Exploring Bound States in the Continuum for Advanced Metamaterial Devices

In the field of wave physics, bound states in the continuum (BICs) have emerged as a revolutionary concept with several applications. In this new study conducted by Nan Gao, Ricardo Martin Abraham-Ekeroth, and Daniel Torrent and published in Wave Motion, it is explored BICs in the context of Lamb waves within composite plates made from isotropic materials

This research is framed within the Horizon Europe DYNAMO project, funded by the European Union.


What are the BICs?

BICs are unique, non-radiating wave modes that can exist within the spectrum of radiating waves. Initially theorized in quantum mechanics, these states have raised interest across various fields, including optics, acoustics, and now, elastic waves. BICs can lead to the development of highly efficient sensors, filters, and lasers due to their ability to confine energy without radiation losses.

Fig. 1. Strategy to find BICs and Geometries considered in this work. (a) Perspective view of a thin infinite Si plate with a SiO2 inclusion whose length is L. The height of the whole plate, h, is common to both media. (b) Simplified 2D model for (a), showing the constraints imposed to the eigenstates of the system to facilitate the appearance of BICs. (c) View of the geometry for the 3D problem of the disc with a central inclusion. The details of the methodology used are summarized in panels 1a and 1c.

Study Highlights

The study focuses on designing and observing BICs for Lamb waves (waves that propagate in thin plates and have practical applications in material science and engineering) 

The researchers utilized a numerical approach to demonstrate that BICs can be achieved in both two-dimensional (2D) and three-dimensional (3D) configurations by introducing a softer material than the background’s, such as silica (SiO2), into a thin silicon (Si) plate.

Key findings include:

  • Design Strategy: By selecting the aspect ratio and material properties, the team was able to predict and simulate BICs effectively. This involves ensuring the wave velocities in the inclusion are lower than those in the host material.
  • 2D and 3D Models: The study explores both 2D rectangular plates and 3D disk structures, highlighting how BICs can be tuned by adjusting the plate’s thickness or the inclusion’s dimensions.
  • Modal Contributions: Investigations into the modal contributions of both the host and inclusion materials provided deeper insights into the physical mechanisms behind BIC formation.
Fig. 3. Variation of the eigenfrequencies with the plate’s aspect ratio. (a-b) [(c-d)] tracks the behavior of the mode n = 1 [n = 2]. Blue [orange] lines with circles in (a) and (c) represent the real [imaginary] part of the eigenvalues. Star symbols on the horizontal axis highlight the selected BIC cases. The displacement field distributions for these BICs are shown on the insets, with the colorbar representing their absolute value. Green lines in (b) and (d) denote the variation of the Q factor in n = 1, 2 states, where the axes are all in 10-based logarithmic scale.

Applications and Future Directions 



This innovative method of generating BICs in non-periodic, asymmetric elastic structures paves the way for advanced metamaterial device prototyping. Potential applications include ultra-sensitive mechanical oscillators and quantum information processors, where precise control over wave propagation is crucial.

The research presented by Gao and colleagues represents a significant advancement in the field of elastic wave systems. By expanding the possibilities of BICs beyond traditional periodic structures, this study opens new paths for practical implementations in various high-tech fields.

For those interested in the detailed methodologies and simulation results, the complete article is available for download. Dive deeper into this innovative research.