Large magnonic band gaps and defect modes in one-dimensional comblike structures

Abstract

We report the existence of large gaps in the band structure of a comblike structure composed of a one-dimensional magnonic waveguide along which ${N}^{\ensuremath{'}}$ dangling side branches are grafted at N equidistant sites. These gaps originate not only from the periodicity of the system but also from the resonance states of the grafted branches (which play the role of resonators). The width of these gaps is sensitive to the length of the side branches as well as to the numbers N and ${N}^{\ensuremath{'}}.$ The presence of defect branches in the comblike structure can give rise to localized states inside the gaps. We show that these states are very sensitive to the length of the side branches, to the periodicity, to N or/and ${N}^{\ensuremath{'}}$ and to the length of the defect branches. Analytic expressions are given for the band structure of combs for large N and for the transmission coefficient for an arbitrary value of N and ${N}^{\ensuremath{'}}$ with and without defects.