Optimization Design And Uncertainty Modeling Of Photonic Crystal Structures

Photonic crystals have many unique optical properties and broad application prospects due to their periodic microstructure.In the past,the optimal design and analysis of photonic crystal structures were usually based on deterministic assumptions.However,the negative effects of uncertain material distribution and manufacturing errors on their optical properties during the manufacturing process can't be ignored.Therefore,how to design a more robust microstructure to reduce the influence of these uncertain factors is very important for the optical performance of photonic crystals.In this paper,we first discuss the finite element analysis model of the photonic crystal.Based on this,the description method of random uncertainty of photonic crystal and the method of random response analysis are introduced.The uncertainty of photonic crystal materials is regarded as a random field with given probability distribution characteristics and correlation length.The manufacturing error is described by using a stochastic level set model.The series optimal linear estimation method(EOLE)is used to discrete the random field,and the polynomial chaotic expansion(PCE)is used to analyze the stochastic response of the photonic crystal band gap.The accuracy of the method is verified by Monte Carlo method.A robust topology optimization design of the two-dimensional photonic crystal band gap structure considering the uncertainty of the material distribution is solved;the photonic crystal band-gap considering the uncertainty of manufacturing errors was quantified.Finally,the analysis and discussion of some numerical results were carried out.