| 光学Bloch方程的数值解法 |
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| 引用本文： | 郭莹莹,余向阳.光学Bloch方程的数值解法[J].中山大学学报(自然科学版),2005,44(5):108-110. |
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| 作者姓名： | 郭莹莹 余向阳 |
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| 作者单位： | 中山大学光电材料与技术国家重点实验室,广东,广州,510275 |
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| 基金项目： | 国家重点基础研究发展计划(973计划) |
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| 摘 要： | 用常微分方程的经典数值解法Euler法、Heun法、标准四阶Runge-Kutta法和修正四阶预报-校正法求解光学Bloch方程,并与一定条件下的解析解进行了比较,分析了四种算法,尤其是修正四阶预报-校正算法的误差与可靠性.计算的结果表明,四种数值算法在合适步长下,对光学Bloch方程的求解都可以收敛,并能保持算法所具有的相应误差阶数.验证了四阶预报-校正算法的可靠性以及在光学Bloch方程分析光学瞬态相干过程中的应用.该方法对求解光学Bloch方程具有普适意义.
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| 关 键 词： | 光学Bloch方程 二能级体系 光学瞬态过程 微分方程数值解法 |
| 文章编号： | 0529-6579(2005)05-0108-03 |
| 收稿时间： | 01 7 2005 12:00AM |
| 修稿时间： | 2005年1月7日 |
Numerical Methods for Optical Bloch Equations |
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| GUO Ying-ying,YU Xiang-yang.Numerical Methods for Optical Bloch Equations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2005,44(5):108-110. |
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| Authors: | GUO Ying-ying YU Xiang-yang |
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| Institution: | State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China |
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| Abstract: | The classical numerical treatments of ordinary differential equations, including Eider, Heun, fourth-order Runge-Kutta and a new fourth-order predictor-corrector methods, are used to solve the optical Bloch equations. By comparing the numerical results and with analytical results, the four numerical methods, especially for the new method's errors and reliability are analyzed. The numerical results prove that, if the steps are suitable, the four numerical methods for the Bloch equations are possible convengence and can keep the numerical method's corresponding errors. The new method is reliable, can be used to optical transient coherent process, and is significant for solving the optical Bloch equations. |
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| Keywords: | optical bloch equations two-level system optical transient process ordinary differential numerical method |
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