  Crystal-symmetry-protected photonic topological edge states (PTESs) based on
air rods in conventional dielectric materials are designed as photonic
topological waveguides (PTWs) coupled with side optical cavities. We
demonstrate that the cavity coupled with the PTW can change the reflection-free
transport of the PTESs, where the cavities with single mode and twofold
degenerate modes are taken as examples. The single-mode cavities are able to
perfectly reflect the PTESs at their resonant frequencies, forming a dip in the
transmission spectra. The dip full width at half depth depends on the coupling
strength between the cavity and PTW and thus on the cavity geometry and
distance relative to the PTW. While the cavities with twofold degenerate modes
lead to a more complex PTES transport whose transmission spectra can be in the
Fano form. These effects well agree with the one-dimensional PTW-cavity
transport theory we build, in which the coupling of the PTW with cavity is
taken as $\delta$ or non-$\delta$ type. Such PTWs coupled with side cavities,
combining topological properties and convenient tunability, have wide
diversities for topological photonic devices.
