Low-frequency forbidden bandgap engineering via a cascade of multiple 1D superlattices

Abstract

Low-frequency forbidden bandgap (LFB) in solid-fluid superlattice (SFSL) provides a novel degree of freedom to control the propagation of low frequency acoustic waves. However, its narrow angle range seriously restricts its practical applications. To engineer the angle range of LFB, the transmission coefficient of a cascade of multiple 1D superlattices was calculated using the transfer matrix method and also verified by finite element simulations. It was found that the LFB with ultra-wide angle range can be created using only 4 cells of a two-phased cascade structure and can be adjusted by changing the solid filling fraction of each sub-SFSL. By introducing two or more 1D superlattices into the layered cascade structure, the LFB with multiple angle ranges and/or ultra-wide angle range can be engineered for low frequency acoustic waves whose wavelengths are much larger than the lattice constant. Such acoustic low-frequency forbidden bandgap materials are useful for making perfect acoustic low-frequency filters with broad bandwidth in selective angle ranges, which are useful in subwavelength acoustic devices.