Planes approximation method for investigating the physical origins of deep, wide phononic bandgaps

The objective of this paper is to formulate a simple analytical model that describes Bragg and Mie scattering leading to the creation of bandgaps in phononic crystals (PnCs). The model is a homogenized, mean-field 1D model, dubbed the Planes Approximation Method (PAM). Bragg and Mie scattering are decoupled into independent 1D models and then recombined graphically to understand better and visualize bandgap creation. Due to the model's simplicity, it allows for rapid solutions compared to other computational methods. This paper argues that acoustic impedance mismatches yield bandgaps based on the formulation. PAM is demonstrated using a square lattice of microscale circular inclusions of tungsten with a lattice constant of 45 μm in a SiO2 matrix and then compared to results from finite difference time domain and plane wave expansion simulations. •Analytical model is developed enabling fundamental understanding of the interplay between Bragg and Mie Scattering in phononic crystals.•Homogenized, Mean-Field 1D model is applied to 2D phononic crystals and compared more computationally expensive plane wave expansion and finite difference time domain models.•Model shows that acoustic impedance mismatch is responsible for phononic bandgaps.•Combining Bragg and Mie Scattering mechanisms creates deep, wide phononic bandgaps.