  In this article, it is experimentally verified that nonreciprocal photonic
systems with a continuous translation symmetry may have an ill-defined
topology. The topological classification of such systems is only feasible when
the material response is regularized with a spatial-frequency cutoff. Here, we
experimentally demonstrate that inserting a small air gap in between two
materials may effectively imitate an idealized spatial cutoff that suppresses
the nonreciprocal response for short wavelengths and regularizes the topology.
Furthermore, it is experimentally verified that nonreciprocal systems with an
ill-defined topology may be used to abruptly halt the energy flow in a
unidirectional waveguide due to the violation of the bulk-edge correspondence.
In particular, we report the formation of an energy sink that absorbs the
incoming electromagnetic waves with a large field enhancement at the
singularity.
