Polarization-insensitive and broad-angle self-collimation in a two-dimensional photonic crystal with rectangular air holes.

In this paper, we have systematically investigated the polarization-insensitive and broad-angle self-collimation behavior in a square-lattice two-dimensional photonic crystal (PhC) with rectangular air holes. By analyzing the band structures and the corresponding equi-frequency contours (EFCs), it is found that such PhC can show special dispersion properties when the half-length L and half-width W of rectangular air holes are appropriately changed. First, compared with conventional square-lattice PhCs with circular or square air holes, such PhC is easier to support polarization-insensitive self-collimation (PISC) based on the EFCs for the second band. Meanwhile, the PISC behavior such as working frequency range and effective incident angle can be more flexibly adjusted by changing the structural parameters of rectangular air holes. Second, such PhC can show long flat EFCs for the TM-3 band. This is quite helpful for supporting broad-angle self-collimation. In particular, when L=0.5a and W/L=0.8, this PhC will degenerate to a one-dimensional grating PhC. It can show good all-angle self-collimation behavior with an improved relative bandwidth (about 19.98%) compared with previous works. It also presents advantages in practical applications due to a relatively convenient fabrication process.