非均匀展宽体系Maxwell-Bloch方程的求解及应用

 建立了高精度快速求解非均匀展宽二能级体系Maxwell Bloch(MB)耦合方程的数值算法。通过与特定条件下MB方程解析解及面积定理的比较，表明算法具有良好的收敛性和稳定性。作为示例，应用所建立的数值算法求解了一般条件下的MB方程，由计算结果分析了失谐量、弛豫时间以及非均匀展宽线宽对光脉冲在介质中传播的影响。该数值算法为进一步研究光与物质相互作用的物理过程提供了一个很好的工具，对MB方程以及修正的这类偏微分方程组具有普适性。

Numerical Method and Application for Optical Maxweil-Bloch Equations in Inhomogeneously Broadened Medium

An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations that are used to describe the optical pulse propagation and interaction with inhomogeneously broadened two-level medium. The convergence and stability of this numerical method are proved by comparing with the analytic solutions and area theorem derived under special condition.The simulations of arbitrary conditions is discussed by employing this method and analyze the pulse evolution for different detunings, relaxation times and inhomogeneously broadened linewidthes. The established numerical method provides a good way to have further study about the coherent interaction of short optical pulses with resonant mediums, and can be used to solve the corrections of Maxwell-Bloch equations.