Resolvent expansion for discrete non-Hermitian resonant systems [Invited]
Abstract
The linear response of non-Hermitian resonant systems demonstrates various intriguing features such as the emergence of non-Lorentzian lineshapes. Recently, we have developed a systematic theory to understand the scattering lineshapes in such systems and, in doing so, established the connection with the input/output scattering channels. Here, we follow up on that work by presenting a different, more transparent derivation of the resolvent operator associated with a non-Hermitian system under general conditions and highlight the connection with the structure of the underlying eigenspace decomposition. Finally, we also present a simple solution to the problem of self-orthogonality associated with the left and right Jordan canonical vectors and show how the left basis can be constructed in a systematic fashion. Our work provides a unifying mathematical framework for studying non-Hermitian systems such as those implemented using dielectric cavities, metamaterials, and plasmonic resonators.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 20, 2022
- Source ID
- 10.1364/ome.477436
Entities
People
- Kurt Busch
- L. Simonson
- R. El-ganainy
- Şahin Kaya Özdemir
Organizations
- Air Force Office of Scientific Research
- Alexander von Humboldt Foundation
- German Research Foundation
- Humboldt-Universität zu Berlin
- Leibniz Association
- Michigan Technological University
- National Science Foundation
- Pennsylvania State University