Acoustic Zitterbewegung And Device Design In Two-Dimensional Sonic Crystals

The sonic crystals (SCs) have attracted much interest in recent years. SCs are a marriage of solid-state physics and acoustic. Crystal structures are citizens of solid-state physics, but in SCs the electrons are replaced by acoustic waves. SCs can tailor the properties of acoustic waves by a periodic elastic structure. Now SCs band structure and the basic properties have been systematically analyzed and several calculation methods have been established to do the theoretical research. In recent years, the research focuses on two major areas.One is the analog in quantum mechanics. The heart of the subject of phononic crystals is the propagation of acoustic waves in a periodic elastic medium. In a sense, quantum mechanics is also the study of wave propagation, which obeys the Schrodinger equation, and bears some resemblance to a familiar wave equation. It therefore comes as no surprise that some of quantum phenomenon can been observed in the phononic crystals. And with a macroscopic scale, the experimental realization is easier.The other is the construction of functional devices for practical applications. Utilizing the particular dispersion relationship of SCs new acoustic devices are designed, which have been conformed to be effective, such as the waveguides, cavities, superlenses and so on.For simplicity, the theoretical analysis and the design of new device in this paper are based on two-dimensional systems. The ideas generalize easily to the cases of one-and three-dimensional crystals.1. Acoustic Zitterbewegung in Ordinary Sonic Crystals:A General Classical DescriptionZitterbewegung (ZB) is a trembling motion that describes originally the behavior of wave packet solutions of the Dirac equation for relativistic electrons in free space. Based on a classical description, we demonstrate in a direct way that the acoustic ZB could occur in an ordinary sonic crystal without involving Dirac point, similar to the case in electron systems. In contrast to the previous studies in classical systems resort to a framework of quantum mechanics, here we construct a spatial wave-packet by integrating the eigenstates directly, and give a general description for the acoustic ZB. We validate that the trembling motion is indeed originated from the interference of Bloch modes in the neighboring dispersion branches, with an oscillatory frequency approximate to the frequency difference between the modes. The transient behavior of the acoustic ZB in 2D SCs has also been discussed. This study may provide a guide line for the further experimental realization of ZB in acoustic systems.2. Applications of antireflection coatings in sonic crystal-based acoustic devicesThe unwanted reflection seriously baffles the practical applications of sonic crystals, such as for various acoustic lenses designed by utilizing the in-band properties of sonic crystals. Herein we introduce the concept of the antireflection coating into the sonic crystal-based devices. The efficiency of such accessorial structures is demonstrated well by an originally high reflection negative-refraction system. We show that this structure not only can enhance the transmission, but also can effectively reduce it. Promising perspectives can be anticipated in extending the antireflection coating layers into more general acoustic applications through a flexible design process.3. Beam splitter based on acoustic birefringence in sonic crystalsBeam splitter is one of the most important basic acoustic devices. In this chapter, we show a new approach for designing a beam splitter by using the acoustic birefringence phenomenon. As we know, optical waves with different polarizations can lead to birefringence easily in the anisotropic crystals. However, because acoustic waves in the fluid only have the longitudinal mode, such a birefringence is impossible. However, by adding a surface grating onto a two-dimensional phononic crystal slab, the incident acoustic mode which is in the partial band gap can obtain a momentum boost along the surface direction, which makes it possible to couple with the Bloch modes inside the SC. So when a Gaussian beam is normally incident, two refractive outgoing beams are generated. The refraction angles are nearly±45°. The intensities and the distance of the two outgoing beams can be adjusted flexibly.