基于随机激光的时域理论, 建立了横磁与横电光波模式共享反转粒子数情况下的理论模型, 并利用时域有限差分法（FDTD）数值求解麦克斯韦方程组和速率方程组, 从而获得了二维随机介质内横磁与横电光波模式的阈值特性。结果表明, 如果横磁与横电偏振模式之间没有共享反转粒子数, 则横磁光波模式拥有较低的激发阈值; 反之, 则横电光波模式的激发阈值更低。在共享反转粒子数的情况下, 改变样品的表面填充率对两种偏振模式的阈值并没有很大的影响, 而增加样品面积则可以明显的降低横磁模式的阈值。

The theoretical model which transverse magnetic (TM) polarization state and transverse electric (TE) polarization state share the same inverted population is built based on the time dependent theory of random lasers. By using the finite difference time domain (FDTD) method to numerically solve Maxwell equations and rate equations, we can obtain the threshold properties for two polarization states. The results show that TM state has a lower lasing threshold than TE state when they don’t share the inverted population, otherwise, the TM state is strongly suppressed. In the competition condition, the threshold for two states changes hardly by changing the surface-filling fraction, but will decrease for TM state when increasing the sample size.