基于稳态逼近算法的光学双稳态现象研究

Numerical Research on Optical Bistabilityin One-dimensional Nonlinear Photonic Crystals

光子晶体的双稳态现象是光子晶体制作光限幅器和光开关的理论基础,研究具有低阈值的双稳态系统对大规模集成光路具有非常重要的意义。本文采用有限元方法和稳态算法对含有缺陷的一维光子晶体结构中的双稳态效应现象进行了理论推导和数值分析。在频域上,一维双稳态效应问题可化为非线性亥姆霍兹方程的两点边值问题。本文基于非线性亥姆霍兹方程建立了有限元数学模型,构造了基于有限元方法和稳态迭代算法的数值求解算法。研究算例结果表明该数值算法能有效地模拟含有缺陷的一维光子晶体结构中双稳态效应现象,并能推广到高维问题的研究。本文还利用该模型算法进一步研究了结构参数对双稳态效应的影响,当选择非线性强度大的材料,或者增强入射场强度,或增加中间层厚度时可以降低双稳态效应发生的阈值。

In this paper,we discuss a numerical method,which combines the finite element method(FEM)with a special iterative scheme,to study the nonlinear optical response of one-dimensional(1D)finite grating structures.In the frequency domain,the problem ofoptical bistability in one-dimensional nonlinear photonic crystals can be expressed as a two-point boundary value problem(BVP)of the nonlinear Helmholtz equation,which can be solved by combining the linear finite element method with a special iterative method.Results of numerical experiments show that the numerical results agree well with the theory one and our numerical scheme is an efficient algorithm.