Numerical Simulation of Waves in Periodic Structures

作者：Ehrhardt Matthias; Han Houde; Zheng Chunxiong^*

来源：Communications in Computational Physics, 2009, 5(5): 849-870.

• Periodic media
• Helmholtz equation
• Schrodinger equation
• Dirichlet-to-Neumann maps
• Robin-to-Robin maps
• band structure
• Floquet-Bloch theory
• high-order finite elements

In this work we improve and extend a technique named recursive doubling procedure developed by Yuan and Lu [J. Lightwave Technology 25 (2007), 3649-3656] for solving periodic array problems. It turns out that when the periodic array contains an infinite number of periodic cells, our method gives a fast evaluation of the exact boundary Robin-to-Robin mapping if the wave number is complex, or real but in the stop bands. This technique is also used to solve the time-dependent Schrodinger equation in both one and two dimensions, when the periodic potential functions have some local defects.

• 出版日期2009-5
• 单位清华大学