Complex Band Structure of Phononic Crystals and the Diffraction Problem

Vincent Laude*, Younes Achaoui, Sarah Benchabane, Abdelkrim Khelif

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

The diffraction of elastic waves on a two-dimensional finite phononic crystal is investigated by a plane wave technique. It is first remarked that a full solution to the phononic crystal problem requires that all modes of the periodic structure (Bloch waves) are indentified and incorporated in the solution, including evanescent Bloch waves. An extended plane-wave expansion (PWE) method is used to obtain the complex band structure of the phononic crystal, but also the band structure of diffracted waves in the incident and exit media. Complex isofre-quency curves are presented and show sharp variations of the Bloch wave vector with the angle of propagation. Finally, the complex band structures are used to formulate a reflection/transmission problem similar to the one leading to Fresnel formulas for homogeneous media. Some examples of diffracted field computations are given.

Original languageEnglish
Title of host publicationIUTAM Symposium on Recent Advances of Acoustic Waves in Solids - Proceedings of the IUTAM Symposium on Recent Advances of Acoustic Waves in Solids
EditorsTsung-Tsong Wu, Chien-Ching Ma
PublisherSpringer Science and Business Media B.V.
Pages165-173
Number of pages9
ISBN (Print)9789048198924
DOIs
Publication statusPublished - 2010
Externally publishedYes
EventIUTAM Symposium on Recent Advances of Acoustic Waves in Solids, 2009 - Taipei, Taiwan, Province of China
Duration: 25 May 200928 May 2009

Publication series

NameIUTAM Bookseries
Volume26
ISSN (Print)1875-3507
ISSN (Electronic)1875-3493

Conference

ConferenceIUTAM Symposium on Recent Advances of Acoustic Waves in Solids, 2009
Country/TerritoryTaiwan, Province of China
CityTaipei
Period25/05/0928/05/09

Keywords

  • Bloch Wave
  • Diffraction Problem
  • Evanescent Wave
  • Fresnel Formula
  • Phononic Crystal

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