Fast, high-order accurate algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science (e.g. meta-materials), and many other fields of applied science. In this paper, we develop an FFT-accelerated separation of variables solver that can be used to efficiently invert integral equation formulations of Maxwell's equations for scattering from axisymmetric penetrable (dielectric) bodies. Using a standard variant of M\"uller's integral representation of the fields, our numerical solver rapidly and directly inverts the resulting second-kind integral equation. In particular, the algorithm of this work (1) rapidly evaluates the modal Green's functions, and their derivatives, via kernel splitting and the use of novel recursion formulas, (2) discretizes the underlying integral equation using generalized Gaussian quadratures on adaptive meshes, and (3) is applicable to geometries containing edges. Several 查看全文>>