【作者】 刘海；

【导师】 刘劲松；

【作者基本信息】 华中科技大学 ， 物理电子学， 2009， 博士

【摘要】 对二维随机介质内光波模式的偏振特性研究已经成为激光物理界的研究热点之一。在之前对随机介质内光波特性的研究中，都没有考虑到光波的偏振态的影响。也就是说没有考虑到TM偏振态光波和TE偏振态光波模式对反转粒子数的竞争情况。因此有必要对二维随机介质内光波模式的偏振特性进行全面的研究。全文的具体内容包括：(1)引入了随机激光半经典理论并介绍了时域有限差分法(Finite Difference TimeDomain，FDTD)的基本原理和思想方法，以及对稳定性条件、PML吸收边界条件的设定、激励源的设置等问题的分析和处理方法，这些因素都是为了确保计算结果的可靠性。(2)基于FDTD法求解随机激光半经典理论模型，我们建立了一个特有的数值模型用来研究二维随机介质内光波模式的偏振特性。并且研究了TE光波与TM光波模式共享反转粒子数时，两种不同偏振态光波模式的特性差异。结果表明，这种情况下TE偏振光波模式具有更小的抽运阈值且TM偏振光波模式被TE偏振光波模式压制。另外，研究了不同介质模型参数对偏振依赖特性的影响。发现即使改变随机介质模型的参数，TM模式依然会被TE模式压制。但是当增加介质尺寸到一定程度时，TM偏振光波模式也可能被有效地激发。这些结论与之前所研究的不考虑反转粒子数共享的情形有非常大的差异。(3)根据这种偏振依赖特性差异，提出了利用局域泵浦方法进行偏振光波模式的选择。同时对局域泵浦条件下不同偏振态光波模式的阈值特性进行了研究。结果发现，如果局域泵浦区域选择合适的话，TM偏振态光波模式的阈值反而比TE偏振态光波模式的阈值要小。如果局域泵浦区域选择过大的话，TM偏振态光波又逐渐被TE偏振态光波压制。这种特性可以用来获得单偏振态的光波模式。(4)同样在局域泵浦条件下，进一步研究了二维随机介质中内各偏振态光波的频谱时间演化特性，并获得了选定偏振态光波模式的品质因数(Q)值。发现在选择合理的泵浦区域时，TM偏振态光波的峰值强度增加的很快并且有较小的Q值，反之则正好相反。(5)在之前关于随机介质内单一偏振态光波模式的形态依赖特性研究的基础上，研究了不同外形的二维介质内不同偏振态之间的光波特性差异，并且这些介质外形源于同一个随机构形。结果显示不同偏振态的光波在共享反转粒子数的时候仍然是图形依赖的。不过外形的改变对于TM偏振光波模式的选择有较大影响，而对TE偏振光波的选择则影响较小。通过合理的选择介质外形，也能提供一种有效的选模方法。更多还原

【Abstract】 The research on optical properties of the polarized light-waves in two-dimensional random media has become research hotspot in laser physics. In prior research on the polarization property of the light-waves in the random media, the competition on the population inversion between different polarized states is neglected. It is necessary to have a comprehensive research on the polarization property. The main content of this thesis is summarized as follows.(1) We introduce the principle and arithmetic of Finite Difference Time Domain (FDTD) method particularly, including the excitation sources, the conditions of stability of calculation, and Perfectly Matched Layer (PML) boundary conditions. All of these factors ensure the results are reliable.(2) Based on FDTD method, we create a numerical model for the research on polarization property of the light-waves in two-dimensional random media. And the competition on inversed population between the transverse magnetic (TM) polarization state and the transverse electric (TE) polarization state is investigated. The results indicate that TM state has a larger lasing threshold than that of TE state so that TM state is suppressed strongly by TE state in the competition. The larger the size of the medium is, the easier the lasing modes in TM state appear.These conclusions are different from the results of the case without the competition on inversed population between different polarized states.(3) The threshold property of the two polarization states with local pumping is analyzed. Results show that the lasing threshold of TM modes is lower than that of TE ones when the radius of the local pumping region is suitably selected, and the case would be contrary when the selected radius of the local pumping region is excessive.The conclusion provide an effective method to obtain TM polarized light-waves.(4) Under local pumping, the spectral time evolution of polarized modes is also investigated. And the values of quality factor (Q-factor) are obtained for the selected polarized modes by calculating the decay rates of them. The results demonstrate that there exists a critical value of local pumping area for TM modes. If the area is less than this value, the TM modes would have a quicker rising of the peak intensity and smaller Q-factor than that of TE modes. Or else, the conclusions would be contrary.(5) Compare with the prior research, the spectrum for two polarized states with the competition on inversed population in a set of two-dimensional (2D) active random media is calculated. And these random media have same random constitution but different shapes. Results show both two polarized states are morphology dependent and the variety of the shapes has more influence on the selection of TM polarized modes than that of TE polarized modes. Appropriate design of the shapes has obvious effect on the selection of TM polarized modes and can improve the adverse situation of TM polarized state in the competition. Such polarization-dependent difference of morphology property presents a new mode-selecting technique for random lasers.更多还原