Abstract
We present exact and asymptotic results for the electromagnetic field inside a dielectric slab in terms of the given field or source current outside the slab. Exact results for the reflected and transmitted fields are also given. In particular, we provide explicit exact and asymptotic results for the case in which the incident wave is a converging electromagnetic wave generated by a time-harmonic aperture current. In a separate paper our results are used to obtain exact and asymptotic numerical results for the focused field inside the slab.