中文摘要：

研究了量子级联激光器有源核中界面声子的色散关系和静电势分布．根据有源核内部的平移不变性导出了界面声子的色散关系．计算显示有源核中的界面声子可以分为体声子和表面声子模式．体声子的色散曲线构成一系列准连续的声子子带，其静电势分布予整个有源核并呈现出Bloch波的特征．表面声子的色散曲线位于各体声子子带的带隙内，其静电势局域在有源核一侧．这些结果将有助予量子级联激光器和子带跃迁激光器的优化设计．

英文摘要：

We consider the propagation of the interface phonons in the active core of a quantum cascade laser. Based on the translation invariance in the interior of the active core, an implicit dispersion relation is derived. Numerical calculations show that the interface phonons in the active core can be classified as bulk phonons and surface phonons. The dispersion curves of bulk phonons form a series of subbands, and their electrostatics potential is distributed in the whole region of the active core, showing the character of Bloch wave. While the dispersion curves of the sudace phonons are located in the gap between the subbands of the bulk phonons, and the electrostatic potential is localized near the interface between the active core and the waveguide layer. Our results are helpful to the design of quantum cascade lasers and other intersubband lasers.