光学Maxwell-Bloch方程的数值算法研究及其应用
首发时间:2009-05-21
摘要:建立了高精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。作为示例,本文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、驰豫时间、初始光强对光脉冲在介质中的传播及Bloch矢量演化的影响,这对解释用MB方程描述的实验现象提供了很好的工具。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。
关键词: 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
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Numerical Methods and Application for Optical Maxwell-Bloch Equations
Abstract:An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations, which are used to describe the optical pulse propagation and interaction with homogeneously broadened two-level medium. The convergence and stability of this numerical method are proved by comparing with the analytic solutions derived under special condition, and the method maintains its erroneous exponents and is applicable. In this paper, we discussed simulations of arbitrary conditions by employing this new method, and analyzed the evolutions of pulse and Bloch vectors for different detunings, relaxation times and initial input pulse power. The established numerical method can be used to solve the Maxwell-Bloch equations and their corrections.
Keywords: quantum optical light-matter interaction optical Maxwell-Bloch equations numerical method to partial-differential equations the propagation of ultra-short pulse
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