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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 optical transmission properties of two-dimensional photonic crystals with complex permittivity were studied by numerical simulation using plane wave expansion method. The effect of the imaginary part of the dielectric constant on the transmission properties was emphatically discussed. Studies have shown that due to the existence of photonic bandgaps effectively suppress the frequency of spontaneous emission of light in the band gap. When doped with impurities with a gain characteristic in the medium, even if the dielectric constants of the two mediums are very small, strong stimulated emission amplification occurs near the photonic bandgap edge. Usually at the edge of the bandgap, the photon crystal group velocity is small, and the laser threshold is proportional to the square of the group velocity, when the group velocity is small, the laser threshold will be greatly reduced. This provides a basis for realizing zero-threshold laser and also provides a useful theoretical reference for making optical-amplifying micro-devices.