Geometric optical knots from two-mode eikonal interference

We propose the existence of weak geometric optical knots in vacuum $(2+1)$-dimensional space-time within geometrical optics formulated as an intrinsic $U(1)$ gauge theory. The construction arises from the interference of two eikonal modes whose complex ratio defines a gauge connection. The resulting phase structure produces vortex singularities with quantised topological charge. When written in terms of a normalized complex spinor, the field defines a mapping from $S^3$ to $S^2$ analogous to the Hopf map. Consequently, Hopf-type topological structures arise naturally in geometrical optics and admit an interpretation through an Abelian Chern--Simons action.