Multi-objective optimization of dielectric layer photonic crystal filter

The weighting factors method and the response surface methodology are used to achieve multi-objective optimization of a dielectric layer photonic crystal filter. The size of period and the transmission quantity are considered simultaneously and a multi-objective optimization model of filter is established, which takes the size of period and transmission quantity to be minimized in stop-band as objectives. Global approximate expressions of the objective and the constraint functions are found by response surface methodology. Then the weighting factors method is employed to convert the model into a quadratic programming model and the optimal parameters can be obtained using sequence quadratic programming. Examples provide the optimized results in three different weight coefficients. The effect of the weighting factors on the value of the objective function is also discussed. Results show that the present method is precise and efficient for multi-objective optimization of a dielectric layer photonic crystal filter.