Boundary layer method for solving full Maxwell equations in the presence of an electromagnetic inhomogeneity of small diameter

We consider solutions to the time-harmonic Maxwell's equations in two and three dimensions. For such solutions we derive high-order terms in the asymptotic expansions of the perturbations resulting from the presence of diametrically small electromagnetic inhomogeneity with parameters different from the background medium. Our study is rigorous and is founded on layer potential techniques. Our formulas may be awaited to head effective computational identification algorithms, aimed at reconstructing small dielectric object from electromagnetic boundary measurements.