Acoustic Interface States via Material Variation

2020-01-07T15:05:59Z (GMT) by Benjamin Pearce
Interface states at the boundary between two phononic crystals can arise when the two crystals possess overlapping bandgaps and differing signs in the imaginary components of their impedance [1]. The suitability of a given pair of crystals when designing an interface system can be inferred from the parity of the supported standing edge states marking the beginning and end of their band gap [2]. A crystal that supports a standing wave with an even parity pressure distribution at the beginning of its band gap will possess a differing imaginary impedance sign to a crystal supporting an odd parity state at the start of its band gap [2]. Previous works [1,2,3] have designed such systems by varying the geometry of a crystal, such variations result in the band gap of the crystal closing and re-opening, leading to two crystals with geometries that place them either side of a band gap closure. This will meet the previously given criteria for exhibiting an interface state [3]. The present study uses a variation of materials within a phononic crystal to demonstrate an interface system, whilst maintaining a consistent geometry between the two crystals. FEM Modelling was performed, using the commercial COMSOL software, to show that variations in the material properties of one of the materials within a phononic crystal results in an analogous process of band gap opening and closing. Two, two component 1D phononic crystals consisting of alternating layers of materials ‘A’ and ‘B’ were then designed and modelled to confirm the parity of their band gap edge states. Material ‘A’ was set as 3 mm thick ABS plastic, whilst material ‘B’ was either water or aluminium with thickness of 0.3 mm. The crystals were numerically modelled to provide the transmission spectra both individually and as a combined interface system revealing the predicted presence of an interface state. Initial experimental confirmation is underway, with a preliminary sample of an ABS/water crystal having been constructed, and its transmission spectrum obtained. Results thus far show the presence of the expected modes and a band gap. Further investigations are now underway using an improved sample so that data may be better compared with modelling.

References:
1. Xiao, M., Zhang, Z. Q., & Chan, C. T. (2014). Surface impedance and bulk band geometric phases in one-dimensional systems. Physical Review X, 4(2), 1–12.
2. Meng, Y., Wu, X., Zhang, R. Y., Li, X., Hu, P., Ge, L., Wen, W. (2018). Designing topological interface states in phononic crystals based on the full phase diagrams. New Journal of Physics, 20(7).
3. Xiao, M., Ma, G., Yang, Z., Sheng, P., Zhang, Z. Q., & Chan, C. T. (2015). Geometric phase and band inversion in periodic acoustic systems. Nature Physics, 11(3), 240–244.