Polarization-independent self-collimation based on pill-void photonic crystals with square symmetry

We investigate discrepancy and similarity in dispersion relations between transverse-electric (TE) and transverse-magnetic (TM) polarizations in rectangular, square and triangular two-dimensional photonic crystals. It is found that the square lattice is the most appropriate candidate to realize polarization-independent, i.e. absolute self-collimation (ASC) in the first photonic band since it possesses not only a relatively broad angular range for self-collimation but also a small difference in dispersion relations between TE and TM modes. By tailoring the shape of air voids in the square-lattice-based structure, the electric-field vector can be rotated to reduce the discrepancy between TE and TM modes whereby the frequency bandwidth of ASC can be enlarged to approximately 4.8%. The ASC phenomenon is demonstrated by numerical experiments based on a finite-difference time-domain (FDTD) technique with negligible propagation losses.