We investigate the optical transmission spectra of quasi-periodic dielectric multilayer slabs arranged in a fashion that exhibits what has been called deterministic disorders. They can be of the so-called substitutional sequences type, and are characterized by the nature of their Fourier spectrum, which can be dense pure point (e.g. a Fibonacci sequence) or singular continuous (e.g. Thue-Morse and double-period sequences). The transmission coefficients are conveniently derived by using a theoretical model based on the transfer-matrix approach. A comparison between the oblique-incidence optical transmission spectrum and the normal-incidence one shows quite a different transmission behaviours over a particular range of frequency.

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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.

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Optical transmission spectra in quasiperiodic multilayered photonic structures, composed of both positive (SiO 2) and negative refractive index materials, are calculated by using a theoretical model based on the transfer matrix approach for normal incidence geometry. The quasiperiodic structures are substitutional sequences, characterized by the nature of their Fourier spectrum, which can be dense pure point (e.g. Fibonacci sequence) or singular continuous (e.g. Thue-Morse and double-period sequences). The transmission spectra for the case where both refractive indices can be approximated by a different constant show a unique mirror symmetrical profile, with no counterpart for the positive refractive index case, as well as a striking self-similar behaviour related to the Fibonacci sequence. For a more realistic frequency-dependent refractive index, the transmission spectra are characterized by a rich transmission profile of Bragg peaks with no more self-similarity or mirror symmetry.