FMC-based Reconstruction Algorithm And Its Characteristic Analysis For Waveguide Gratings

Waveguide gratings(WGs)have been widely studied and applied in many fields,such as wavelength division multiplexing,signal processing,laser,sensing,optical wave filtering and coupling,as an important structure of integrated photonic devices.The widely used WG is Waveguide Bragg grating(WBG).In the practical application of WGs,the WGs with corresponding response spectra are usually selected according to the required function and applicable occasions.The application prospect of WGs promotes the research of synthetic WGs method.In order to meet the requirements of different occasions and functions,it is necessary to calculate the structural parameters that determine the response spectrua of the WGs.Therefore,it is of great practical significance and academic reference value to carry out the research on the reconstruction and characteristics of WGs.Here is a brief overview of the work of this paper: Firstly,this paper describes the principle and development background of WG,summarizes the widely used reconfiguration design methods of WG,analyzes and compares the advantages and disadvantages of each reconfiguration design method.Secondly,it introduces the Fourier mode coupling(FMC)theory,and based on the FMC theory,we analyzed the uniform-WBG,triangular-WBG,Gaussian apodization-WBG,cosine apodization-WBG,phase shift-WBG,superstructure-WBG,Fabry-Pérot cavity(FPC),and so on.Thirdly,according to the analytical solution of the reflection spectrum,the analytical solution of the structural parameters of the refractive index perturbation is derived reversely.Using the derived analytical solution,the reconstruction design algorithm of the analytical solution of the uniform WBG,triangular WBG/FPC-WBG,common apodization WBG/FPC-WBG,phase shifted WBG and superstructure WBG is designed,according to the proposed reconstruction design algorithm of the WBG structure.The results are verified by the coupled mode theory and the transfer matrix method.The results show that the algorithm can design the WBG structure with the required reflection characteristics.Finally,the error,time efficiency and resolution characteristics of the algorithm are analyzed,and the analysis results show that the algorithm is effective.The resolution of this method is determined by human and computer,because it adopts the analytic solution of refractive index perturbation structure parameters.