Broadband All-angle Negative Refraction by Optimized Phononic Crystals

All-angle negative refraction (AANR) of phononic crystals and its frequency range are dependent on mechanical properties of constituent materials and their spatial distribution. So far, it is impossible to achieve the maximum operation frequency range of AANR theoretically. In this paper, we will present a numerical approach for designing a two-dimensional phononic crystal with broadband AANR without negative index. Through analyzing the mechanism of AANR, a topology optimization problem aiming at broadband AANR is established and solved by bi-directional evolutionary structural optimization method. The optimal steel/air phononic crystal exhibits a record AANR range over 20% and its refractive properties and focusing effects are further investigated. The results demonstrate the multifunctionality of a flat phononic slab including superlensing effect near upper AANR frequencies and self-collimation at lower AANR frequencies.