### Abstract

The influence of linear defect boundaries on the transmission and scattering of elastic waves in quasi-two-dimensional wave-guides is studied using the matching method. A linear defect boundary separating two wave-guide crystalline lattice domains is characterised here by a linear chain of defect masses and by modified elastic constants in the boundary, different from their values in the bulk of the domains. In particular a square lattice is considered to model the domains of the two-dimensional planar wave-guide containing the linear defect. The reflection and transmission probabilities, and the total transmission probabilities are calculated numerically and presented for the scattering processes in a variety of cases. We show that the interaction between the localised modes introduced by the defect boundary and the propagating modes of the system leads to Fano resonances. These resonances shift to higher (lower) frequencies for smaller (larger) defect masses, and for the same mass as function of the angle of the incident wave. Other spectral features shown to exist are due to interference effects especially at oblique incidence and when modifying the boundary elastic constants.

Original language | English |
---|---|

Pages (from-to) | 435-443 |

Number of pages | 9 |

Journal | European Physical Journal B |

Volume | 15 |

Issue number | 3 |

Publication status | Published - 1 Jun 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

- 61.12.Bt Theories of diffraction and scattering
- 61.46.+w Clusters, nanoparticles, and nanocrystalline materials
- 68.65.+g Low-dimensional structures (superlattices, quantum well structures, multilayers): structure, and nonelectronic properties

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*European Physical Journal B*,

*15*(3), 435-443.

**The scattering and transmission of elastic waves in quasi-two-dimensional planar waveguides with linear defect boundaries.** / Belhadi, M.; Rafil, O.; Tigrine, R.; Khater, A.; Hardy, J.; Virlouvet, A.; Maschke, K.

Research output: Contribution to journal › Article

*European Physical Journal B*, vol. 15, no. 3, pp. 435-443.

}

TY - JOUR

T1 - The scattering and transmission of elastic waves in quasi-two-dimensional planar waveguides with linear defect boundaries

AU - Belhadi, M.

AU - Rafil, O.

AU - Tigrine, R.

AU - Khater, A.

AU - Hardy, J.

AU - Virlouvet, A.

AU - Maschke, K.

PY - 2000/6/1

Y1 - 2000/6/1

N2 - The influence of linear defect boundaries on the transmission and scattering of elastic waves in quasi-two-dimensional wave-guides is studied using the matching method. A linear defect boundary separating two wave-guide crystalline lattice domains is characterised here by a linear chain of defect masses and by modified elastic constants in the boundary, different from their values in the bulk of the domains. In particular a square lattice is considered to model the domains of the two-dimensional planar wave-guide containing the linear defect. The reflection and transmission probabilities, and the total transmission probabilities are calculated numerically and presented for the scattering processes in a variety of cases. We show that the interaction between the localised modes introduced by the defect boundary and the propagating modes of the system leads to Fano resonances. These resonances shift to higher (lower) frequencies for smaller (larger) defect masses, and for the same mass as function of the angle of the incident wave. Other spectral features shown to exist are due to interference effects especially at oblique incidence and when modifying the boundary elastic constants.

AB - The influence of linear defect boundaries on the transmission and scattering of elastic waves in quasi-two-dimensional wave-guides is studied using the matching method. A linear defect boundary separating two wave-guide crystalline lattice domains is characterised here by a linear chain of defect masses and by modified elastic constants in the boundary, different from their values in the bulk of the domains. In particular a square lattice is considered to model the domains of the two-dimensional planar wave-guide containing the linear defect. The reflection and transmission probabilities, and the total transmission probabilities are calculated numerically and presented for the scattering processes in a variety of cases. We show that the interaction between the localised modes introduced by the defect boundary and the propagating modes of the system leads to Fano resonances. These resonances shift to higher (lower) frequencies for smaller (larger) defect masses, and for the same mass as function of the angle of the incident wave. Other spectral features shown to exist are due to interference effects especially at oblique incidence and when modifying the boundary elastic constants.

KW - 61.12.Bt Theories of diffraction and scattering

KW - 61.46.+w Clusters, nanoparticles, and nanocrystalline materials

KW - 68.65.+g Low-dimensional structures (superlattices, quantum well structures, multilayers): structure, and nonelectronic properties

UR - http://www.scopus.com/inward/record.url?scp=0001523594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001523594&partnerID=8YFLogxK

M3 - Article

VL - 15

SP - 435

EP - 443

JO - Zeitschrift fur Physik B-Condensed Matter

JF - Zeitschrift fur Physik B-Condensed Matter

SN - 0722-3277

IS - 3

ER -