Optimization of photonic crystal filter based on slack variables

The improved model based on slack variables is designed to optimize a photonic crystal filter. An optimization model of the filter is established, with the transmission quantity in a stop-band as the objective function and the transmission quantity outside a stop-band as the constraint condition. The improved model is obtained by introducing slack variables in the infeasible region. With the treatment of objective and constraint functions, the optimization problem and the improved model are solved by sequential linear programming. Then the convergent solution satisfying the constraints can be found. The change of the objective function and design variables with iteration steps is presented by numerical examples, and the influence of by the constraints on the central frequency of the stop-band is discussed, indicating that the improved model is available and effective for optimization of a photonic crystal filter.