Observation of quincunx-shaped and dipole-like flatband states in photonic rhombic lattices without band-touching

We demonstrate experimentally the existence of compact localized states (CLSs) in a quasi-one-dimensional photonic rhombic lattice in the presence of two distinct refractive-index gradients (i.e., a driven lattice ribbon) acting as external electric fields. Such a lattice is composed of an array of periodically arranged evanescently coupled waveguides, which hosts a perfect flatband that touches both remaining dispersive bands when it is not driven. The external driving is realized by modulating the relative writing beam intensity of adjacent waveguides. We find that a y-gradient set perpendicularly to the ribbon preserves the flatband while removing the band-touching. The undriven dipole-like CLS—which occupies two lattice sites over one unit cell—turns into a quincunx-shaped CLS spanned over two unit cells. Instead, an x-gradient acting parallel to the ribbon yields a Stark ladder of the CLS whose spatial profile is unchanged with respect to the undriven case. We notably find that their superposition leads to Bloch-like oscillations in momentum space.