A duality between scattering poles and transmission eigenvalues in scattering theory
Abstract
In this paper, we develop a conceptually unified approach for characterizing and determining scattering poles and interior eigenvalues for a given scattering problem. Our approach explores a duality stemming from interchanging the roles of incident and scattered fields in our analysis. Both sets are related to the kernel of the relative scattering operator mapping incident fields to scattered fields, corresponding to the exterior scattering problem for the interior eigenvalues and the interior scattering problem for scattering poles. Our discussion includes the scattering problem for a Dirichlet obstacle where duality is between scattering poles and Dirichlet eigenvalues, and the inhomogeneous scattering problem where the duality is between scattering poles and transmission eigenvalues. Our new characterization of the scattering poles suggests a numerical method for their computation in terms of scattering data for the corresponding interior scattering problem.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 01, 2020
- Source ID
- 10.1098/rspa.2020.0612
Entities
People
- David Colton
- Fioralba Cakoni
- Houssem Haddar
Organizations
- Air Force Office of Scientific Research
- National Science Foundation Division of Mathematical Sciences
- Rutgers University
- University of Delaware
- École polytechnique