Wave transmission through a spherical dielectric shell

The transmission of a spherical electromagnetic wave through a dielectric shell is considered. The two surfaces of the shell are spherical (either concave or convex), and their centers are arbitrarily located in relation to the source point. The field solution determined by the geometrical optics (GO) theory is given in a simple closed form. Special attention is given to the lens effect of the dielectric shell which converts the incoming spherical pencil into a focusing pencil.