#### Date of Degree

9-2020

#### Document Type

Dissertation

#### Degree Name

Ph.D.

#### Program

Physics

#### Advisor

Azriel Z. Genack

#### Committee Members

Alexander B. Khanikaev

Alexander A. Lisyansky

Mohammad-Ali Miri

Evgenii E. Narimanov

Chushun Tian

#### Subject Categories

Condensed Matter Physics

#### Abstract

This thesis discusses wave propagation in two kinds of systems, random media and topological insulators. In a disordered system, the wave is randomized by multiple scattering. The scattering matrix and associated delay times are powerful tools with which to describe wave transport. We discuss the relation among the Wigner time, the transmission time, and energy density in a lossless or lossy system. We propose the zeros of the transmission matrix and show how to manipulate the zero-transmission mode in a nonunitary system. In a photonic topological insulator, we realize an edge mode and discuss its robustness in the face of various types of disorder.

There is a powerful relation between time delay and the density of states (DOS) in a lossless system. The Wigner time equals the DOS in a reciprocal lossless system, which is one half the transmission time. It is therefore sufficient to measure the transmission matrix to obtain the DOS. There are two approaches to obtain the local DOS (LDOS), measuring the imaginary part of local Green’s function or calculating the sum of intensity when the sample is excited in all incoming channels with unit flux.

Here, we will discuss the relations between the time delay and the DOS in a nonunitary system. Although the dwell time no longer equals the DOS, we show using the Feshbach formalism that the energy excited by all incident channels can still be expressed as a superposition of Lorentzian lines related to the quasi-normal modes.

Based on the connection between the scattering matrix and the Green’s function, the determinants of both the scattering and reflection matrices can be expressed as a ratio of zeros and poles. In this work, we show that the determinant of the transmission matrix can also be expressed in terms of zeros and poles. We find the structure of the zeros in the complex energy plane. In a unitary reciprocal system, the zeros of transmission either fall on the real axis in the energy plane or appear as conjugate pairs symmetrically disposed relative to the real axis, This leads to the equivalence between transmission time and DOS. Loss or gain breaks the symmetry of zeros of transmission. Differences between the transmission time and the DOS is related to the positions of zeros. This allows us to realize zero-transmission in a random system. We predict that the average transmission time will decrease with increasing loss because more zeros of transmission would be pulled into the lower half of the complex plane.

We also study the edge mode at the interface between quantum-valley-Hall (QVH) and quantum-spin-Hall (QSH) systems. The counterpart of the QSH effect in a photonic system is realized experimentally in a 2D meta-waveguide. We demonstrate valley-dependent waveguiding in a system in which the edge mode is endowed with both the pseudo-spin and valley degrees of freedom. When the edge mode couples to a cavity in the bulk, we observe in experiments that the reflection effect is evident. Based on the coupled-mode theory, we estimate the reflection rate and explain the negative transmission time. We also find the statistics of time delay and find the modes of the medium in the analysis of the transmitted field and the field inside the medium in the presence of a coherent background.

#### Recommended Citation

Kang, Yuhao, "Wave Propagation in Random and Topological Media" (2020). *CUNY Academic Works.*

https://academicworks.cuny.edu/gc_etds/3920