Self-collimation in planar photonic crystals

Self-collimation in planar photonic crystals

Representation of a square lattice planar photonic crystal and of the two first photonic bands.

Abstract:
We analyze, in three dimensions, the dispersion properties of dielectric slabs perforated with two-dimensional photonic crystals (PCs) of square symmetry. The band diagrams are calculated for all k-vectors in the first Brillouin zone, and not only along the characteristic high-symmetry directions. We have analyzed the equal-frequency contours of the first two bands, and we found that the square lattice planar photonic crystal is a good candidate for the self-collimation of light beams. We map out the group velocities for the second band of a square lattice planar PC and show that the group velocity is the highest in the region of maximum self-collimation. Such a self-collimated beam is predicted to show beating patterns due to the specific shape of the equal-frequency contours. A geometrical transformation maps the region of the first and second photonic bands where self-collimation takes place one onto the other and gives additional insights on the structural similarities of self-collimation in those two bands.
J. Witzens, M. Loncar, and A. Scherer, Self-Collimation in Planar Photonic Crystals, IEEE J. Sel. Top. Quant. Electron. 8, 1246-1257 (2002).