Numerical Optimization Of Photonic Crystal Structures

The efficiency of various deterministic and stochastic optimization algorithms for the optimization of photonic crystal structures is studied. The focus of these investigations is on problems with a relatively small search space but with very time-consuming evaluation of the fitness or merit functions obtained by different electromagnetic field solvers. To obtain information to what extend the field solvers accuracy influences the optimization algorithms a domain method (finite elements) and a boundary method (multiple multipole program) were used. It was found that deterministic optimization algorithms is very efficient when a sufficiently accurate field solver is applied and when a good initial guess is available that is sufficiently close to the desired optimal solution. In other words, deterministic solvers are very well suited for fine tuning. A good initial guess can also be obtained from a previous run of a stochastic optimizer that is terminated before finding the optimum.