Universal Right-Hand Chirality of Evanescent Vector Fields

Abstract

A locking between propagation direction $\hat{\bf q}$, spin $\hat{\bf S}$, and surface or interface normal $\hat{\bf n}$ -- a phenomenon broadly termed \textit{chirality} -- pervades evanescent or surface waves in optics, magnetism, plasmonics, and acoustics. Yet, it is not known whether the phenomenon is universal or bound to conditions. Here, we unveil that any \textit{source-free} vector field that propagates along $\hat{\bf q}$ and is evanescent along $\hat{\bf n}$, the existence of a spin automatically enforces a rigid, right-handed locking among $\hat{\bf q}$, $\hat{\bf S}$, and $\hat{\bf n}$, that is characterized by a chirality index $C_{\bf q}\equiv \hat{\bf n}\cdot(\hat{\bf S}\times \hat{\bf q})>0$. For an arbitrary propagation direction defined by $\hat{\bf q}\cdot \hat{\bf S}\equiv \eta\in [-1,1]$, i.e., not necessarily transverse spin, we derive a fundamental upper bound $C_{\bf q}\le \sqrt{1-\eta^2}$. The universal absence of left-handed evanescent (source-less) vector fields underscores the fundamental physical non-equivalence of mirror-image configurations -- a principle echoed by parity violation, the natural excess of enantiomers in chiral molecules, and the fixed chirality of DNA.