Low-Frequency Electromagnetic Scattering

Source abstract

The main result of this paper is to reduce the calculation of higher-order terms in the asymptotic expansions of the electric and magnetic fields at low frequencies to the solutions of certain canonical problems. Our approach is based on coupling the power series representation of the scattered fields with expansion of the exact nonlocal radiation condition. We also provide a new and simple variational proof of the convergence of the electric and magnetic fields solutions of the scattering problem for the Maxwell equations as the frequency goes to zero. Besides its theoretical interest, our analysis is motivated by its application to the numerical computation of the higher-order terms. These higher-order terms may be combined to Padé approximations to enlarge the domain of applicability of the low-frequency scattering to predict more accurately the reponse of diffraction problems for heteregeneous Maxwell's equations in the resonance region where the wavelength and the dimension of the dielectric material are of the same order.