  A 1D model is developed for defective gap mode (DGM) with two types of
boundary conditions: conducting mesh and conducting sleeve. For a periodically
modulated system without defect, the normalized width of spectral gaps equals
to the modulation factor, which is consistent with previous studies. For a
periodic system with local defects introduced by the boundary conditions, it
shows that the conducting-mesh-induced DGM is always well confined by spectral
gaps while the conducting-sleeve-induced DGM is not. The defect location can be
a useful tool to dynamically control the frequency and spatial periodicity of
DGM inside spectral gaps. This controllability can be applied to optical
microcavities and waveguides in photonic crystals and the interaction between
gap eigenmodes and energetic particles in fusion plasmas.
