Spectral Properties of Periodic and Disordered Dielectric and Acoustic Media

摘要

For the reported period I, Dr. Yu. Godin, Dr. I. Khalfin and Dr. V. Gorentsveig worked on the problems on the band-gap structure of 2D and 3D photonic crystals and the localization of electromagnetic and acoustic waves in periodic media and in media with single defects: (1) The model and time efficient code for the computation of the optimal parameters for the 2D photonic crystals have been developed. The results of the work have been used to compute the optimal design parameter of 2D photonic crystals for Dr. L. Webb and Dr. G. Sullivan from Boeing (former Rockwell). An asymptotic model of 3D photonic crystals has been developed and we has begun its computer implementation. (2) The mathematical theory of cavity eigenmodes has been extended to the case of electromagnetic and acoustic waves. We have also developed algorithms based on the lattice models for the computing of localized classical waves generated by defects in the background periodic media. The algorithms have been implemented in a code which demonstrated all expected phenomena including tunneling. It also gives an estimation of the localization radius of a cavity eigenmode. The code produces also nice graphical images of the cavity eigenmodes and spectra.