Bound States in the Continuum in Elasticity

It is shown that Bound States in the Continuum (BSC) exist in an elastic structure consisting of a periodic double array of thin (subwavelength) cylindrical scatterers embedded in a background material, where the distance between the arrays is taken to be large in comparison to both the wavelength a...

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Bibliographic Details
Published in:Wave motion 2021-06, Vol.103, p.102718, Article 102718
Main Authors: Haq, Omer, Shabanov, Sergei
Format: Article
Language:English
Subjects:
Arrays
Dipoles
Electromagnetics
Mathematical analysis
Phase transitions
Phase velocity
Studies
Thin films
Transverse electromagnetic modes
Velocity
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Summary:It is shown that Bound States in the Continuum (BSC) exist in an elastic structure consisting of a periodic double array of thin (subwavelength) cylindrical scatterers embedded in a background material, where the distance between the arrays is taken to be large in comparison to both the wavelength and the period of the array. The background medium supports waves with all polarizations, one longitudinal and two transverse, each of which has a different phase velocity. The transverse mode polarized parallel to the cylinders is decoupled from the other two and the corresponding BSCs are similar to those found earlier in the electromagnetic theory. The longitudinal and transverse modes in the plane perpendicular to the array remain coupled, and the corresponding BSCs are shown to exist only for specific distances between the arrays and for specific values of the Bloch phase or ratio of the phase velocities. The latter condition stems from the fact that both the longitudinal and transverse modes acquire different round-trip phases as they propagate between the two arrays. An analytic form of such BSCs is obtained by solving the Lippmann–Schwinger equation in the dipole approximation with arbitrary mass densities and Lamé coefficients.
ISSN:0165-2125
1878-433X
DOI:10.1016/j.wavemoti.2021.102718