The characteristics of the periodic band gaps of the one dimension magnetized plasma photonic crystals are studied with the piecewise linear current density recursive convolution (PLCDRC) finite-differential time-doma...The characteristics of the periodic band gaps of the one dimension magnetized plasma photonic crystals are studied with the piecewise linear current density recursive convolution (PLCDRC) finite-differential time-domain (FDTD) method. In frequency-domain, the transmission coefficients of electromagnetic Gaussian pulses are computed, and the effects of the periodic structure constant, plasma layer thickness and parameters of plasma on the properties of periodic band gaps of magnetized photonic crystals are analyzed. The results show that the periodic band gaps depend strongly on the plasma parameters.展开更多
A computational study on the enhancement of the second harmonic generation(SHG)in one-dimensional(1D)photonic crystals is presented.The mathematical model is derived from a nonlinear system of Maxwell’s equations,whi...A computational study on the enhancement of the second harmonic generation(SHG)in one-dimensional(1D)photonic crystals is presented.The mathematical model is derived from a nonlinear system of Maxwell’s equations,which partly overcomes the shortcoming of some existing models based on the undepleted pump approximation.We designed an iterative scheme coupled with the finite element method which can be applied to simulate the SHG in one dimensional nonlinear photonic band gap structures in our previous work.For the case that the nonlinearity is strong which is desirable to enhance the conversion efficiency,a continuation method is introduced to ensure the convergence of the iterative procedure.The convergence of our method is fast.Numerical experiments also indicate the conversion efficiency of SHG can be significantly enhanced when the frequencies of the fundamental and the second harmonic wave are tuned at the photonic band edges.The maximum total conversion efficiency available reaches more than 50%in all the cases studied.展开更多
Based on a subspace method and a linear approximation method,a convex algorithm is designed to solve a kind of non-convex PDE constrained fractional optimization problem in this paper.This PDE constrained problem is a...Based on a subspace method and a linear approximation method,a convex algorithm is designed to solve a kind of non-convex PDE constrained fractional optimization problem in this paper.This PDE constrained problem is an infinitedimensional Hermitian eigenvalue optimization problem with non-convex and low regularity.Usually,such a continuous optimization problem can be transformed into a large-scale discrete optimization problem by using the finite element methods.We use a subspace technique to reduce the scale of discrete problem,which is really effective to deal with the large-scale problem.To overcome the difficulties caused by the low regularity and non-convexity,we creatively introduce several new artificial variables to transform the non-convex problem into a convex linear semidefinite programming.By introducing linear approximation vectors,this linear semidefinite programming can be approximated by a very simple linear relaxation problem.Moreover,we theoretically prove this approximation.Our proposed algorithm is used to optimize the photonic band gaps of two-dimensional Gallium Arsenide-based photonic crystals as an application.The results of numerical examples show the effectiveness of our proposed algorithm,while they also provide several optimized photonic crystal structures with a desired wide-band-gap.In addition,our proposed algorithm provides a technical way for solving a kind of PDE constrained fractional optimization problems with a generalized eigenvalue constraint.展开更多
基金supported by the National Natural ScienceFoundation of China (Grant No. 60471002)
文摘The characteristics of the periodic band gaps of the one dimension magnetized plasma photonic crystals are studied with the piecewise linear current density recursive convolution (PLCDRC) finite-differential time-domain (FDTD) method. In frequency-domain, the transmission coefficients of electromagnetic Gaussian pulses are computed, and the effects of the periodic structure constant, plasma layer thickness and parameters of plasma on the properties of periodic band gaps of magnetized photonic crystals are analyzed. The results show that the periodic band gaps depend strongly on the plasma parameters.
基金supported by the fundamental research funds for the central universities(BUPT2009RC0706)the Project 11001030 supported by National Natural Science Foundation of China+3 种基金the open fund of key laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications)of Ministry of Educationsupported in part by the NSF grants DMS-0604790,DMS-0908325,CCF-0830161,EAR-0724527,and DMS-0968360the ONR grant N00014-09-1-0384a special research grant from Zhejiang University.
文摘A computational study on the enhancement of the second harmonic generation(SHG)in one-dimensional(1D)photonic crystals is presented.The mathematical model is derived from a nonlinear system of Maxwell’s equations,which partly overcomes the shortcoming of some existing models based on the undepleted pump approximation.We designed an iterative scheme coupled with the finite element method which can be applied to simulate the SHG in one dimensional nonlinear photonic band gap structures in our previous work.For the case that the nonlinearity is strong which is desirable to enhance the conversion efficiency,a continuation method is introduced to ensure the convergence of the iterative procedure.The convergence of our method is fast.Numerical experiments also indicate the conversion efficiency of SHG can be significantly enhanced when the frequencies of the fundamental and the second harmonic wave are tuned at the photonic band edges.The maximum total conversion efficiency available reaches more than 50%in all the cases studied.
基金supported by National Natural Science Foundation of China(Grant Nos.12171052 and 11871115)BUPT Excellent Ph.D.Students Foundation(Grant No.CX2021320).
文摘Based on a subspace method and a linear approximation method,a convex algorithm is designed to solve a kind of non-convex PDE constrained fractional optimization problem in this paper.This PDE constrained problem is an infinitedimensional Hermitian eigenvalue optimization problem with non-convex and low regularity.Usually,such a continuous optimization problem can be transformed into a large-scale discrete optimization problem by using the finite element methods.We use a subspace technique to reduce the scale of discrete problem,which is really effective to deal with the large-scale problem.To overcome the difficulties caused by the low regularity and non-convexity,we creatively introduce several new artificial variables to transform the non-convex problem into a convex linear semidefinite programming.By introducing linear approximation vectors,this linear semidefinite programming can be approximated by a very simple linear relaxation problem.Moreover,we theoretically prove this approximation.Our proposed algorithm is used to optimize the photonic band gaps of two-dimensional Gallium Arsenide-based photonic crystals as an application.The results of numerical examples show the effectiveness of our proposed algorithm,while they also provide several optimized photonic crystal structures with a desired wide-band-gap.In addition,our proposed algorithm provides a technical way for solving a kind of PDE constrained fractional optimization problems with a generalized eigenvalue constraint.
