  We study the effects of single impurities on the transmission in microwave
realizations of the photonic Kronig-Penney model, consisting of arrays of
Teflon pieces alternating with air spacings in a microwave guide. As only the
first propagating mode is considered, the system is essentially one dimensional
obeying the Helmholtz equation. We derive analytical closed form expressions
from which the band structure, frequency of defect modes, and band profiles can
be determined. These agree very well with experimental data for all types of
single defects considered (e.g. interstitial, substitutional) and shows that
our experimental set-up serves to explore some of the phenomena occurring in
more sophisticated experiments. Conversely, based on the understanding provided
by our formulas, information about the unknown impurity can be determined by
simply observing certain features in the experimental data for the
transmission. Further, our results are directly applicable to the closely
related quantum 1D Kronig-Penney model.
