  In this work, we use Wannier functions to analyze topological phase
transitions in one dimensional photonic crystals. We first review the
construction of exponentially localized Wannier functions in one dimension, and
show how to numerically construct them for photonic systems. We then apply
these tools to study a photonic analog of the Su-Schrieffer-Heeger model. We
use photonic Wannier functions to construct a quantitatively accurate
approximate model for the topological phase transition, and compute the
localization of topological defect states. Finally, we discuss the implications
of our work for the study of band representations for photonic crystals.
