Phonon polaritons in photonic crystals at terahertz frequency range

We investigate the phonon-polariton band gaps in periodic and quasi-periodic (Fibonacci-type) multilayers made up of both positive (SiO2) and negative refractive index materials (metamaterials) following the Fibonacci sequence in the terahertz region. The behavior of the polaritonic band gaps as a function of the multilayer period is investigated systematically. Our theoretical model makes use of a transfer matrix approach to simplify the algebra involved and to set up analytical phonon-polariton dispersion relations (bulk and surface modes). We also present a quantitative analysis of the results, pointing out the distribution of the allowed polaritonic bandwidths for high Fibonacci generations, which gives good insight about their localization and power laws.