Optimization of photonic crystal structures.

We report on the numerical structural optimization of two-dimensional photonic crystal (PhC) power dividers by using two different classes of optimization algorithms, namely, a modified truncated Newton (TN) gradient search as deterministic local optimization scheme and an evolutionary optimization representing the probabilistic global search strategies. Because of the severe accuracy requirements during optimization, the proper PhC device has been simulated by using the multiple-multipole program that is contained in the MaX-1 software package. With both optimizer classes, we found reliable and promising solutions that provide vanishing power reflection and perfect power balance at any specified frequency within the photonic bandgap. This outcome is astonishing in light of the discrete nature inherent in the underlying PhC structure, especially when the optimizer is allowed to intervene only within a very small volume of the device. Even under such limiting constraints structural optimization is not only feasible but has proven to be highly successful.