Numerical Simulation of Waves in Periodic Structures

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 Schrödinger equation in both one and two dimensions, when the periodic potential functions have some local defects. AMS subject classifications: 35B27, 65M99, 35Q60, 35J05 PACS: 02.70.Bf, 31.15.-p, 42.82.Et, 85.35.-p, 85.35.Be

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