  Topologically protected edge states arise at the interface of two
topologically distinct valley photonic crystals. In this work, we investigate
how tailoring the interface geometry, specifically from a zigzag interface to a
glide plane, profoundly affects these edge states. Near-field measurements
demonstrate how this transformation significantly changes the dispersion
relation of the edge mode. We observe a transition from gapless edge states to
gapped ones, accompanied by the occurrence of slow light within the Brillouin
zone, rather than at its edge. Additionally, we simulate the propagation of the
modified edge states through a specially designed valley-conserving defect. The
simulations show, by monitoring the transmittance of this defect, how the
robustness to backscattering gradually decreases, suggesting a disruption of
valley-dependent transport. These findings demonstrate how the gradual
emergence of valley-dependent gapless edge states in a valley photonic crystal
depends on the geometry of its interface.
