  Recent interest in optical analogues to the quantum spin Hall and quantum
valley Hall effects is driven by the promise to establish topologically
protected photonic edge modes at telecommunication and optical wavelengths on a
simple platform suitable for industrial applications. While first theoretical
and experimental efforts have been made, these approaches so far both lack a
rigorous understanding of the nature of topological protection and the limits
of backscattering immunity. We here use a generic group theoretical methodology
to fill this gap and obtain general design principles for purely dielectric
two-dimensional topological photonic systems. The method comprehensively
characterizes possible 2D hexagonal designs and reveals their topological
nature, potential and limits.
