Date of Degree
Alexander B. Khanikaev
Vinod M. Menon
Condensed Matter Physics | Optics
Topological insulator, Photonics, Metamaterial, Photonic crystal
Topological phases in classical wave systems, such as photonic and acoustic, have been actively investigated and applied for wave guiding, lasing, and numerous other novel phenomena and device applications Topological phase transitions enable robust boundary states, and the field has been broadening recently into a vast variety of systems with temporal modulations and interactions. Floquet modulation, for example, is the modulation applied periodically in time which may break symmetries and leads to novel topological phases.
Introducing non-Hermitian Floquet modulation enables more interesting phenomena including bandgap in imaginary part of the spectrum and gainy/lossy topological edge states with complex energy values. An example of interactions, on the other hand, is introducing excitons or phonons to create polaritons - half-light and half-matter quasiparticles - in respective photonic systems. In the latter case, the strong coupling between photonic and solid-state degrees of freedom introduces avoided crossing and band repelling, opening bandgaps where topological properties transit partly from photonic bands to polaritonic bands.
Recently, a new kind of topological states in topological structures, known as higher order topological insulators (HOTIs), have drawn attention of research. HOTIs hold higher order topological boundary states, including 0D corner states in 2D structures, as well as 0D and 1D states in 3D systems, which are induced by non-zero bulk polarization. We investigated different types of HOTIs, including Wannier-type and multipolar HOTIs, in acoustic and photonic systems, as well as the effect of long-range interaction in photonic HOTI system.
The layout of this dissertation is as follows. The first section contains the basic, introductory concepts of topological insulators, topological invariants, Floquet topology, higher order topological insulators, and exciton/phonon polaritons.
In Chapter 2, we introduced a new type of Floquet modulation, which is diagonal and non-Hermitian, to an analytically treatable classical wave system based on kagome lattice, which has potential implementations in photonic, acoustic of mechanic systems. In the case of purely imaginary on-site Floquet modulation, novel phases and transitions take place with the increasing amplitude of modulations, including a pseudo-Hermitian phase induced by a small modulation, and distinguishable bands in complex space under larger modulations, which give rise to the emergence of complex edge states, thus enabling the possibilities of new edge state applications, including edge-state lasing.
In Chapter 3, we look into Wannier type higher-order topological states. We observed a new kind of corner state that had not been seen in other classical systems such as acoustic. By conducting analytical, numerical, and experimental studies, we confirmed this new corner state is induced by long-range interactions in photonic systems. We designed and experimentally studied two photonic metasurfaces, one is the design in waveguide under microwave, and the other is for near and mid IR which also is an all-dielectric structure distinguish from the previous one. The observation of corner modes in both photonic systems, especially this new type II corner mode, is a strong prove of the existence and formation of long-range interaction induced corner mode.
Chapter 4 is a follow-up on higher order topological (HOT) states, but we present a broader variety of HOTIs in this chapter, with higher dimensions such as 3D octupole system. Different from Wannier type in the previous chapter, multipole HOT states are induced by nontrivial nested Wilson loop in a hierarchy of gapped boundary states. We overcame the technical and design difficulties and successfully fabricated 3D octupole lattice, and we experimentally observed 0D corner states in the proposed 3D system.
Chapter 5 includes examples of interactions between exciton or phonon with photonic topological systems. While different in the origin of quasi-particle flat bands, their interactions are very similar and leads to novel results under strong coupling, including topological transitions from photonic bands to polaritonic bands, and edge states carrying exciton or phonon fractions. Both types of polaritons have been observed experimentally, and related techniques, such as tuning the position of flat band by temperature, which enabled a more flexible approach in possible applications and tuning of topological phases and boundary states.
Li, Mengyao, "Topological Classical Wave Systems With Modulations, Interactions, and Higher-order Topological States" (2021). CUNY Academic Works.