Quantitative spectral analysis of electromagnetic scattering. II: Evolution semigroups and non-perturbative solutions

Abstract

We carry out quantitative studies on the Green operator $\hat{\mathcal{G}}$ associated with the Born equation, an integral equation that models electromagnetic scattering, building the strong stability of the evolution semigroup $\{\exp (-i\tau \hat{\mathcal{G}})|\tau \ge 0\}$ on polynomial compactness and the Arendt-Batty-Lyubich-Vũ theorem. The strongly-stable evolution semigroup inspires our proposal of a non-perturbative method to solve the light scattering problem and improve the Born approximation.

(v1) 22 pages, 3 TikZ figures. Continuation of arXiv:1007.4375v3. Updated from Chapter 5 and Appendix D in https://www.proquest.com/docview/634514288?accountid=13151 (v2) 22 pages, 3 TikZ figures. Accepted version with updated references

References in corpus (1)

• The discrete dipole approximation: an overview and recent developments

Cited by in corpus (1)

• Spectral structure of electromagnetic scattering on arbitrarily shaped dielectrics