光子学报, 2009, 38 (12): 3138, 网络出版: 2010-05-10
光学Maxwell-Bloch方程的数值算法研究及其应用
Numerical Methods and Application for Optical Maxwell-Bloch Equations
量子光学 光与物质相互作用 光学Maxwell-Bloch方程 偏微分方程数值解法 超短激光脉冲的传播 Quantum optics Light-matter interaction Optical Maxwell-Bloch equations Numerical method to partial-differential equations Propagation of ultra-short pulse
摘要
建立了高准确度快速求解均匀展宽二能级体系光学Maxwell-Bloch耦合方程的数值算法.通过与特定条件得到的解析解的比较，验证了算法所具有的高收敛性和稳定性，并可保持算法的误差阶数，因此算法是可靠并实用的.应用该算法数值求解了一般条件下的MB方程，并由计算结果分析了失谐量、弛豫时间、初始光强对光脉冲在介质中的传播及对Bloch矢量演化的影响.所建立的数值算法对MB方程以及修正的这类偏微分方程组具有普适性.
Abstract
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations,which describe the optical pulse propagation and interaction with homogeneously broadened two-level medium.The convergence and stability of this numerical method are also proved by comparing with the analytic solutions derived under special condition,and the method maintains its erroneous exponents and is applicable.Simulations of arbitrary conditions are discussed by employing this new method,and the evolutions of pulse and Bloch vectors for different detunings,relaxation times and initial input pulse power are analyzed.The established numerical method can be used to solve the Maxwell-Bloch equations and their corrections.
李成, 张华荣, 余向阳. 光学Maxwell-Bloch方程的数值算法研究及其应用[J]. 光子学报, 2009, 38(12): 3138. LI Cheng, ZHANG Hua-Rong, YU Xiang-Yang. Numerical Methods and Application for Optical Maxwell-Bloch Equations[J]. ACTA PHOTONICA SINICA, 2009, 38(12): 3138.
PDF全文
