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Photonic crystal and unit cell (insets). (a–c) The best three photonic crystals created by the evolutionary algorithm with the following band gaps: (a) 0.3189, (b) 0.3153, (c) 0.3115. (d) Best human designed photonic crystal with a band gap of 0.2835.
Band diagram of the best photonic crystal discovered by the evolutionary algorithm. Horizontal axis is the brillouin zone points. The vertical axis is the frequency normalized to the lattice constant. The inset shows the reciprocal lattice and the corresponding Brillouin zone points.
Band diagram of a randomly generated PC with no band gap. The inset shows the reciprocal lattice and the corresponding Brillouin zone points. The shaded light-gray boxes indicate the areas where the two bands overlap each other. The bounds of the boxes are obtained from the points in the band diagram where the top band is below the top of band 1. The height of the boxes is always the same; it is defined from the bottom of band 2 (At the X1 point) to the top of band 1 (At the M point). The width is from the left-most to the right-most points (including the interpolated halfway points) that fall below the top of band 1. The total overlap area [Eq. (1)] can be obtained from the sum of the areas of the individual shaded boxes.
Best fitness of the population as a function of generation. The tree and bitmap representation performance is compared. A random search is also included as a base line. Error bars are derived from three independent runs started from randomized initial populations.
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