On the Bloch Theorem and Orthogonality Relations
Optics
2015-09-03 v2
Abstract
Bloch theorem for a periodic operator is being revisited here, and we notice extra orthogonality relationships. It is shown that solutions are bi-periodic, in the sense that eigenfunctions are periodic with respect to one argument, and pseudo-periodic with respect to the other. An additional kind of symmetry between r-space and k-space exists between the envelope and eignfunctions not apparently noticed before, which allows to define new invertible modified Wannier functions. As opposed to the Wannier functions in r-space, these modified Wannier functions are defined in the k-spaces, but satisfy similar basic properties. These could result in new algorithms and other novel applications in the computational tools of periodic structures.
Keywords
Cite
@article{arxiv.1505.00319,
title = {On the Bloch Theorem and Orthogonality Relations},
author = {Sina Khorasani},
journal= {arXiv preprint arXiv:1505.00319},
year = {2015}
}