We employ a microscopic theory to investigate spin wave (magnon) propagation through their dispersion and transmission spectra in magnonic crystals arranged to display deterministic disorder. In this work the quasiperiodic arrangement investigated is the well-known generalized Fibonacci sequence, which is characterized by the σ(p,q) parameter, where p and q are non-zero integers. In order to determine the bulk modes and transmission spectra of the spin waves, the calculations are carried out for the exchange dominated regime within the framework of the Heisenberg model and taking into account the random phase approximation. We have considered magnetic materials that have a ferromagnetic order, and the transfer-matrix treatment is applied to simplify the algebra. The results reveal that spin wave spectra display a rich and interesting magnonic pass- and stop-bands structures, including an almost symmetric band gap distribution around of a mid-gap frequency, which depends on the Fibonacci sequence type.

The study of photonic crystals, artificial materials whose dielectric properties can be tailored according to the stacking of its constituents, remains an attractive research area. In this article we have employed a transfer matrix treatment to study the propagation of light waves in Fibonacci quasiperiodic dielectric multilayers with graphene embedded. We calculated their dispersion and transmission spectra in order to investigate the effects of the graphene monolayers and quasiperiodic disorder on the system physical behavior. The quasiperiodic dielectric multilayer is composed of two building blocks, silicon dioxide (building block $A={\mathrm{SiO}}_2$) and titanium dioxide (building block $B={\mathrm{TiO}}_2$). Our numerical results show that the presence of graphene monolayers reduces the transmissivity on the whole range of frequency and induces a transmission gap in the low frequency region. Regarding the polarization of the light wave, we found that the transmission coefficient is higher for the transverse magnetic (TM) case than for the transverse electric (TE) one. We also conclude from our numerical results that the graphene induced photonic band gaps (GIPBGs) do not depend on the polarization (TE or TM) of the light wave nor on the Fibonacci generation index $n$. Moreover, the GIPBGs are omnidirectional photonic band gaps, therefore light cannot propagate in these structures for frequencies lower than a certain value, whatever the incidence angle. Finally, a plot of the transmission spectra versus chemical potential shows that one can, in principle, adjust the width of the photonic band gap by tuning the chemical potential via a gate voltage.

In this paper, we have employed the transfer-matrix method to study theoretically the light waves propagation in extrinsic magnetized plasma multilayer, which is composed of a bulk plasma system influenced by the presence of spatially varying external magnetic field, which leads to a photonic bandgap device. The multilayered structures are arranged in periodic, quasiperiodic (Fibonacci, Octonacci, Thue-Morse, and double period), and Gaussian random fashions. The numerical results show the emergence of two main photonic bandgaps: the first gap for low frequencies and the second one for higher frequencies. We investigate the robust nature of the higher frequencies bandgap since it shows up to be invariant to different values of applied external magnetic fields and electron density as well as changes in the position and thickness of the layers introduced by the quasiperiodic and the Gaussian random sequences, respectively. The most surprising result is that this desired robust bandgap is broadening without any intermediate resonant peaks while the randomness in the layer thickness is introduced, which had not been observed in previous works about this same system.