We investigate the optical transmission fingerprints in structures that exhibit deterministic disorders. A class of models that has attracted particular attention in this context are the quasiperiodic dielectric multilayers that obey a substitutional sequence. These substitutional sequence are characterized by the nature of their Fourier spectrum, which can be dense pure point (Fibonacci sequences), singular continuous (Thue-Morse and double-period sequences), and absolutely continuous (Rudin-Shapiro sequence). We use a transfer-matrix approach to derive the optical transmission coefficients. Numerical results are presented to illustrate the self-similar aspect of the spectra, as well as to show the optical fingerprint through a return map of the transmission coefficients.

We use a tight-binding formulation to investigate the transmissivity and wave-packet dynamics of sequences of single-strand DNA molecules made up from the nucleotides guanine $G$, adenine $A$, cytosine $C$, and thymine $T$. In order to reveal the relevance of the underlying correlations in the nucleotides distribution, we compare the results for the genomic DNA sequence with those of two artificial sequences: (i) the Rudin-Shapiro one, which has long-range correlations; (ii) a random sequence, which is a kind of prototype of a short-range correlated system, presented here with the same first-neighbor pair correlations of the human DNA sequence. We found that the long-range character of the correlations is important to the persistence of resonances of finite segments. On the other hand, the wave-packet dynamics seems to be mostly influenced by the short-range correlations.

We carry out a theoretical analysis for the spectra of plasmon polaritons in multiple semiconductor layers arranged in a quasiperiodical fashion. This quasiperiodicity can be of the type of so-called substitutional sequences. They are characterized by the nature of their Fourier spectrum, which can be dense pure point (Fibonacci sequences) or singular continuous (Thue-Morse and double-period sequences). These substitutional sequences are described in terms of a series of generations that obey peculiar recursion relations. In order to study the plasmon-polariton spectra, we use a convenient theoretical model based on a transfer-matrix treatment, with the layers characterized by a frequency-dependent dielectric function, including the effect of retardation. We present numerical results to discuss the fractal aspect of the spectra, and compare it with the nonfractal spectra presented in the periodic case.

We investigate the photonic band gaps in quasiperiodic photonic crystals made up of both positive $\left(\mathrm{Si}{\mathrm{O}}_2\right)$ and negative refractive index materials using a theoretical model based on a transfer matrix treatment. The quasiperiodic structures are characterized by the nature of their Fourier spectrum, which can be dense pure point (Fibonacci sequences) or singular continuous (Thue-Morse and double-period sequences). These substitutional sequences are described in terms of a series of generations that obey peculiar recursion relations. We discussed the photonic band gap spectra for both the ideal cases, where the negative refractive index material can be approximated as a constant in the frequency range considered, as well as the more realistic case, taking into account the frequency-dependent electric permittivity $ϵ$ and magnetic permeability $\mu$. We also present a quantitative analysis of the results, pointing out the distribution of the allowed photonic bandwidths for high generations, which gives a good insight about their localization and power laws.