Next Article in Journal
Bottom-Up Assembly and Applications of Photonic Materials
Next Article in Special Issue
Phononic Crystal Plate with Hollow Pillars Actively Controlled by Fluid Filling
Previous Article in Journal / Special Issue
Broadband Transmission Loss Using the Overlap of Resonances in 3D Sonic Crystals
Article Menu

Export Article

Open AccessArticle
Crystals 2016, 6(5), 52; doi:10.3390/cryst6050052

Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model

1
Franche-Comté Electronique Mécanique Thermique et Optique, CNRS UMR 6174, Université de Franche-Comté, Besançon F-25030, France
2
Department of Chemistry, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Victor J. Sanchez-Morcillo, Vicent Romero-Garcia and Luis M. Garcia-Raffi
Received: 25 March 2016 / Revised: 25 April 2016 / Accepted: 3 May 2016 / Published: 11 May 2016
(This article belongs to the Special Issue Phononic Crystals)
View Full-Text   |   Download PDF [3801 KB, uploaded 11 May 2016]   |  

Abstract

Bragg band gaps of phononic crystals generally, but not always, open at Brillouin zone boundaries. The commonly accepted explanation stems from the empty lattice model: assuming a small material contrast between the constituents of the unit cell, avoided crossings in the phononic band structure appear at frequencies and wavenumbers corresponding to band intersections; for scalar waves the lowest intersections coincide with boundaries of the first Brillouin zone. However, if a phononic crystal contains elastically anisotropic materials, its overall symmetry is not dictated solely by the lattice symmetry. We construct an empty lattice model for phononic crystals made of isotropic and anisotropic materials, based on their slowness curves. We find that, in the anisotropic case, avoided crossings generally do not appear at the boundaries of traditionally defined Brillouin zones. Furthermore, the Bragg “planes” which give rise to phononic band gaps, are generally not flat planes but curved surfaces. The same is found to be the case for avoided crossings between shear (transverse) and longitudinal bands in the isotropic case. View Full-Text
Keywords: phononic crystal; anisotropy; slowness curves; empty lattice model; avoided crossing phononic crystal; anisotropy; slowness curves; empty lattice model; avoided crossing
Figures

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Wang, Y.-F.; Maznev, A.A.; Laude, V. Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model. Crystals 2016, 6, 52.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Crystals EISSN 2073-4352 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top