薄板光子晶体的表面模式在设计制造性能更加优异的光子元件领域发挥了重要的作用.本文扩展了Dirichlet-to-Neumann(DtN)映射方法,将其用于计算二维薄板光子晶体的表面模式.这种方法以单元晶格的DtN映射为基础,利用标准与非标准单元晶格...薄板光子晶体的表面模式在设计制造性能更加优异的光子元件领域发挥了重要的作用.本文扩展了Dirichlet-to-Neumann(DtN)映射方法,将其用于计算二维薄板光子晶体的表面模式.这种方法以单元晶格的DtN映射为基础,利用标准与非标准单元晶格的DtN映射,构造出超级晶格的DtN映射,然后在超级晶格的边界上建立起特征值问题来进行求解.由于只需要在区域的边界上进行离散,所以特征值问题涉及到的矩阵是比较小的.在文章的算例部分验证了这种方法的有效性,并且应用这种方法在薄板光子晶体与完美磁导体(Perfect Magnetic Conductor)的交界面上发现了一种新的表面模式.展开更多
The band structures of flexural waves in a phononic crystal thin plate with straight, bending or branching linear defects are theoretically investigated using the supercell technique based on the improved plane wave e...The band structures of flexural waves in a phononic crystal thin plate with straight, bending or branching linear defects are theoretically investigated using the supercell technique based on the improved plane wave expansion method. We show the existence of an absolute band gap of the perfect phononic crystal and linear defect modes inside the gap caused by localization of flexural waves at or near the defects. The displacement distributions show that flexural waves can transmit well along the straight linear defect created by removing one row of cylinders from the perfect phononic crystals for almost all the frequencies falling in the band gap, which indicates that this structure can act as a high efficiency waveguide. However, for bending or branching linear defects, there exist both guided and localized modes, and therefore the phononic crystals could be served as waveguides or filters.展开更多
文摘薄板光子晶体的表面模式在设计制造性能更加优异的光子元件领域发挥了重要的作用.本文扩展了Dirichlet-to-Neumann(DtN)映射方法,将其用于计算二维薄板光子晶体的表面模式.这种方法以单元晶格的DtN映射为基础,利用标准与非标准单元晶格的DtN映射,构造出超级晶格的DtN映射,然后在超级晶格的边界上建立起特征值问题来进行求解.由于只需要在区域的边界上进行离散,所以特征值问题涉及到的矩阵是比较小的.在文章的算例部分验证了这种方法的有效性,并且应用这种方法在薄板光子晶体与完美磁导体(Perfect Magnetic Conductor)的交界面上发现了一种新的表面模式.
基金Project (Nos 10632020 and 90715006) supported by the National Natural Science Foundation of China
文摘The band structures of flexural waves in a phononic crystal thin plate with straight, bending or branching linear defects are theoretically investigated using the supercell technique based on the improved plane wave expansion method. We show the existence of an absolute band gap of the perfect phononic crystal and linear defect modes inside the gap caused by localization of flexural waves at or near the defects. The displacement distributions show that flexural waves can transmit well along the straight linear defect created by removing one row of cylinders from the perfect phononic crystals for almost all the frequencies falling in the band gap, which indicates that this structure can act as a high efficiency waveguide. However, for bending or branching linear defects, there exist both guided and localized modes, and therefore the phononic crystals could be served as waveguides or filters.
