  Topological on-chip photonics based on tailored photonic crystals (PhC) that
emulate quantum valley Hall effects has recently gained widespread interest due
to its promise of robust unidirectional transport of classical and quantum
information. We present a direct quantitative evaluation of topological
photonic edge eigenstates and their transport properties in the telecom
wavelength range using phase-resolved near-field optical microscopy.
Experimentally visualizing the detailed sub-wavelength structure of these modes
propagating along the interface between two topologically non-trivial
mirror-symmetric lattices allows us to map their dispersion relation and
differentiate between the contributions of several higher-order Bloch
harmonics. Selective probing of forward and backward propagating modes as
defined by their phase velocities enables a direct quantification of
topological robustness. Studying near-field propagation in controlled defects
allows to extract upper limits to topological protection in on-chip photonic
systems in comparison to conventional PhC waveguides. We find that protected
edge states are two orders of magnitude more robust as compared to conventional
PhC waveguides. This direct experimental quantification of topological
robustness comprises a crucial step towards the application of topologically
protected guiding in integrated photonics, allowing for unprecedented
error-free photonic quantum networks.
