Abelian gauge structure from two-mode eikonal interference

We propose a novel framework in geometrical optics where an Abelian gauge structure emerges from the interference of two eikonal modes. Using the complex ratio $\phi = \psi_1 / \psi_2$, we define an intrinsic connection whose field strength is non-trivial near amplitude zeros. This approach shows that gauge structures can emerge from phase relations in classical wave fields, providing a minimal and transparent mechanism to study emergent Abelian connections in optical systems.