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Published November 1, 2002 | public
Journal Article Open

Self-Collimation in Planar Photonic Crystals


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 -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.

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"©2002 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE." Manuscript received September 3, 2002; revised September 30, 2002. This work was supported in part by DARPA under Contract MDA972–00-1–0022 and Contract MDA972–00-1–0019, as well as the Air Force Office of Scientific Research under Contract F49620–01-1–0497. The authors would like to acknowledge T. Baehr-Jones from Luxtera, Inc., for the development of the distributed 3-D FDTD code and to thank Luxtera, Inc., for making computing power available.


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