Topological photonics in non-Hermitian and scattering systems
Abstract/Contents
- Abstract
- In photonics, topological effects can be used to design systems with robust and novel behavior. These topological effects are traditionally studied in closed systems without gain, described by Hermitian Hamiltonians. However, many systems in photonics do have gain or loss and can be described by non-Hermitian Hamiltonians. Systems with inputs and outputs are also widespread in photonics and are usually described by a scattering matrix. In this Thesis, we study topological features in non-Hermitian and scattering systems in photonics. First, we give a characterization of the space of all gapped non-Hermitian Hamiltonians using the mathematical framework of homotopy theory. We do this pedagogically in two-band systems, starting with the familiar Hermitian case before generalizing to the non-Hermitian setting, and then giving several physical interpretations of the results. Next, we study the topology of many-band non-Hermitian systems, and we see the importance of braid-group eigenvalue topology emerge. We provide a complete description of eigenvalue topology in gapped and gapless systems, again using the mathematics of homotopy theory. Finally, we move to scattering systems, where we study a topological feature in the spectrum of the scattering matrix known as a scattering threshold. Here, the scattering matrix has a square-root branch point, and we show that this singularity leads to a universal behavior in a wide variety of physical systems.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2022; ©2022 |
| Publication date | 2022; 2022 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Wojcik, Charles C |
|---|---|
| Degree supervisor | Fan, Shanhui, 1972- |
| Thesis advisor | Fan, Shanhui, 1972- |
| Thesis advisor | Brongersma, Mark L |
| Thesis advisor | Miller, D. A. B |
| Degree committee member | Brongersma, Mark L |
| Degree committee member | Miller, D. A. B |
| Associated with | Stanford University, Department of Electrical Engineering |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Charles C. Wojcik. |
|---|---|
| Note | Submitted to the Department of Electrical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2022. |
| Location | https://purl.stanford.edu/mj287tr1114 |
Access conditions
- Copyright
- © 2022 by Charles C Wojcik
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