(1) PAPER TITLE Two-dimensional photonic crystals designed by evolutionary algorithms (2) AUTHORS Stefan Preble Cornell University 409 Phillips Hall Ithaca, NY 14853 607-262-0016 sfp24@cornell.edu Hod Lipson Cornell University 216 Upson Hall Ithaca, NY 14853 607-255-1686 hod.lipson@cornell.edu Michal Lipson Cornell University 411 Phillips Hall Ithaca, NY 14853 607-255-7877 lipson@ece.cornell.edu (3) CORRESPONDING AUTHOR Hod Lipson (4) ABSTRACT Photonic crystals are nanoscale patterns of high and low index materials that can trap and manipulate electromagnetic radiation. They have a growing number of application in the photonic industry, but their design is challenging and unintuitive. We used GP to design photonic crystal structures with large photonic band gaps (ability to trap light). Starting from randomly generated photonic crystals, the algorithm yielded a photonic crystal with a band gap defined as the gap to midgap ratio as large as 0.3189. This band gap is an improvement of 12.5% OVER THE BEST HUMAN DESIGN using the same index contrast platform. (5) CRITERIA (B) The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal. (D) The result is publishable in its own right as a new scientific result 3/4 independent of the fact that the result was mechanically created. (E) The result is equal to or better than the most recent human-created solution to a long-standing problem for which there has been a succession of increasingly better human-created solutions. (6) STATEMENT Photonic crystals (PCs) are structures that possess a photonic band gap - a range of frequencies where light is forbidden from propagating in the crystal. The band gap enables unprecedented control of light on the nano-scale, for example, allowing light to be channeled around sharp corners or to be strongly confined to ultra-small volumes. This control is achieved by introducing intentional "defects" in the crystal. In turn, light can only propagate in these defect regions, as long as the frequency of the light is within the photonic band gap. Consequently, it is the goal of photonic crystal designers to maximize the size of the band gap so that devices implemented in photonic crystals operate over the widest possible frequency range. Photonic crystals have traditionally been hand designed by trial and error. This has yielded relatively simple crystals, such as a square lattice of circular rods. However, it is not known whether these simple crystals truly achieve the maximum possible band gap. In our work we used an evolutionary algorithm to systematically search for photonic crystals with maximal band gaps. Our submission satisfies the following criteria for a human-competitive result: (B) The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal. AND (E) The result is equal to or better than the most recent human-created solution to a long-standing problem for which there has been a succession of increasingly better human-created solutions. The most recent best human design for a photonic crystal with a square lattice has a band gap of 0.2835. Our evolutionary algorithm discovered a vastly different photonic crystal with a band gap of 0.3189. Therefore, the algorithm improved over the previous design by 12.5%. (D) The result is publishable in its own right as a new scientific result 3/4 independent of the fact that the result was mechanically created. The unit cell of the discovered photonic crystal is skewed and unsymmetrical which was unexpected and physically interesting in its own right. (6) CITATION S. Preble, H. Lipson, and M. Lipson, "Two-dimensional photonic crystals designed by evolutionary algorithms", Applied Physics Letters, Volume 86, Pg. 061111 (Feb. 2005) http://www.mae.cornell.edu/ccsl/papers/APL05_Preble.pdf