Waves in periodic media: Fourier analysis shortcuts and physical insights, case of 2D phononic crystals
| Autor: | S Dupont, J Gazalet, J C Kastelik |
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| Přispěvatelé: | Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF) |
| Rok vydání: | 2014 |
| Předmět: |
History
Partial differential equation Discretization Band gap Mathematical analysis 01 natural sciences Domain (mathematical analysis) 010305 fluids & plasmas Computer Science Applications Education Brillouin zone symbols.namesake Theoretical physics Fourier transform Fourier analysis 0103 physical sciences symbols 010306 general physics Electronic band structure Mathematics |
| Zdroj: | Journal of Physics: Conference Series Journal of Physics: Conference Series, IOP Publishing, 2014, 490 (1), 012120, 4 p. ⟨10.1088/1742-6596/490/1/012120⟩ |
| ISSN: | 1742-6596 1742-6588 |
| DOI: | 10.1088/1742-6596/490/1/012120 |
| Popis: | International audience; Phononic crystal is a structured media with periodic modulation of its physical properties that influences the propagation of elastic waves and leads to a peculiar behaviour, for instance the phononic band gap effect by which elastic waves cannot propagate in certain frequency ranges. The formulation of the problem leads to a second order partial differential equation with periodic coefficients; different methods exist to determine the structure of the eigenmodes propagating in the material, both in the real or Fourier domain. Brillouin explains the periodicity of the band structure as a direct result of the discretization of the crystal in the real domain. Extending the Brillouin vision, we introduce digital signal processing tools developed in the frame of distribution functions theory. These tools associate physical meaning to mathematical expressions and reveal the correspondence between real and Fourier domains whatever is the physical domain under consideration. We present an illustrative practical example concerning two dimensions phononic crystals and highlight the appreciable shortcuts brought by the method and the benefits for physical interpretation. ©2014 IOP Publishing |
| Databáze: | OpenAIRE |
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