Engineering acoustic band gaps in phononic crystals

In recent years, the study of acoustic and elastic waves propagation in periodic materials, known as "phononic crystals", has received increasing amount of attention. Analogous to photonic crystals, a large and robust band gap is essential to all applications of phononic crystals. In this work, a perturbative approach is applied to phononic crystals and two main results are obtained. Firstly, we show that a perturbation analysis can provide us an efficient method to enlarge an existing acoustic band gap. Secondly, by extending the perturbative analysis to disordered phononic crystals, we can quantitatively estimate the effect of the disorder on the size of an acoustic band gap. Due to the difference in the mathematical structures between Maxwell equations in a photonic crystal and acoustic wave equation in a phononic crystal, we find that it is much more efficient to enlarge an acoustic band gap than a photonic band gap. Numerical simulations using the Multiple Scattering Method verify all the conclusions above.