  Non-Hermitian skin effect (NHSE) is one of the most fundamental phenomena in
non-Hermitian physics. Although it is established that one-dimensional NHSE
originates from the nontrivial spectral winding topology, the topological
origin behind the higher-dimensional NHSE remains unclear so far. This poses a
substantial challenge in constructing and manipulating high-dimensional NHSEs.
Here, an intuitive bottom-to-top scheme to construct high-dimensional NHSEs is
proposed, through assembling multiple independent one-dimensional NHSEs. Not
only the elusive high-dimensional NHSEs can be effectively predicted from the
well-defined one-dimensional spectral winding topologies, but also the
high-dimensional generalized Brillouin zones can be directly synthesized from
the one-dimensional counterparts. As examples, two two-dimensional
nonreciprocal acoustic metamaterials are experimentally implemented to
demonstrate highly controllable multi-polar NHSEs and hybrid skin-topological
effects, where the sound fields can be frequency-selectively localized at any
desired corners and boundaries. These results offer a practicable strategy for
engineering high-dimensional NHSEs, which could boost advanced applications
such as selective filters and directional amplifiers.
