Self-Collimation in Square Lattice Two Dimensional Photonic Crystals with Ring-Shaped Holes

We demonstrate self-collimation phenomena based on a new type of photonic crystals made of square lattice with ring shaped holes. The plane wave expansion (PWE) method is used to get the three dimensional band diagram and equi-frequency of the second band which displays the self-collimation phenomena for the structure we proposed in this paper. The collimation angle is mainly depending on the maximum flatness half width (MFHW) of the equi-frequency. The FDTD method is employed to demonstrate the electric field amplitude distributions for the collimation phenomena. Partly, in order to achieve high efficient coupling of the input and output port, we modify both surface structures to modulate the wave-front to obtain desired effect. The parameter of the input surface is modified which will prevent the production of surface modes which takes away the EM power and enhance the transmittance. For a square lattice with the modified parameters at each side of the input surface, the surface modes are suppressed to couple with the continuum of the dielectric waveguide modes. More importantly, they might have potential application in integrated optical circuits.