Appendix A Plane wave method

  • Published 2004

Abstract

The plane wave method (PWM) for the calculation of the band structure of PCs is presented in this appendix. First, the general formalism of this method in briefly introduced. The expansion of the inverse dielectric function has been used for all calculations instead the expansion of the dielectric function itself, since better convergence is obtained in this way [55]. The case of a one dimensional periodic arrangement is discussed for illustrative purposes and to introduce the notation used thereafter. Successively, the formalism of the PWM for two dimensional models periodic along orthogonal directions is presented. For rectangular elements aligned with these orthogonal directions, the use of plane wave basis functions collinear with the lattice vectors is straightforward and yields accurate results, as in the case of lamellar gratings discussed in section 1.5.2. The two-dimensional PWM has been employed in the study of rectangular and centred rectangular structures discussed in chapter 2 and consequently, the formalism is treated in relation to the applications.

Cite this paper

@inproceedings{2004AppendixAP, title={Appendix A Plane wave method}, author={}, year={2004} }