  We show that anisotropic planar anti-guiding waveguide structures with two
radiation channels towards the surrounding cladding materials can support
unidirectional guided resonances (UGRs), where radiation is cancelled in one of
the radiation channels and redirected into the other. Their formation is subtle
as it requires breaking the so-called polar anisotropy-symmetry of the
structures. Then, UGRs appear at specific wavelengths and light propagation
directions, are robust, and are characterised by phase singularities in the
channel in which radiation is cancelled. The mechanism we describe allows for
ready selection of the radiation direction, as well as tuning of the wavelength
and the propagation angle at which UGRs occur.
