Meta-Weaves: Sector-way non-reciprocal meta surfaces

Confluent with the single dimension of time, breach of time-reversal symmetry is usually perceived as a one-dimensional concept. In its ultimate realization--the one-way guiding device--it allows optical propagation in one direction, say $+z$, and forbids it in the opposite direction, $-z$. Hence, in studies of time-reversal asymmetry the mapping $t\mapsto -t$ is naturally associated with $z\mapsto -z$. However, strongly non-reciprocal or one-way nano-scale threads can be used \emph{to weave meta-surfaces} thus adding dimensions to this concept. In this new family of surfaces the aforementioned association \emph{cannot be made}. An example of appropriate threads are the planar one-way particle chains based on the two-type rotation principle. The resulting surfaces--the meta-weaves--posses generalized non-reciprocity such as "sector-way" propagation, and offer new possibilities for controlling light in thin surfaces. We study several meta-weave designs and their asymmetries in the wave-vector space.