Strongly localized mode at the intersection of the phase slips in a photonic crystal without band gap

A two-dimensional photonic crystal with a rectangular symmetry and low contrast (<1) of the dielectric constant is considered. We demonstrate that, despite the absence of a band gap, strong localization of a photon can be achieved for certain "magic" geometries of a unit cell by introducing two pi/2 phase slips along the major axes. The long-living photon mode is bound to the intersection of the phase slips. We calculate analytically the lifetime of this mode for the simplest geometry-a square lattice of cylinders of a radius, r. We find the magic radius r(c) of a cylinder to be 43.10% of the lattice constant. For this value of r, the quality factor of the bound mode exceeds 10(6). A small ( approximately 1%) deviation of r from r(c) results in a drastic damping of the bound mode.