  In this tutorial paper, we consider the problem of electromagnetic scattering
by a bounded two-dimensional dielectric object, and discuss certain interesting
properties of the scattered field. Using the electric field integral equation,
along with the techniques of Fourier theory and the properties of Bessel
functions, we show analytically and numerically, that in the case of transverse
electric polarization, the scattered fields are spatially bandlimited. Further,
we derive an upper bound on the number of incidence angles that are useful as
constraints in an inverse problem setting (determining permittivity given
measurements of the scattered field). We also show that the above results are
independent of the dielectric properties of the scattering object and depend
only on geometry. Though these results have previously been derived in the
literature using the framework of functional analysis, our approach is
conceptually far easier. Implications of these results on the inverse problem
are also discussed.
