Résumé
A new method is proposed to predict the topological properties of
one-dimensional periodic structures in wave physics, including quantum
mechanics. From Bloch waves, a unique complex valued function is constructed,
exhibiting poles and zeros. The sequence of poles and zeros of this function is
a topological invariant that can be linked to the Berry-Zak phase. Since the
characterization of the topological properties is done in the complex plane, it
can easily be extended to the case of non-hermitian systems. The sequence of
poles and zeros allows to predict topological phase transitions.