The Transmission Properties And Optimized Design Of Rectangular Photonic Crystal Waveguide

Rectangular photonic crystal waveguide is widely used in microwavecommunications. The analysis method on transmission characteristic and optimizationdesign on structures and properties of the rectangular photonic crystal waveguide areof important theoretical and practical significance. Because of the particularity ofphotonic crystal structure, it has become hot topic in the field of microwavecommunications for rectangular photonic crystal waveguide to explore the precisenumerical analysis method and the optimization method which is rapid and effective.In this paper, the transmission characteristics of rectangular photonic crystalwaveguide are analyzed and calculated by precise integration method in symplecticsystem, and the structures and properties of the rectangular photonic crystalwaveguide are optimized by mixed integer linear programming. The maincontributions are as follows.(1) The transmission characteristics of rectangular photonic crystal waveguide areanalyzed and simulated by precise integration method in symplectic system.Firstly, the transmission characteristics of one-dimensional photonic crystal areanalyzed and simulated using the precise integration method. One-dimension photoniccrystal is divided into sections according to vertical uniformity, and then the exportstiff matrices could be calculated by precision integration based on Riccati equations,and the whole waveguide discontinuity problem can be solved by the combination ofsubstructures. This proposed method is programmed based on Matlab and it isverified to be more accurate and efficient compared with transfer matrix method. Inthe next place, the transmission characteristics of rectangular photonic crystalwaveguide are further analyzed and simulated combined with boundary constraints,and the effect of the length of cycle and number of cycles on the transmissioncharacteristics of rectangular photonic crystal waveguide are discussed.(2) The filter characteristic of rectangular photonic crystal waveguide is optimizedby mixed integer linear programming.Rectangular photonic crystal waveguide is analyzed by precise integrationalgorithm in symplectic system, and an optimization model of the rectangularphotonic crystal waveguide is established, which takes the transmission quantity to beminimized in stop-band as the objective and cycle length, dielectric thickness, relative dielectric constant and the number of cycles as variables. With the treatment ofobjective function and constraint functions by linear sequence method, the model issolved by mixed integer linear programming and the optimized design variables of themodel are obtained. Examples show that this method can optimize the filtercharacteristic of the structure efficiently.(3)Multi-objective optimal design of rectangular photonic crystal waveguide isanalyzed by mixed integer linear programming.The multi-objective optimization model of the rectangular photonic crystalwaveguide is established which takes both the transmission quantity in stop-band andthe length of waveguide to be minimized as the objective and cycle length, dielectricthickness, relative dielectric constant and the number of cycles as variables. Themodel is disposed as single-object optimization by linear weighting method, and theoptimization model is solved by mixed integer linear programming. The curves aboutobject function and design variables versus iteration numbers of different weightingfactors are analyzed. The influence of weighting factors on objective value isdiscussed and a proper weighting factors scope is given.