  We study the optical properties of bi-anisotropic optical waveguides with
nontrivial topological structure in wavevector space, placed in an ordinary
dielectric matrix. We derive an exact analytical description of the eigenmodes
of the systems with arbitrary parameters that allows us to investigate
topologically protected surface states (TPSS) in details. In particular, we
find that the TPSS on the waveguides would disappear (1) if their radius is
smaller than a critical radius due to the dimensional quantization of azimuthal
wavenumber, and also (2) if the permittivity of the host-medium exceeds a
critical value. Interestingly, we also find that the TPSS in the waveguides
have negative refraction for some geometries. We have found a TPSS phase
diagram that will pave the way for development of the topological waveguides
for optical interconnects and devices.
