Nonlinear spectral singularities for confined nonlinearities
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Updated: May 9, 2026

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
Published on: January 3, 2016
1Department of Mathematics, Koç University, Istanbul, Turkey.
Abstract:
We introduce a notion of spectral singularity that applies for a general class of nonlinear Schrödinger operators involving a confined nonlinearity. The presence of the nonlinearity does not break the parity-reflection symmetry of spectral singularities but makes them amplitude dependent. Nonlinear spectral singularities are, therefore, associated with a resonance effect that produces amplified waves with a specific amplitude-wavelength profile. We explore the consequences of this phenomenon for a complex δ-function potential that is subject to a general confined nonlinearity.
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