Shape And Topology Optimization Design Of Electromagnetic Metamaterials

Photonic crystal has the property of photonic band gap,which enables us to control and guide electromagnetic waves in the wavelength range.Its potential application in integrated optics is inestimable.The main contents of this paper include the topology optimization design of the two-dimensional photonic crystal microstructure and the shape optimization design of the two-dimensional photonic crystal waveguide.(1)A finite element model of the two-dimensional photonic crystal energy band structure is established.The corresponding calculation program is compiled based on MATLAB and compared with the COMSOL calculation results to verify the correctness of the program.Similarly,we also establish a finite element model of a two-dimensional photonic crystal waveguide,using COMSOL to perform numerical calculations,and verify the correctness of the calculation results by comparing with the results in the existing literature.(2)With the goal of maximizing the photonic band gap and the complete photonic band gap,we achieve the topology optimization design of two-dimensional square symmetric lattice photonic crystal using genetic algorithms.Through numerical calculations,we give the photonic crystal unit cell topologies with the optimal first 10 order photonic band gaps for TM and TE modes,respectively.The optimal photonic band gaps are the best results reported so far.At the same time,we also obtain some novel photonic crystal unit cell topologies with larger complete photonic band gaps.(3)Multiple hyper-ellipses are used to construct the shape of dielectric columns in multiple unit cells near the band of a two-dimensional photonic crystal waveguide.The optimal parameters of these hyper-ellipses are searched using genetic algorithms to maximize the energy transmission efficiency of the photonic crystal waveguide.Two-dimensional photonic crystal L-shaped and T-shaped waveguides are taken as examples to design the optimized structure at different working frequencies.Compared with the traditional two-dimensional photonic crystal waveguides,the optimized structure effectively improves the energy transfer efficiency.And the designed structures have smooth boundaries which are easy to process and manufacture.