Spectral structure of electromagnetic scattering on arbitrarily shaped dielectrics

Spectral analysis is performed on the Born equation, a strongly singular integral equation modeling interactions between electromagnetic waves and arbitrarily shaped dielectric scatterers. Compact Hilbert--Schmidt operator polynomials are constructed from Green of scattering scatterers with smooth boundaries. As consequence, it shown that has discrete spectrum, spectral series $ \sum_\lambda|\lambda|^2|1+2\lambda|^4$ convergent, counting multiplicities eigenvalues \lambda$. This reveals shape-independent optical resonance mode corresponding to critical permittivity \epsilon_r=-1$.