Therefore, we focused our studies on spin wave (SW) dynamics in 2D magnonic quasicrystals, which is promising but not extensively explored subject. For all kinds of mentioned media, the two-dimensional (2D) quasiperiodic structures, ,, , give more possibility to adjust structural parameters and to mold the spectrum of excitation than the one-dimensional (1D) quasiperiodic structures. The dynamical properties of quasiperiodic composite structures were investigated for different kinds of media, – electronic, , photonic, ,, plasmonic, phononic, and magnonic systems. Surprisingly, the introduction, of a particular amount of structural defects into quasiperiodic structure, which render achieving Anderson localization regime, can cause the disorder-enhanced transport. This affects (deteriorates) the transport properties in quasiperiodic structures. The rich spectrum of the gaps and the increase of localization can lead to the strong suppression of group velocity. For self-similar quasicrystals, the system form the hierarchical structure in which the localization can be expected. For the system with translational symmetry every unit cell is equivalent and there is no reason for localization. The Bloch waves in periodic structures are spatially extended in the absence of defects and surfaces, whereas the eigenmodes in quasiperiodic system can be localized, in the bulk region of the structure. The quasiperiodic structures are also interesting due to different localization mechanisms than in periodic systems. It is fundamentally different for periodic structures of the same contrast of constituent materials which can be also useful for applications. In quasiperiodic system, there is a possibility to obtain omnidirectional frequency gap by optimizing the structure with rotational symmetry, which is a unique property of quasicrystals,. Due to this feature, the spectrum of scattered waves from quasiperiodic structures can have fractal structure, ,, which can be used for advanced signal filtering and processing. The quasiperiodic system has more complex band structure resulting from countable set of Bragg peaks densely filling reciprocal space, and, connected to them, frequency gaps. It is known that the long-range order in periodic and quasiperiodic structures can be revealed by the presence of forbidden frequency gaps in the spectrum. The spectrum of wave excitations reflects the structural properties of the system.
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