Abstract
We propose a novel type of phononic crystal for which the materials parameters are continuous functions of space coordinates without discontinuities corresponding to a seamless fusion of the constituent materials within the crystal lattice. With the help of an adaptation of this fundamental approach, we extend the well-established concept of phononic crystals, allowing an investigation of the transition from conventional phononic crystals with a regulated step-like parameter function to the realm of so-called function phononic crystals. Our study is based on a first-principle theory assisted by high-performance computer simulations and focuses on an understanding of the effects of a deviation from the typical parameter step function on the phononic density of states (DOS). Our exploration of the DOS reveals a characteristic rapid convergence: even a slight deviation from an ideal step function has the potential to induce radical changes in the band structure leading to the emergence of desirable features, especially multiple complete phononic band gaps.
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