A Method Based On FIR Filtering And Fourier Transform For Solving The Eigen Problems In Optoelectronic Devices

With the rapid developing of semiconductor technology and optoelectronic integrated devices,people are able to integrate many optical and electronic components on a same substrate.Meanwhile,the design of these optoelectronic components more and more relies on simulation software with high reliability and accuracy.Since the simulation of optoelectronic devices with computer-aided design tools saves more time and energy compared with the experimental method,these CAD tools are becoming indispensable in designing the optoelectronic devices.Also,the improvement and optimization of the numerical methods which play a role in the CAD tools are key to achieving high reliability and accuracy of these simulation software.This thesis first summarizes the principles and relative merits/demerits of several commonly used numerical methods,such as finite difference method(FDM),finite element method(FEM),transfer matrix method(TMM),etc.Then we propose an efficient method based on finite impulse response filtering and Fourier transform techniques(denoted as the FIR-FTM)to solve the eigen problems with inhomogeneous-core.The basic principle is that FIR-FTM takes advantage of the Fourier transform and relevant theorems to transform the eigen problems of the original domain(space domain)into the eigen problems of the transformed domain(special frequency domain).Then it uses the finite impulse response filtering technique,specifically the Fourier expansion of structural parameters and the frequency shift theorem,to circumvent the convolution operation after the Fourier transform.Afterwards,the differential equations in space domain is transformed into eigen-equations in special frequency domain.This method goes especially well with eigen problems with gradually varied parameters,since the effective range of the variables in transformed domain of these problems is quite limited.To verify the accuracy and efficiency of the FIRFTM,it is then applied to solving the optical eigen modes in graded-index optical waveguides and electronic eigen states in intermixed quantum wells.The results are then compared with those from conventional FDM and TMM in the literature.Simulation examples show that the computation cost of the proposed method is approximately at least one order of magnitude smaller than that of the three-point finite difference method.The main content of this paper is as follows:(1)We have summarized the principles as well as relative merits/demerits of several commonly used numerical methods(2)The basic theory and formulation have been established based on the finite impulse response filtering and Fourier transform techniques.(3)The accuracy of the proposed method has then been validated by simulating two typical examples and comparing results with the existing numerical methods.(4)We have also compared the computation cost of FIR-FTM with that of the FDM by analyzing the eigensystems of band diagonal matrix and tri-diagonal matrix.