  In physics, synthetic dimensions trigger great interest to manipulate light
in different ways, while in technology, lithium niobate shows important
capability towards on-chip applications. Here, based on the state-of-art
technology, we propose and study a theoretical model of dynamically-modulated
waveguide arrays with the Su-Schrieffer-Heeger configuration in the spatial
dimension. The propagation of light through the one-dimensional waveguide
arrays mimics time evolution of field in a synthetic two-dimensional lattice
including the frequency dimension. By adding the effective gauge potential, we
find quasi-edge state that the intensity distribution manifests not at the
boundary as the traditional edge state, which leads to an exotic topologically
protected one-way transmission along adjacent boundary. Furthermore, a
cosine-shape isolated band exhibits, supporting the topological Bloch
oscillation in the frequency dimension under the effective constant force,
which is localized at the spatial boundary and shows the topological feature.
Our work therefore points out further capability of light transmission under
topological protections in both spatial and spectral regimes, and provides
future on-chip applications in the lithium niobate platform.
