSON] et al. studied the localization and propagation of electromagnetic waves in a Fibonacci coaxial photonic circuits made of two blocks in which each block is composed by a loop and segment arranged following a FS. They have found that the symmetrical loop structure is equivalent to simple alternating layers. However, the asymmetrical loops play the role of resonators giving rise to transmission zeros (like in Mach-Zehnder interferometer [63]) and hence new gaps which does not exist in the case of layered media. [PERSON] et al. [61] have examined the properties of Fibonacci 1D serial loop structures where each block is made of a segment or a loop. Particular properties have been deduced when the FS was inserted horizontally between two waveguides or attached vertically along a guide, such as self-similarity, scaling behavior and critical localized modes. Furthermore [PERSON] et al. [62] have extensively studied the behavior of the surface modes in Fibonacci superlattices made from a periodic repetition of a given Fibonacci generation. It is worth mentioning that a number of interesting physical properties related to the electronic transport, charge density distribution and energy spectra in periodic and Fibonacci stub structures have been performed theoretically by [PERSON] et al. [64] and [PERSON] and [PERSON] [65]. Also, [PERSON] et al. [66] have developed a method showing the single-electron transport through quantum stub waveguides arranged in a Fibonacci quasi-periodic pattern. The similarity between scattering properties (equation of motion and boundary conditions) of electrons and photons, points out that this type of features can also appear for photons [67]. Furthermore, because of their noninteracting nature, electromagnetic waves represent an interesting tool for studying the localization phenomena [37; 47] in comparison with electrons. Therefore, photonic circuits based coaxial cables represent an excellent platform to observe several properties of Fibonacci stubbed structures. Indeed, these systems are more appealing for this goal than their optical counterparts since they only require simple equipments. In addition, the propagation in these waveguides is monomode (see below) and one can obtain experimental results with a good precision as well as theoretical results using a simple 1D model with a very good agreement between both results [67]. In this paper, we give a theoretical and experimental study of the localization and propagation of electromagnetic waves in Fibonacci stub structures. Such structures have been studied only for periodic structures with or without defects [68; 69]. However, to our knowledge, no similar study has been carried out for photonic Fibonacci structures. In this work, a theoretical and an experimental evidence of the features of the transmission modes through a Fibonacci stubbed circuit structure inserted either between two semi-infinite waveguides or grafted vertically along a guide are investigated. The geometry of the FS proposed here is original and simple in comparison with the symmetrical loop geometries studied before [60; 61; 62] as the stubs may present transmission zeros which do not exist in loop structures, also the boundary conditions on the stub extremities can be changed easily which is not the case for loop systems. Furthermore, the study of the FS in the two geometries (horizontal and vertical) enables us to deduce typical properties of these systems such as: (i) the fragmentation of the frequency spectrum into small bands and primary and secondary gaps, (ii) the self-similarity of the modes in the transmission spectra as well as in the electric field distribution around a central frequency where the quasi-periodicity is more effective, (iii) the analysis of the behavior of the eigenmodes of the FS with different boundary conditions imposed on its both extremities.