光学学报, 2018, 38(12): 1205001, 网络出版: 2019-05-10

波导布拉格光栅时延响应谱的通解

General Solution to Delay-Response Spectra of Waveguide Bragg Gratings
作者单位

1重庆理工大学电气与电子工程学院, 重庆 400054

2重庆工程学院电子信息学院, 重庆 400056

摘要
采用波导布拉格光栅(WBG)微扰的傅里叶变换和流守恒定律求解耦合模方程,得到WBG相位响应的解析解。通过对该相位响应的解析解进行微分,建立了WBG时延谱的半解析型通解。基于该时延谱通解,仿真分析了均匀和线性啁啾WBG的时延谱,并与用其他方法得到的时延谱及其实测谱进行对比分析,以验证时延谱通解的分析精度和效率。对比结果表明,基于该时延谱通解的分析结果在整个反射带内与用其他方法得到的时延谱计算值及实测值一致。该时延谱通解可用于快速、精确分析任意复杂WBG的时延谱,对有解析型和离散型傅里叶变换的WBG分别具有O(N),O(N1b N)的线性复杂度(N是计算点数)。该方法可为分析、设计和应用WBG的相位和时延特性提供通用的基础理论和解析化方法。
Abstract
The study gets a closed form of the phase-response of a waveguide Bragg grating (WBG) by solving its coupled-mode equation with the Fourier transform (FT) of its index perturbation and the law of flux conservation, and then establishes the semi-analytic general solution of its delay spectrum by differentiating the phase response. Based on this delay general solution, the delay spectra of uniform and linearly-chirped WBGs are simulated, which are compared with those delay spectra obtained by other methods and the measured spectra in order to verify the analysis precision and efficiency of delay general solution. The comparison results show that the delay spectra calculated with this general solution agree well with those measured or calculated by other methods in the whole reflection band. Moreover, this general solution can be employed for the fast and exact analysis of arbitrarily complicated delay spectra of WBGs. The WBGs with analytic FT and discrete FT possess the linear complexities of O(N), and O(Nlb N)(N is the number of calculation points), respectively. This method may provide a universal basic theory and an analytic method for the analysis, design, and application of the delay properties and phases of WBGs.
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