Abstract
We study resonance for the Helmholtz equation with a finite frequency in a plasmonic material of negative dielectric constant in two and three dimensions. We show that the quasi-static approximation is valid for diametrically small inclusions. In fact, we quantitatively prove that if the diameter of an inclusion is small compared to the loss parameter, then resonance occurs exactly at eigenvalues of the Neumann{Poincare operator associated with the inclusion. © 2016 Society for Industrial and Applied Mathematics
| Original language | English |
|---|---|
| Pages (from-to) | 731-749 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 76 |
| Issue number | 2 |
| Online published | 31 Mar 2016 |
| DOIs | |
| Publication status | Published - 2016 |
| Externally published | Yes |
Research Keywords
- eigenvalues
- finite frequency
- Helmholtz equation
- Neumann-Poincaré operator
- plasmon resonance
- quasi-static limit
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