Giant gaps in photonic band structures

We have investigated electromagnetic transmission through a one-dimensional waveguide along which stars of ${N}^{\ensuremath{'}}$ side branches were grafted at $N$ equidistant sites, $N$ and ${N}^{\ensuremath{'}}$ being integers. Analytic expressions are reported for the corresponding band structure for large $N$ and for the transmission coefficient for any value of $N$ and ${N}^{\ensuremath{'}}.$ Numerical results exhibit the existence of periodic very narrow photonic bands separated by large gaps, for $N$ and ${N}^{\ensuremath{'}}\ensuremath{\sim}5$ to 10. The above generic and universal behaviors of these waveguides were confirmed by experiments using coaxial cables.