Phonon polaritons in metamaterial 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. (C) 2009 Optical Society of America