  We map the topological properties of a one dimensional superlattice to the
optical properties of an electronic system. We find that the nonlinear-optical
response is optimized for electrons that live in the transitional morphology
between topologically protected edge states and delocalized eigenstates. This
provides a novel means of tuning the nonlinear-optical response of hybrid
quantum systems. We show how these characteristics can be used to mimic
saturable absorption and illustrate how `quantum cords' can be used to build an
efficient all-optical switch.
