Low-frequency electromagnetic scattering

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 l ow frequencies to the solutions of certain canonical problems. Our approach is based on coupling the power series representation of the scattered fiel ds with expansion of the exact nonlocal radiation condition. We also provid e a new and simple variational proof of the convergence of the electric and magnetic fields solutions of the scattering problem for the Maxwell equati ons as the frequency goes to zero. Besides its theoretical interest, our an alysis is motivated by its application to the numerical computation of the higher-order terms. These higher-order terms may be combined to Pade approx imations to enlarge the domain of applicability of the low-frequency scatte ring to predict more accurately the response of diffraction problems for he teregeneous Maxwell's equations in the resonance region where the wavelengt h and the dimension of the dielectric material are of the same order.