Evanescent coupling between surface and linear-defect guided modes in phononic crystals

Abstract

Evanescent coupling between surface and linear-defect waveguide modes in a two-dimensional phononic crystal of steel cylinders in air is numerically demonstrated. When the ratio of scatterer radii to the lattice constant is set to 0.47 in the square phononic crystal, the two types of modes start interacting if there is one-row separation between the surface and waveguide. Supercell band structure computations through the Finite Element Method suggest that the waveguide band is displaced significantly, whereas the surface band remains almost intact when the waveguide and surface are in close proximity. The two resultant hybrid bands are such that the coupling length, which varies between 8 and 22 periods, initially changes linearly with frequency, while a much sharper variation is observed towards the top of the lower hybrid band. Such small values facilitate the design of compact devices based on heterogeneous coupling. Finite-element simulations demonstrate bilateral coupling behaviour, where waves incident from either the surface or waveguide can efficiently couple to the other side. The coupling lengths calculated from simulation results are in agreement with the values predicted from the supercell band structure. The possible utilisation of the coupling scheme in sensing applications, especially in acoustic Doppler velocimetry, is discussed.