Reduced Bloch mode expansion for periodic media band structure calculations

By Mahmoud I. Hussein. Proceedings of the Royal Society A, 2008

228 citations recorded by the source corpus.

Reduced Bloch mode expansion (RBME) is presented for fast periodic media band structure calculations. The expansion employs a natural basis composed of a selected reduced set of Bloch eigenfunctions. The reduced basis is selected within the irreducible Brillouin zone at high symmetry points determined by the medium’s crystal structure and group theory (and possibly at additional related points). At each of the reciprocal lattice selection points, a number of Bloch eigenfunctions are selected up to the frequency/energy range of interest for the band structure calculations. As it is common to initially discretize the periodic unit cell and solution field using some choice of basis, RBME is practically a secondary expansion that uses a selected set of Bloch eigenvectors. Such expansion therefore keeps, and builds on, any favourable attributes a primary expansion approach might exhibit. Being in line with the well-known concept of modal analysis, the proposed approach maintains accuracy while reducing the computation time by up to two orders of magnitudes or more depending on the size and extent of the calculations. Results are presented for phononic, photonic and electronic band structures.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/2b4f2622670470e1f4698bd641722056a6ab1b2c

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In Atomic and Molecular Physics, and Optics

1. Jean-Mathieu Mencik
2. Michael J. Frazier
3. Mahmoud I. Hussein

In Electrical and Electronic Engineering

1. Jean-Mathieu Mencik
2. Michael J. Frazier
3. Mahmoud I. Hussein

Citations in the corpus

• New advances in the forced response computation of periodic structures using the wave finite element (WFE) method (2014, methodology): “In [9], a so-called reduced Bloch mode expansion (RBME) method has been proposed for fast band structure calculations in infinite periodic media.”
• Band structure of phononic crystals with general damping (2010, methodology): “In this paper, and building on our earlier work [17, 18] we have extended the application of these techniques to the study of the dynamics of materials within the framework of Bloch theory.”