We present a Gaussian-beam theory of the spin Hall effect (SHE) of light for smoothly inhomogeneous media, extending the complex geometrical optics (CGO) framework to incorporate spin-orbit coupling through a linear eikonal correction term ${\mathsf{q}}^T{\mathsf{b}}_{\sigma }$, where $\mathsf{q}$ is the column vector of transverse coordinates relative to the central ray in a certain frame and ${\mathsf{b}}_{\sigma }$ is a spin-dependent coefficient vector in the same frame. This correction introduces a helicity-dependent transverse force, yielding the spin-Hall displacement ${\mathsf{d}}_{\sigma }=-{\left(\mathrm{Im}\mathsf{M}\right)}^{-1}\mathrm{Im}{\mathsf{b}}_{\sigma }$, where $\mathsf{M}$ is the complex curvature matrix governing beam diffraction in CGO. Applied to a helical-ray geometry in a gradient-index medium, the displacement is, in the Frenet-Serret frame, found to be predominantly binormal. Numerical results show persistent shear oscillations in $\mathrm{Re}{\mathsf{M}}^F\left(s\right)$, dynamically transferring spin-orbit drive from normal to binormal. Simultaneously, $\mathrm{Im}{\mathsf{M}}^F\left(s\right)$ develops strong anisotropy, locking the beam ellipse to the Frenet-Serret axes. Although $\mathrm{Im}{\mathsf{b}}_{\sigma }^F$ is predominantly normal, the extreme anisotropy of ${\left(\mathrm{Im}{\mathsf{M}}^F\right)}^{-1}$ amplifies the binormal contribution.

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• Geometrical & wave optics
• Polarization of light
• Spin-orbit coupling