  The introduction of synthetic dimensions in topological photonic systems
enriches the exploration of topological phase of light in higher-dimensional
space beyond three-dimensional real-space. Recently, the gapless corner modes
of topological photonic crystals under translational deformation have been
proposed, but their experimental observation is still absent. Here, we observe
the gapless corner modes in a photonic crystal slab under translational
deformation. The corner mode exhibits a frequency dependence that can be tuned
through the translation of the slab. Importantly, we find that the existence of
gapless corner modes is independent of the specific corner configuration. The
gapless corner modes are experimentally imaged via the near-field scanning
measurement, and validated numerically by full-wave simulations. Our work
contributes to the advancement of topological photonics and provides valuable
insights into the exploration of gapless corner modes in synthetic dimensions.
