# Nano- and Micropatterning on Optical Fibers by Bottom-Up Approach: The Importance of Being Ordered
## 2 The Importance of Order
### Aperiodic Ordered Structures  
The concept of order is often erroneously restricted to the concept of \"periodic\" order [13]. In the last decades, the \"order without periodicity\" has emerged to properly describe an increasing number of complex systems. Namely, \"quasicrystals\" are materials or structures exhibiting long-range order and yet do not have translational periodicity. Quasicrystals permit symmetry operations forbidden in classical crystallography, for example, five-, eight-, ten- and 12-fold rotations. [PERSON], awarded with Nobel Prize in 2011 for the discovery of quasicrystals, observed for the first time the quasicrystals in a diffraction experiment by electron microscopy in April 1982 [14] during his study of the structural morphology (icosahedral) of a rapidly solidified (AI, Mn) alloy [15]. The discovery spurred a lot of debate, but also intense activity aimed at synthesizing new quasicrystals. Within a few years, the icosahedral quasicrystals were joined by axial quasicrystals with decagonal and pentagonal symmetry [16; 17], octagonal symmetry [18], dodecagonal symmetry [19] and enneagonal symmetry [20]. Later, quasicrystals were demonstrated in the soft matter too. Supramolecular structures of organic dendrimers [21] and tri-block copolymers [22] were synthetized. Colloidal inorganic nanoparticles were self-assembled into binary aperiodic superlattices with dodecagonal quasicrystalline order [23]. It is worth noting that the synthesis of quasiperiodic crystals in principle can be scaled up to micrometer feature sizes by a bottom-up approach too. Indeed, in 2008, micron-sized colloidal spheres were arranged into quasicrystalline arrays by using intense laser beams that create quasi-periodic optical standing-wave patterns [24]. Alongside the fabrication and discovery of different quasicrystals, the studies of phenomena exhibiting aperiodic arrangements of matter in space and/or time were spurred, and the basic knowledge gained from these studies has naturally extended to several research domains. The photonic properties of quasicrystals have been a subject of intense research. Many studies were devoted to assessing the phenomena that govern wave transport and interference in aperiodic systems [25]. It has been shown that photonic quasicrystals could exhibit photonic band [26; 27] as well as light wave localization [28]. The frequencies where the bandgaps occur are not necessarily explained using single scattering and should therefore involve multiple scattering [29]. Aperiodic structures in two spatial dimensions combine long-range structural order with higher-order rotational axes (i.e., forbidden symmetries) leading to more isotropic band gaps, omnidirectional reflection spectra, and unusual localization of optical modes. The possibilities of quasicrystals to support guided resonances have been the subject of a series of theoretical and experimental works. In a pioneering work from [PERSON] et al. [30], the transmittance response and the modal analysis of a photonic quasicrystal slab demonstrated the possibility to excite guided-resonance modes, and highlighted similarities and differences with the periodic case. In particular, it is shown that, as for the periodic case, guided resonances arise from the coupling of the incident plane-wave with degenerate modes of the photonic quasicrystal slab that exhibit a matching symmetry in the spatial distribution, and can still be parameterized via a Fano-like model. Further studies demonstrated the possibility to excite otherwise uncoupled guided resonances via the judicious introduction of symmetry-breaking point-defects [31] as well as the potential for both sensing and telecommunication applications [32]. Following such theoretical and numerical studies, in 2010, [PERSON] et al. provided the first experimental evidence of Fano-type guided resonances in aperiodically-ordered photonic quasicrystal slabs (Ammann-Beenker octagonal tiling) as shown in Figure 1c [33; 34].