  One-way edge states at the surface of photonic topological insulators are of
significant interest for communications, nonlinear and quantum optics.
Moreover, when reciprocity is broken in a photonic topological insulator, these
states provide protection against disorder, which is of particular importance
for slow light applications. Achieving such a one-way edge state, however,
requires the construction of a two-dimensional structure. Here, we show how
unidiriectional Floquet bands can arise in purely one-dimensional,
adiabatically-modulated dynamic systems, in contrasts with the higher
dimensionality needed in topological insulators. We also show that, using
realistic experimental parameters, the concept can be implemented using both a
coupled-resonator optical waveguide and a photonic crystal waveguide.
Furthermore, we illustrate the associated protection against disorder, and find
it to be of a novel nature when compared to Floquet topological insulators.
