Absolute band gaps and electromagnetic transmission in quasi-one-dimensional comb structures

We demonstrate the existence of absolute gaps in the band structure of a quasi-one-dimensional electromagnetic comb composed of a one-dimensional wave guide along which an infinity of side branches are grafted periodically. We show that the width of the gaps is very sensitive to the length of the side branches, to the periodicity, as well as to the contrast in dielectric properties of the constituent materials. Nevertheless, relatively wide gaps still remain when the constituent materials are identical. We also present results of the transmission coefficient of an electromagnetic wave propagating along the wave guide for a finite number of side branches. For an increasing number of side branches the behavior of the transmission coefficient parallels the calculated band structure of the infinite comblike structure. The convergence, as concerns the band-gap limits, can be achieved for most of the gaps for a small number of side branches (N\ensuremath{\cong}10\char21{}20).