There have been huge efforts performed on the study of photonic crystals due to their potential to manipulate the flow of light waves at the optical domain. One of the precious features of the photonic crystals is that they have photonic band gaps, i.e. frequency bands in which optical modes are suppressed to exist. The creation of complete photonic band gap is an important concept especially for the design of polarization-insensitive optical devices. There are various studies targeting the generation of larger band gaps in two-dimensional photonic crystals by means of engineering the lattice geometry or by a change of the shape and orientation of the unit cells of the structure. In the present work, we study the creation of complete band gaps by breaking the structural symmetry of the annular photonic crystals which is called as modified annular photonic crystals. This new structure enables us to engineer dispersion characteristics of photonic crystals that facilitate the design of configurable polarization-insensitive optical devices for different practical applications such as self-collimation waveguides, defect-based linear waveguides, and beam splitters. © 2012 IEEE.