光学学报, 2018, 38(12): 1205001, 网络出版: 2019-05-10
General Solution to Delay-Response Spectra of Waveguide Bragg Gratings
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
光栅 波导布拉格光栅 时延 相位 响应谱 半解析通解 gratings waveguide Bragg gratings delay phase response spectrum semi-analytic general solution
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。
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.