Study on several novel topological phases in classical wave systems

Abstract

Topological phases of matter have attracted great research interests in the last two decades among various fields, ranging from condensed matter physics to photonics and acoustics. In classical wave systems like photonics and acoustics, the discoveries of topological states offer exciting playgrounds for both new theoretical studies and novel applications. This thesis studies several novel topological phases of matter in classical wave systems which includes experimental demonstrations of photonic valley-Hall phases and acoustic higher-order topological states, and theoretical discovery of non-Hermitian Dirac cones. In Chapter 1, I briefly review the development history of topological phases of matter in condensed matter physics and classical wave systems, introduce basic knowledge and concepts for topological physics, and introduce several novel topological phases which will be studied in detail in the following chapters. In Chapter 2, I study photonic topological valley Hall phases. Topologically protected refraction of valley kink states and spin-valley controlled topological phases are experimentally demonstrated in 2D photonic crystals. In Chapter 3, I study acoustic higher-order topological phases which include experimental demonstrations of a second-order topological insulator on a kagome lattice, a third-order topological insulator on a diamond lattice and an octupole topological insulator in acoustic systems. In Chapter 4, I present a general theory for non-Hermitian systems to host diabolic points. I show how gain and loss, which is available in various classical wave systems, can interact with diabolic points in unexpected manners.