采用平面波展开法,通过数值模拟研究了具有复介电常量的二维光子晶体的能带结构和光传输特性,重点讨论介电常量的虚部为负值情形时对传输特性的影响。研究表明由于光子带隙的存在有效地抑制了频率位于带隙内光的自发辐射。当在介质中掺入具有增益特性的杂质时,即使两种介质的介电常量相差很小,在靠近光子带隙边缘,出现了较强的受激辐射放大。通常在带隙的边缘处,光子晶体的群速度较小,而激光阈值正比于群速度的平方,当群速度很小时,激光阈值将大大减小。这为实现零阈值激光器提供了基础,也为制作光放大微器件提供了一个有益的理论参考。

The band structure and the optical transmission properties of the two-dimensional photonic crystal with complex dielectric constant, especially discussing on the case of negative imaginary part, are analyzed numerically with the plane-wave expansion method. The results show that the spontaneous emission of special light frequency that is in the range of photonic band gap is effectively restrained. A large enhancement of stimulated emission appears at the photonic band edges where the group velocity is small if the photonic crystal is with a little impurity atoms that have population inversion. This phenomenon will happen even if the dielectric constant difference between two dielectrics is very small. Generally, there is a small group velocity near the photonic band gap. Because the threshold of emitting laser is proportional to the square of group velocity, the lasing threshold decreases with a decrease in the group velocity. This might be used either to realize lasing operation near zero thresholds, or to supply a beneficial reference for fabricating optical amplification device.