Optical transmission spectra in quasiperiodic multilayered photonic structure

Optical transmission spectra in quasiperiodic multilayered photonic structures, composed of both positive (SiO2) 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.