Eikonal approximation in electromagnetic scattering

Eikonal approximation, which uses the intuition of geometrical optics, has been used in high energy scattering theories for more than a hundred years. More recently, eikonal approximation has been used in quantum mechanics in the form of WKB approximation, although it originated in the field of electromagnetism and optics. In this work, we revisit eikonal approximation in the context of electromagnetic scattering. We study the scattering of a monochromatic electromagnetic wave off a weak dielectric sphere in the eikonal approximation. Scattering of a monochromatic electromagnetic wave off a weak dielectric sphere can also be solved exactly. We use the Green function formalism to exactly solve the scattering cross section for our electromagnetic configuration using partial wave method. We numerically solve and compare the scattering cross section obtained using eikonal approximation with the partial wave method. We expect our work to shed some light on the regime of validity of eikonal approximation.