Transmission spectra in photonic band-gap Fibonacci nanostructures

Optical transmission spectra of photonic band-gap Fibonacci quasiperiodic nanostructures composed of both positive (SiO2) and negative refractive index materials, the so-called metamaterials, are calculated by using a theoretical model based on the transfer matrix approach for normal incidence geometry. The transmission spectra of these Fibonacci nanostructures, for the case where both refractive index can be approximated as a constant, show a strike self-similarity behavior, and perfect transmission peaks are observed due to its internal coupling between localized modes and propagation modes, enabling the structure to be used as an ideal optical filter. For more realistic case, where the permittivity ϵ(ω) is modelled by a plasmonic dielectric function, and the magnetic permissivity μ(ω) is modelled by a similar model, there is no more a self-similar pattern, although keeping Bragg refraction gaps. In both cases, however, our transmission spectra unveil smooth structure due to the phase compensation effect. The zero-n gap case is also investigated, showing a peculiar independence to the details of the crystal structure (unlike the usual Bragg refraction).