All-angle self-collimation in two-dimensional rhombic-lattice photonic crystals

In this work, the self-collimating phenomenon in two-dimensional rhombic-lattice photonic crystals is discussed in detail. The equi-frequency contours of a rhombic-lattice rod-type photonic crystal structure are calculated with the plane wave expansion method for different lattice angles and rod radii. A broad range of flat and open equi-frequency contours is found. A rhombic-lattice photonic crystal made of 301 x 21 silicon rods (n = D 3.5) in air is presented as an illustration to demonstrate the broadband all-angle self-collimation. The bandwidth for all-angle self-collimation is verified to be 17.42% of the central frequency by simulations based on the finite-difference time-domain method. The all-angle self-collimation is found to be polarization-independent and the frequency for simultaneous TM and TE all-angle self-collimation is identified and verified by finite-difference time-domain simulations.