采用麦克斯韦方程和速率方程相结合的模型和时域有限差分法,利用引入的有效增益分布因子概念研究了光子晶体中本征模的阈值特性。增益介质的大小以及在光子晶体中的位置直接影响光子晶体带边激光器的输出特性；有效增益分布因子描述了光子晶体中增益介质的空间分布特性。结果显示,带边本征模的激射阈值依赖于有效增益分布因子。不同的本征模具有不同的有效增益分布因子,那些有效增益分布因子较大的模式具有较低的阈值。通过调整增益介质的位置和长度,可以提高有效增益分布因子的值,从而降低激光器的阈值,这对于实现激光器的低阈值运行有指导作用。

On the basis of Maxwell’s equations coupled with the rate equations, the lasing threshold of one-dimensional photonic band edge laser is investigated by finite-difference time-domain method with the introduced effective gain distribution factor (EGDF). The size and position in the photonic crystal of gain mdeium directly influence the output properties of the photonic band edge laser, and the EGDF describes the spatial distribution of gain medium in photonic crystal. The numerical results show that the lasing threshold of an eigenmode depends on the EGDF, different eigenmode has different value of EGDF. Those eigenmodes corresponding to higher value of EGDF have lower threshold. With suitable design of size and position of the gain medium, higher EGDF can be obtained, which directly leads to a lower value of lasing threshold. This gives a new approach to decrease the lasing threshold of the photonic band edge laser.