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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。
The threshold characteristic of eigenmodes in photonic crystals was studied by using the model of Maxwell’s equations and velocity equations and the finite-difference time-domain method, using the concept of effective gain distribution factor introduced. The size of the gain medium and its position in the photonic crystal directly affect the output characteristics of the photonic crystal band-edge laser. The effective gain distribution factor describes the spatial distribution of the gain medium in the photonic crystal. The results show that the lasing threshold of the edge-dependent eigenmodes depends on the effective gain distribution factor. Different eigenmodes have different effective gain distribution factors, and those with larger effective gain distribution factors have lower thresholds. By adjusting the position and length of the gain medium, it is possible to increase the value of the effective gain distribution factor, thereby lowering the threshold of the laser, which is instructive for achieving a low threshold operation of the laser.